< 2019 >
November
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  • Seminars

    Seminars Colloquia & Seminar
    11/1/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • CMSA EVENT: Learning from health data in the million genome era
    11:26 am
    11/01/2019

    On November 12019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system.

    Speakers: 

    • Heidi Rehm, Ph.D.
      Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform.
    • Saiju Pyarajan, Ph.D.
      Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS
    • Tianxi Cai, Sci.D
      John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health
    • Susan Redline, M.D., M.P.H
      Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center
    • Avinash Sahu, Ph.D.
      Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health
    • Peter J. Park, Ph.D.
      Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School
    • David Roberson
      Community Engagement Manager, Seven Bridges

    Registration & Schedule

  • General Relativity Seminar
    2:30 pm-3:30 pm
    11/01/2019-04/26/2020
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< 2019 >
November
«
»
Sun
Mon
Tue
Wed
Thu
Fri
Sat
October
October
October
October
October
1
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-16-2018 Mathematical Physics Seminar

    12:00 am
    11/01/2019
  • Seminars

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

    12:00 am-1:00 pm
    11/01/2019
  • CMSA EVENT: Quantum Matter Workshop
    All day
    11/01/2019
    Layer-2-600x338

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

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

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

     

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

    Speakers:

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-9-2018 Math Physics Seminar

    12:00 am
    11/01/2019
  • Colloquium
    5:00 am
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Workshop on Quantum Information
    8:00 am-6:07 pm
    11/01/2019-04/24/2017
    banner-image-1

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

    Register for the event here.

    The following speakers are confirmed:

  • CMSA EVENT: From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
    8:30 am-5:20 pm
    11/01/2019-08/20/2018
    Mumford-3

    David_Mumford-1

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

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

    Speakers:

    Organizers:

     

    Publication:

    Pure and Applied Mathematics Quarterly

    Special Issue: In Honor of David Mumford

    Guest Editors: Ching-Li Chai, Amnon Neeman

     

  • CMSA EVENT: Big Data Conference 2018
    8:30 am-2:50 pm
    11/01/2019-08/24/2018
    1 Oxford Street, Cambridge MA 02138
    Big-Data-2018-1

     

    shutterstock_547250785-e1527881194717

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

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

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

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

    Please register here. 

    Confirmed Speakers: 

    Organizers: 

    • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
    • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
    • Richard Freeman, Herbert Ascherman Professor of Economics, Harvard University
    • Jun Liu, Professor of Statistics, Harvard University
    • Horng-Tzer Yau, Professor of Mathematics, Harvard University
  • CMSA EVENT: F-Theory Conference
    8:30 am-3:00 pm
    11/01/2019-09/30/2018

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

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

    Click here for videos of the talks. 

    Organizers:

    Speakers:

  • CMSA EVENT: Workshop on Foundations of Computational Science
    8:30 am-2:45 pm
    11/01/2019-08/31/2019
    AI-Poster-3

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

    Please register here. 

    Speakers:

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

  • CMSA EVENT: Workshop on Aspects of General Relativity
    8:30 am-3:30 pm
    11/01/2019-05/26/2017

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

    Speakers:

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

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

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

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

    Schedule:

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

    Organizers: Piotr T. Chruściel and Shing-Tung Yau

  • CMSA EVENT: Workshop on Morphometrics, Morphogenesis and Mathematics
    8:30 am-2:00 pm
    11/01/2019-10/24/2018

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

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

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

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

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

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

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

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

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

    Videos of the talks

    Confirmed Speakers:

  • CMSA EVENT: Morphogenesis: Geometry and Physics
    8:30 am-2:30 pm
    11/01/2019-12/05/2018

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

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

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

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

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

    Videos

    Please Register Here

    PDF of the Schedule

    Speakers:

  • CMSA EVENT: Geometric Analysis Approach to AI Workshop
    8:30 am-5:30 pm
    11/01/2019-01/21/2019
    Geo-Analysis-Poster-final-e1547584167900

    Geo-Analysis-1-e1543848888343

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

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

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

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

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

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

    Please register here

    Speakers: 

  • CMSA EVENT: 2019 Big Data Conference
    8:30 am-4:40 pm
    11/01/2019-08/20/2019
    1 Oxford Street, Cambridge MA 02138
    Big-Data-2019-Poster-5-2

    shutterstock_547250785-e1527881194717

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

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

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

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

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

  • CMSA EVENT: 2015 Conference on Big Data
    8:45 am-4:00 pm
    11/01/2019-10/26/2015
    1 Oxford Street, Cambridge MA 02138

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

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

     

    Registration for the conference is now closed.

    Please click here for a downloadable version of this schedule.

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

    Monday, August 24

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

    Tuesday, August 25

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

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

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

     Wednesday, August 26 

    TimeSpeakerTitle
    8:45amMeet and Greet
    9:00amAnkur MoitraBeyond Matrix Completion
    9:45amFlorent KrzakalaOptimal compressed sensing with spatial coupling and message passing
    10:30amBreak
    10:45amPiotr IndykFast Algorithms for Structured Sparsity
    11:30amGuido ImbensExact p-values for network inference
    12:15pmBreak for lunch
    2:00pmEdo AiroldiSome fundamental ideas for causal inference on large networks
    2:45pmRonitt RubinfeldSomething for almost nothing: sublinear time approximation algorithms
    3:30pmBreak
    3:45pmLenka ZdeborovaClustering of sparse networks:  Phase transitions and optimal algorithms
    4:30pmJelani NelsonDimensionality reductions via sparse matrices
  • CMSA EVENT: Workshop on Probabilistic and Extremal Combinatorics
    9:00 am-1:30 pm
    11/01/2019-02/09/2018

    The workshop on Probabilistic and Extremal Combinatorics will take place February 5-9, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    Extremal and Probabilistic Combinatorics are two of the most central branches of modern combinatorial theory. Extremal Combinatorics deals with problems of determining or estimating the maximum or minimum possible cardinality of a collection of finite objects satisfying certain requirements. Such problems are often related to other areas including Computer Science, Information Theory, Number Theory and Geometry. This branch of Combinatorics has developed spectacularly over the last few decades. Probabilistic Combinatorics can be described informally as a (very successful) hybrid between Combinatorics and Probability, whose main object of study is probability distributions on discrete structures.

    There are many points of interaction between these fields. There are deep similarities in methodology. Both subjects are mostly asymptotic in nature. Quite a few important results from Extremal Combinatorics have been proven applying probabilistic methods, and vice versa. Such emerging subjects as Extremal Problems in Random Graphs or the theory of graph limits stand explicitly at the intersection of the two fields and indicate their natural symbiosis.

    The symposia will focus on the interactions between the above areas. These topics include Extremal Problems for Graphs and Set Systems, Ramsey Theory, Combinatorial Number Theory, Combinatorial Geometry, Random Graphs, Probabilistic Methods and Graph Limits.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Benny Sudakov and David Conlon.  More details about this event, including participants, will be updated soon.

  • CMSA EVENT: Simons Collaboration on Homological Mirror Symmetry
    9:00 am-5:00 pm
    11/01/2019-05/08/2016

    The Center of Mathematical Sciences and Applications will be hosting a 3-day workshop on Homological Mirror Symmetry and related areas on May 6 – May 8, 2016 at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

    Organizers:

    D. Auroux, S.C. Lau, N.C. Leung, Bong Lian, C.C. Liu, S.T. Yau

    Speakers:

    1. Netanel Blaier (MIT)
    2. Kwokwai Chan (CUHK)
    3. Bohan Fang (Peking University)
    4. Amanda Francis (BYU)
    5. Hansol Hong (CUHK)
    6. Heather Lee (Purdue University)
    7. Si Li (Tsinghua University)
    8. Yu-Shen Lin (Stanford University)
    9. Alex Perry (Harvard University)
    10. Hiro Tanaka (Harvard University)
    11. Sara Tukachinsky (HUJ)
    12. Michael Viscardi (MIT)
    13. Eric Zaslow (Northwestern University)
    14. Jingyu Zhao (Columbia University)

    Please click here for the conference Main Website.

    Please click Simons Workshop Schedule with Abstract for a downloadable schedule with talk abstracts.

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

    Schedule:

    May 6 – Day 1
    9:00amBreakfast
    9:35amOpening remarks
    9:45am – 10:45amSi Li, “Quantum master equation, chiral algebra, and integrability”
    10:45am – 11:15amBreak
    11:15am – 12:15pmSara Tukachinsky, “Point like bounding chains and open WDVV
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmBohan Fang, “Mirror B model for toric Calabi Yau 3 folds
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmHiro Tanaka, “Toward Fukaya categories over arbitrary coefficients
    4:00pm – 4:15pmBreak
    4:15pm – 5:15pmHansol Hong, “Noncommutative mirror functors
    May 7 – Day 2
    9:00amBreakfast
    9:45am – 10:45amEric Zaslow, “Lagrangian fillings what does the sheaf say?
    10:45am – 11:15amBreak
    11:15am – 12:15pmAlex Perry, “Derived categories of Gushel Mukai varieties
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmAmanda Francis, “A Landau Ginzburg mirror theorem inspired by Borcea Voisin symmetry
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmHeather Lee, “Homological mirror symmetry for open Riemann surfaces from pair of pants decompositions
    4:00pm – 4:15pmBreak
    4:15pm – 5:15pmYu-Shen Lin, “Counting Holomorphic Discs via Tropical Discs on K3 Surfaces
    May 8 – Day 3
    9:00amBreakfast
    9:45am – 10:45amKwokwai Chan, “HMS for local CY manifolds via SYZ
    10:45am – 11:15amBreak
    11:15am – 12:15pmNetanel Blaier, “The quantum Johnson homomorphism, formality and symplectic isotopy
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmJingyu Zhao, “Periodic symplectic cohomology and the Hodge filtration
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmMichael Viscardi, “Equivariant quantum cohomology and the geometric Satake equivalence
    * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Simons Collaboration on Homological Mirror symmetry“.

    This event is sponsored by the Simons Foundation and CMSA Harvard University.

  • CMSA EVENT: Workshop on Geometry, Imaging, and Computing
    9:00 am-6:15 pm
    11/01/2019-03/26/2018
    GIC-Poster-2-e1520002551865

    On March 24-26, The Center of Mathematical Sciences and Applications will be hosting a workshop on Geometry, Imaging, and Computing, based off  the journal of the same name. The workshop will take place in CMSA building, G10.

    The organizing committee consists of Yang Wang (HKUST), Ronald Lui (CUHK), David Gu (Stony Brook), and Shing-Tung Yau (Harvard).

    Please click here to register for the event.

    Confirmed Speakers:

  • CMSA EVENT: Workshop on Optimization in Image Processing
    9:00 am-12:30 pm
    11/01/2019-06/30/2016

    The Center of Mathematical Sciences and Applications will be hosting a workshop on Optimization in Image Processing on June 27 – 30, 2016. This 4-day workshop aims to bring together researchers to exchange and stimulate ideas in imaging sciences, with a special focus on new approaches based on optimization methods. This is a cutting-edge topic with crucial impact in various areas of imaging science including inverse problems, image processing and computer vision. 16 speakers will participate in this event, which we think will be a very stimulating and exciting workshop. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Titles, abstracts and schedule will be provided nearer to the event.

    Speakers:

    1. Antonin Chambolle, CMAP, Ecole Polytechnique
    2. Raymond Chan, The Chinese University of Hong Kong
    3. Ke Chen, University of Liverpool
    4. Patrick Louis Combettes, Université Pierre et Marie Curie
    5. Mario Figueiredo, Instituto Superior Técnico
    6. Alfred Hero, University of Michigan
    7. Ronald Lok Ming Lui, The Chinese University of Hong Kong
    8. Mila Nikolova, Ecole Normale Superieure Cachan
    9. Shoham Sabach, Israel Institute of Technology
    10. Martin Benning, University of Cambridge
    11. Jin Keun Seo, Yonsei University
    12. Fiorella Sgallari, University of Bologna
    13. Gabriele Steidl, Kaiserslautern University of Technology
    14. Joachim Weickert, Saarland University
    15. Isao Yamada, Tokyo Institute of Technology
    16. Wotao Yin, UCLA

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

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

    Please click here for registration – Registration Deadline: June 7, 2016; Registration is capped at 70 participants.

    Schedule:

    June 27 – Day 1
    9:00amBreakfast
    9:20amOpening remarks
    9:30am – 10:20amJoachim Weickert, “FSI Schemes: Fast Semi-Iterative Methods for Diffusive or Variational Image Analysis Problems”
    10:20am – 10:50amBreak
    10:50am – 11:40pmPatrick Louis Combettes“Block-Iterative Asynchronous Variational Image Recovery”
    11:40am – 12:30pmIsao Yamada“Spicing up Convex Optimization for Certain Inverse Problems”
    12:30pm – 2:00pmLunch
    2:30pm – 3:20pmFiorella Sgallari, “Majorization-Minimization for Nonconvex Optimization”
    3:20pm – 3:50pmBreak
    3:50pm – 4:40pmShoham Sabach“A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Problems”
    June 28 – Day 2
    9:00amBreakfast
    9:30am – 10:20amAntonin Chambolle“Acceleration of alternating minimisations”
    10:20am – 10:50amBreak
    10:50am – 11:40amMario Figueiredo“ADMM in Image Restoration and Related Problems: Some History and Recent Advances”
    11:40am – 12:30pmKe Chen“Image Restoration and Registration Based on Total Fractional-Order Variation Regularization”
    12:30pm – 2:30pmLunch
    2:30pm – 4:40pmDiscussions
    June 29 – Day 3
    9:00amBreakfast
    9:30am – 10:20amAlfred Hero“Continuum relaxations for discrete optimization”
    10:20am – 10:50amBreak
    10:50am – 11:40amWotao Yin“Coordinate Update Algorithms for Computational Imaging and Machine Learning”
    11:40am – 12:30pmMila Nikolova“Limits on noise removal using log-likelihood and regularization”
    12:30pm – 2:30pmLunch
    2:30pm – 3:20pmMartin Benning, “Nonlinear spectral decompositions and the inverse scale space method”
    3:20pm – 3:50pmBreak
    3:50pm – 4:40pmRonald Ming Lui“TEMPO: Feature-endowed Teichmuller extremal mappings of point cloud for shape classification”
    June 30 – Day 4
    9:00amBreakfast
    9:30am – 10:20amJin Keun Seo“Mathematical methods for biomedical impedance imaging”
    10:20am – 10:50amBreak
    10:50am – 11:40amGabriele Steidl, “Iterative Multiplicative Filters for Data Labeling”
    11:40am – 12:30pmRaymond Chan, “Point-spread function reconstruction in ground-based astronomy”
    * This event is sponsored by CMSA Harvard University.

    Organizers: Raymond Chan and Shing-Tung Yau

  • CMSA EVENT: Machine Learning for Multiscale Model Reduction Workshop
    9:00 am-11:55 am
    11/01/2019-03/29/2019
    Machine-Learning-Poster

    The Machine Learning for Multiscale Model Reduction Workshop will take place on March 27-29, 2019. This is the second of two workshops organized by Michael BrennerShmuel Rubinstein, and Tom Hou.  The first, Fluid turbulence and Singularities of the Euler/ Navier Stokes equations, will take place on March 13-15, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

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

    List of registrants

    Speakers:

  • CMSA EVENT: Simons Collaboration Workshop, Jan. 10-13, 2018
    9:00 am-12:00 pm
    11/01/2019-01/13/2017
    banner-image-1

    The CMSA will be hosting a four-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on January 10-13, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

    We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

     

    Confirmed Participants:

  • CMSA EVENT: Mini-school on Nonlinear Equations, December 3-4, 2016
    9:00 am-5:00 pm
    11/01/2019-12/04/2016

    The Center of Mathematical Sciences and Applications will be hosting a Mini-school on Nonlinear Equations on December 3-4, 2016. The conference will have speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138.

    The mini-school will consist of lectures by experts in geometry and analysis detailing important developments in the theory of nonlinear equations and their applications from the last 20-30 years.  The mini-school is aimed at graduate students and young researchers working in geometry, analysis, physics and related fields.

    Please click here to register for this event.

    Speakers:

    1. Cliff Taubes (Harvard University)
    2. Valentino Tosatti (Northwestern University)
    3. Pengfei Guan (McGill University)
    4. Jared Speck (MIT)

    Schedule:

    December 3rd – Day 1
    9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
    10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
    12:15pm – 1:45pmLUNCH
    1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
    3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”
    December 4th – Day 2
    9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
    10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
    12:15pm – 1:45pmLUNCH
    1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
    3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”

    Please click Mini-School Program for a downloadable schedule with talk abstracts.

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

    * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

  • CMSA EVENT: Workshop on Coding and Information Theory
    9:00 am-3:30 pm
    11/01/2019-04/13/2018

    The workshop on coding and information theory will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

    Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory.  One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program.  Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities.  Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics.  All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    Click here for a list of registrants. 

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

  • CMSA EVENT: Topology and Dynamics in Quantum Matter Workshop
    9:15 am-3:25 pm
    11/01/2019-09/11/2019
    Topology-Poster

    On September 10-11, 2019, the CMSA will be hosting a second workshop on Topological Aspects of Condensed Matter.

    New ideas rooted in topology have recently had a major impact on condensed matter physics, and have led to new connections with high energy physics, mathematics and quantum information theory.  The aim of this program will be to deepen these connections and spark new progress by fostering discussion and new collaborations within and across disciplines.

    Topics include i) the classification of topological states  ii) topological orders in two and three dimensions including quantum spin liquids, quantum Hall states and fracton phases and iii)  interplay of symmetry and topology in quantum many body systems, including symmetry protected topological phases, symmetry fractionalization and anomalies iv) topological phenomena in quantum systems  driven far from equlibrium v) quantum field theory approaches to topological matter.

    This workshop is part of the CMSA’s program on Program on Topological Aspects of Condensed Matterand is the second of two workshops, in addition to a visitor program and seminars.

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

    Click here for a list of restaurants in the area. 

    Organizers: Michael Hermele (CU Boulder) and Ashvin Vishwanath (Harvard)

    Partial list of speakers:

    Videos of the lectures can be found in the Youtube playlist below. Links to talks are also available on the schedule below.

  • CMSA EVENT: Workshop on Invariance and Geometry in Sensation, Action and Cognition
    9:15 am-10:00 am
    11/01/2019-04/17/2019

    As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

    Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, it has traditionally not been an important part of biology, except in the context of aspects of structural biology. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use.

    This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines? The aim is to revisit these old neuro-cognitive problems using a series of modern lenses experimentally, theoretically and computationally, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models.

    In addition to talks, there will be a set of tutorial talks on the mathematical description of invariance (P.J. Olver), the computer vision aspects of invariant algorithms (S. Soatto), and the neuroscientific and cognitive aspects of invariance (TBA). The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by L. Mahadevan (Harvard), Talia Konkle (Harvard), Samuel Gershman (Harvard), and Vivek Jayaraman (HHMI).

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

    List of registrants

    Videos

    Tentative Speaker List:

    Schedule:

    Monday, April 15

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:15amWelcome and Introduction
    9:15 – 10:00amVivek JayaramanTitle: Insect cognition: Small tales of geometry & invariance

    Abstract: Decades of field and laboratory experiments have allowed ethologists to discover the remarkable sophistication of insect behavior. Over the past couple of decades, physiologists have been able to peek under the hood to uncover sophistication in insect brain dynamics as well. In my talk, I will describe phenomena that relate to the workshop’s theme of geometry and invariance. I will outline how studying insects —and flies in particular— may enable an understanding of the neural mechanisms underlying these intriguing phenomena.

    10:00 – 10:45amElizabeth TorresTitle: Connecting Cognition and Biophysical Motions Through Geometric Invariants and Motion Variability

    Abstract: In the 1930s Nikolai Bernstein defined the degrees of freedom (DoF) problem. He asked how the brain could control abundant DoF and produce consistent solutions, when the internal space of bodily configurations had much higher dimensions than the space defining the purpose(s) of our actions. His question opened two fundamental problems in the field of motor control. One relates to the uniqueness or consistency of a solution to the DoF problem, while the other refers to the characterization of the diverse patterns of variability that such solution produces.

    In this talk I present a general geometric solution to Bernstein’s DoF problem and provide empirical evidence for symmetries and invariances that this solution provides during the coordination of complex naturalistic actions. I further introduce fundamentally different patterns of variability that emerge in deliberate vs. spontaneous movements discovered in my lab while studying athletes and dancers performing interactive actions. I here reformulate the DoF problem from the standpoint of the social brain and recast it considering graph theory and network connectivity analyses amenable to study one of the most poignant developmental disorders of our times: Autism Spectrum Disorders.

    I offer a new unifying framework to recast dynamic and complex cognitive and social behaviors of the full organism and to characterize biophysical motion patterns during migration of induced pluripotent stem cell colonies on their way to become neurons.

    10:45 – 11:15amCoffee Break
    11:15 – 12:00pmPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

    Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical prerequisites will be kept to a bare minimum.

    12:00 – 12:45pmStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

    Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

    While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

    12:45 – 2:00pmLunch
    2:00 – 2:45pmAnitha PasupathyTitle: Invariant and non-invariant representations in mid-level ventral visual cortex

    My laboratory investigates how visual form is encoded in area V4, a critical mid-level stage of form processing in the macaque monkey. Our goal is to reveal how V4 representations underlie our ability to segment visual scenes and recognize objects. In my talk I will present results from two experiments that highlight the different strategies used by the visual to achieve these goals. First, most V4 neurons exhibit form tuning that is exquisitely invariant to size and position, properties likely important to support invariant object recognition. On the other hand, form tuning in a majority of neurons is also highly dependent on the interior fill. Interestingly, unlike primate V4 neurons, units in a convolutional neural network trained to recognize objects (AlexNet) overwhelmingly exhibit fill-outline invariance. I will argue that this divergence between real and artificial circuits reflects the importance of local contrast in parsing visual scenes and overall scene understanding.

    2:45 – 3:30pmJacob FeldmanTitle: Bayesian skeleton estimation for shape representation and perceptual organization

    Abstract: In this talk I will briefly summarize a framework in which shape representation and perceptual organization are reframed as probabilistic estimation problems. The approach centers around the goal of identifying the skeletal model that best “explains” a given shape. A Bayesian solution to this problem requires identifying a prior over shape skeletons, which penalizes complexity, and a likelihood model, which quantifies how well any particular skeleton model fits the data observed in the image. The maximum-posterior skeletal model thus constitutes the most “rational” interpretation of the image data consistent with the given assumptions. This approach can easily be extended and generalized in a number of ways, allowing a number of traditional problems in perceptual organization to be “probabilized.” I will briefly illustrate several such extensions, including (1) figure/ground and grouping (3) 3D shape and (2) shape similarity.

    3:30 – 4:00pmTea Break
    4:00 – 4:45pmMoira DillonTitle: Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development

    Abstract: Formal geometry lies at the foundation of millennia of human achievement in domains such as mathematics, science, and art. While formal geometry’s propositions rely on abstract entities like dimensionless points and infinitely long lines, the points and lines of our everyday world all have dimension and are finite. How, then, do we get to abstract geometric thought? In this talk, I will provide evidence that evolutionarily ancient and developmentally precocious sensitivities to the geometry of our everyday world form the foundation of, but also limit, our mathematical reasoning. I will also suggest that successful geometric reasoning may emerge through development when children abandon incorrect, axiomatic-based strategies and come to rely on dynamic simulations of physical entities. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations.

    4:45 – 5:30pmMichael McCloskeyTitle: Axes and Coordinate Systems in Representing Object Shape and Orientation

    Abstract: I describe a theoretical perspective in which a) object shape is represented in an object-centered reference frame constructed around orthogonal axes; and b) object orientation is represented by mapping the object-centered frame onto an extrinsic (egocentric or environment-centered) frame.  I first show that this perspective is motivated by, and sheds light on, object orientation errors observed in neurotypical children and adults, and in a remarkable case of impaired orientation perception. I then suggest that orientation errors can be used to address questions concerning how object axes are defined on the basis of object geometry—for example, what aspects of object geometry (e.g., elongation, symmetry, structural centrality of parts) play a role in defining an object principal axis?

    5:30 – 6:30pmReception

     

    Tuesday, April 16

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:45amPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

    Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical pre

    9:45 – 10:30amStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

    Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

    While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

    10:30 – 11:00amCoffee Break
    11:00 – 11:45amJeannette BohgTitle: On perceptual representations and how they interact with actions and physical representations

    Abstract: I will discuss the hypothesis that perception is active and shaped by our task and our expectations on how the world behaves upon physical interaction. Recent approaches in robotics follow this insight that perception is facilitated by physical interaction with the environment. First, interaction creates a rich sensory signal that would otherwise not be present. And second, knowledge of the regularity in the combined space of sensory data and action parameters facilitate the prediction and interpretation of the signal. In this talk, I will present two examples from our previous work where a predictive task facilitates autonomous robot manipulation by biasing the representation of the raw sensory data. I will present results on visual but also haptic data.

    11:45 – 12:30pmDagmar SternadTitle: Exploiting the Geometry of the Solution Space to Reduce Sensitivity to Neuromotor Noise

    Abstract: Control and coordination of skilled action is frequently examined in isolation as a neuromuscular problem. However, goal-directed actions are guided by information that creates solutions that are defined as a relation between the actor and the environment. We have developed a task-dynamic approach that starts with a physical model of the task and mathematical analysis of the solution spaces for the task. Based on this analysis we can trace how humans develop strategies that meet complex demands by exploiting the geometry of the solution space. Using three interactive tasks – throwing or bouncing a ball and transporting a “cup of coffee” – we show that humans develop skill by: 1) finding noise-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, and 3) optimizing predictability of the object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, attractors with few invariant types that overcome substantial delays and noise in the neuro-mechanical system.

    12:30 – 2:00pmLunch
    2:00 – 2:45pmSam OckoTitle: Emergent Elasticity in the Neural Code for Space

    Abstract: To navigate a novel environment, animals must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such internal maps, and how are these maps used to maintain representations of an animal’s position within an environment. We demonstrate analytically how a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent internal map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network during exploration. Moreover, we verify several experimentally testable predictions of our model, including: (1) systematic deformations of grid cells in irregular environments, (2) path-dependent shifts in grid cells towards the most recently encountered landmark, (3) a dynamical phase transition in which grid cells can break free of landmarks in altered virtual reality environments and (4) the creation of topological defects in grid cells. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

    2:45 – 3:30pmTatyana SharpeeTitle: Hyperbolic geometry of the olfactory space

    Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the production of a specific poison by a plant or bacteria will be accompanied by the emission of certain sets of volatile compounds. An animal can therefore judge the presence of poisons in the food by how the food smells. This perspective suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendrograms, and more generally between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

    3:30 – 4:00pmTea Break
    4:00 – 4:45pmEd ConnorTitle: Representation of solid geometry in object vision cortex

    Abstract: There is a fundamental tension in object vision between the 2D nature of retinal images and the 3D nature of physical reality. Studies of object processing in the ventral pathway of primate visual cortex have focused mainly on 2D image information. Our latest results, however, show that representations of 3D geometry predominate even in V4, the first object-specific stage in the ventral pathway. The majority of V4 neurons exhibit strong responses and clear selectivity for solid, 3D shape fragments. These responses are remarkably invariant across radically different image cues for 3D shape: shading, specularity, reflection, refraction, and binocular disparity (stereopsis). In V4 and in subsequent stages of the ventral pathway, solid shape geometry is represented in terms of surface fragments and medial axis fragments. Whole objects are represented by ensembles of neurons signaling the shapes and relative positions of their constituent parts. The neural tuning dimensionality of these representations includes principal surface curvatures and their orientations, surface normal orientation, medial axis orientation, axial curvature, axial topology, and position relative to object center of mass. Thus, the ventral pathway implements a rapid transformation of 2D image data into explicit representations 3D geometry, providing cognitive access to the detailed structure of physical reality.

    4:45 – 5:30pmL. MahadevanTitle: Simple aspects of geometry and probability in perception

    Abstract: Inspired by problems associated with noisy perception, I will discuss two questions: (i) how might we test people’s perception of probability in a geometric context ? (ii) can one construct invariant descriptions of 2D images using simple notions of probabilistic geometry? Along the way, I will highlight other questions that the intertwining of geometry and probability raises in a broader perceptual context.


    Wednesday, April 17

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:45amGily GinosarTitle: The 3D geometry of grid cells in flying bats

    Abstract: The medial entorhinal cortex (MEC) contains a variety of spatial cells, including grid cells and border cells. In 2D, grid cells fire when the animal passes near the vertices of a 2D spatial lattice (or grid), which is characterized by circular firing-fields separated by fixed distances, and 60 local angles – resulting in a hexagonal structure. Although many animals navigate in 3D space, no studies have examined the 3D volumetric firing of MEC neurons. Here we addressed this by training Egyptian fruit bats to fly in a large room (5.84.62.7m), while we wirelessly recorded single neurons in MEC. We found 3D border cells and 3D head-direction cells, as well as many neurons with multiple spherical firing-fields. 20% of the multi-field neurons were 3D grid cells, exhibiting a narrow distribution of characteristic distances between neighboring fields – but not a perfect 3D global lattice. The 3D grid cells formed a functional continuum with less structured multi-field neurons. Both 3D grid cells and multi-field cells exhibited an anatomical gradient of spatial scale along the dorso-ventral axis of MEC, with inter-field spacing increasing ventrally – similar to 2D grid cells in rodents. We modeled 3D grid cells and multi-field cells as emerging from pairwise-interactions between fields, using an energy potential that induces repulsion at short distances and attraction at long distances. Our analysis shows that the model explains the data significantly better than a random arrangement of fields. Interestingly, simulating the exact same model in 2D yielded a hexagonal-like structure, akin to grid cells in rodents. Together, the experimental data and preliminary modeling suggest that the global property of grid cells is multiple fields that repel each other with a characteristic distance-scale between adjacent fields – which in 2D yields a global hexagonal lattice while in 3D yields only local structure but no global lattice.

    Gily Ginosar 1 , Johnatan Aljadeff 2 , Yoram Burak 3 , Haim Sompolinsky 3 , Liora Las 1 , Nachum Ulanovsky 1

    (1) Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel

    (2) Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK

    (3) The Edmond and Lily Safra Center for Brain Sciences, and Racah Institute of Physics, The Hebrew

    University of Jerusalem, Jerusalem, 91904, Israel

    9:45 – 10:30amSandro RomaniTitle: Neural networks for 3D rotations

    Abstract: Studies in rodents, bats, and humans have uncovered the existence of neurons that encode the orientation of the head in 3D. Classical theories of the head-direction (HD) system in 2D rely on continuous attractor neural networks, where neurons with similar heading preference excite each other, while inhibiting other HD neurons. Local excitation and long-range inhibition promote the formation of a stable “bump” of activity that maintains a representation of heading. The extension of HD models to 3D is hindered by complications (i) 3D rotations are non-commutative (ii) the space described by all possible rotations of an object has a non-trivial topology. This topology is not captured by standard parametrizations such as Euler angles (e.g. yaw, pitch, roll). For instance, with these parametrizations, a small change of the orientation of the head could result in a dramatic change of neural representation. We used methods from the representation theory of groups to develop neural network models that exhibit patterns of persistent activity of neurons mapped continuously to the group of 3D rotations. I will further discuss how these networks can (i) integrate vestibular inputs to update the representation of heading, and (ii) be used to interpret “mental rotation” experiments in humans.

    This is joint work with Hervé Rouault (CENTURI) and Alon Rubin (Weizmann Institute of Science).

    10:30 – 11:00amCoffee Break
    11:00 – 11:45amSam GershmanTitle: The hippocampus as a predictive map

    Abstract: A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. I approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? I show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, I argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning.

    11:45 – 12:30pmLucia JacobsTitle: The adaptive geometry of a chemosensor: the origin and function of the vertebrate nose

    Abstract: A defining feature of a living organism, from prokaryotes to plants and animals, is the ability to orient to chemicals. The distribution of chemicals, whether in water, air or on land, is used by organisms to locate and exploit spatially distributed resources, such as nutrients and reproductive partners. In animals, the evolution of a nervous system coincided with the evolution of paired chemosensors. In contemporary insects, crustaceans, mollusks and vertebrates, including humans, paired chemosensors confer a stereo olfaction advantage on the animal’s ability to orient in space. Among vertebrates, however, this function faced a new challenge with the invasion of land. Locomotion on land created a new conflict between respiration and spatial olfaction in vertebrates. The need to resolve this conflict could explain the current diversity of vertebrate nose geometries, which could have arisen due to species differences in the demand for stereo olfaction. I will examine this idea in more detail in the order Primates, focusing on Old World primates, in particular, the evolution of an external nose in the genus Homo.

    12:30 – 1:30pmLunch
    1:30 – 2:15pmTalia KonkleTitle: The shape of things and the organization of object-selective cortex

    Abstract: When we look at the world, we effortlessly recognize the objects around us and can bring to mind a wealth of knowledge about their properties. In part 1, I’ll present evidence that neural responses to objects are organized by high-level dimensions of animacy and size, but with underlying neural tuning to mid-level shape features. In part 2, I’ll present evidence that representational structure across much of the visual system has the requisite structure to predict visual behavior. Together, these projects suggest that there is a ubiquitous “shape space” mapped across all of occipitotemporal cortex that underlies our visual object processing capacities. Based on these findings, I’ll speculate that the large-scale spatial topography of these neural responses is critical for pulling explicit content out of a representational geometry.

    2:15 – 3:00pmVijay BalasubramanianTitle: Becoming what you smell: adaptive sensing in the olfactory system

    Abstract: I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors.  In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors.  The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules.  I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors.  The resulting algorithm for “estimation by elimination” can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain.  The theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans.   It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb.

    3:00 – 3:45pmIla FeiteTitle: Invariance, stability, geometry, and flexibility in spatial navigation circuits

    Abstract: I will describe how the geometric invariances or symmetries of the external world are reflected in the symmetries of neural circuits that represent it, using the example of the brain’s networks for spatial navigation. I will discuss how these symmetries enable spatial memory, evidence integration, and robust representation. At the same time, I will discuss how these seemingly rigid circuits with their inscribed symmetries can be harnessed to represent a range of spatial and non-spatial cognitive variables with high flexibility.

    3:45 – 4:00pmL Mahadevan – summary
  • CMSA EVENT: The 2017 Charles River Lectures
    9:15 am-5:30 pm
    11/01/2019

    The 2017 Charles River Lectures

    Charles River with Bench at Sunset

    Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community.

    The 2017 lectures will take place 9:15am – 5:30pm on Monday, October 2 at Harvard University  in the Harvard Science Center.


    ***************************************************

    UPDATED LOCATION

    Harvard University

    Harvard Science Center (Halls C & E)

    1 Oxford Street, Cambridge, MA 02138 (Map)

    Monday, October 2, 2017

    9:15 AM – 5:30 PM

    **************************************************

    Please note that registration has closed.

    Speakers:

    Agenda:

    In Harvard Science Center Hall C:

    8:45 am – 9:15 amCoffee/light breakfast

    9:15 am – 10:15 am: Ofer Zeitouni

    Title: Noise stability of the spectrum of large matrices

    Abstract: The spectrum of large non-normal matrices is notoriously sensitive to perturbations, as the example of nilpotent matrices shows. Remarkably, the spectrum of these matrices perturbed by polynomially (in the dimension) vanishing additive noise is remarkably stable. I will describe some results and the beginning of a theory.

    The talk is based on joint work with Anirban Basak and Elliot Paquette, and earlier works with Feldheim, Guionnet, Paquette and Wood.

    10:20 am – 11:20 am: Andrea Montanari

    Title: Algorithms for estimating low-rank matrices 

    Abstract: Many interesting problems in statistics can be formulated as follows. The signal of interest is a large low-rank matrix with additional structure, and we are given a single noisy view of this matrix. We would like to estimate the low rank signal by taking into account optimally the signal structure. I will discuss two types of efficient estimation procedures based on message-passing algorithms and semidefinite programming relaxations, with an emphasis on asymptotically exact results.

    11:20 am – 11:45 amBreak

    11:45 am – 12:45 pm: Paul Bourgade

    Title: Random matrices, the Riemann zeta function and trees

    Abstract: Fyodorov, Hiary & Keating have conjectured that the maximum of the characteristic polynomial of random unitary matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the typical size of local maxima of the Riemann zeta function along the critical axis. I will first explain the origins of this conjecture, and then outline the proof for the leading order of the maximum, for unitary matrices and the zeta function. This talk is based on joint works with Arguin, Belius, Radziwill and Soundararajan.

    1:00 pm – 2:30 pm: Lunch

    In Harvard Science Center Hall E:

    2:45 pm – 3:45 pm: Roman Vershynin

    Title: Deviations of random matrices and applications

    Abstract: Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This lecture will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science.

    3:45 pm – 4:15 pm: Break

    4:15 pm – 5:15 pm: Massimiliano Gubinelli

    Title: Weak universality and Singular SPDEs

    Abstract: Mesoscopic fluctuations of microscopic (discrete or continuous) dynamics can be described in terms of nonlinear stochastic partial differential equations which are universal: they depend on very few details of the microscopic model. This universality comes at a price: due to the extreme irregular nature of the random field sample paths, these equations turn out to not be well-posed in any classical analytic sense. I will review recent progress in the mathematical understanding of such singular equations and of their (weak) universality and their relation with the Wilsonian renormalisation group framework of theoretical physics.

    Poster:

    2017 Charles River Lectures Poster

    Organizers:

     Alexei BorodinHenry CohnVadim GorinElchanan MosselPhilippe RigolletScott Sheffield, and H.T. Yau

  • CMSA EVENT: Kickoff Workshop on Topology and Quantum Phases of Matter
    9:20 am-3:15 pm
    11/01/2019-08/28/2018
    Topological-1

    Screen-Shot-2018-08-13-at-2.28.22-PM

    On August 27-28, 2018, the CMSA will be hosting a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines.

    This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter,  and will be the first of two workshops, in addition to a visitor program and seminars.

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

    Please register here

    Speakers: 

  • Special Seminar
    9:30 am-11:00 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/18/2019 General Relativity Seminar

    9:30 am-10:30 am
    11/01/2019
  • CMSA EVENT: Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
    9:30 am-5:00 pm
    11/01/2019-03/01/2019

    From February 25 to March 1, the CMSA will be hosting a workshop on Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations. 

    Key participants of this workshop include David Jerison (MIT), Alexander Logunov (IAS), and Eugenia Malinnikova (IAS).  This workshop will have morning sessions on Monday-Friday of this week from 9:30-11:30am, and afternoon sessions on Monday, Tuesday, and Thursday from 3:00-5:00pm.
    The sessions will be held in  \(G02\) (downstairs) at 20 Garden, except for Tuesday afternoon, when the talk will be in \(G10\).

  • Special Seminar
    9:30 am
    11/01/2019
  • Seminars
    9:50 am-10:50 am
    11/01/2019

    The seminar for evolution equations, hyperbolic equations, and fluid dynamics will be held on Thursdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule of speakers is below. Titles for the talks will be added as they are received.

    DateNameTitle
    09-03-2015Long JinScattering Resonances for Convex Obstacles
    09-10-2015Chunjing XieWell/ill-posedness for the rotating shallow water system
    09-17-2015Xiangdi HuangGlobal classical and weak Solutions to the 3D fully compressible Navier-Stokes-Fourier system
    09-24-2015Felix FinsterCausal fermion systems and the causal action principle
    10-01-2015Pin YuConstruction of Cauchy data of vacuum Einstein field equations evolving to black holes
    10-08-2015Chunjing XieSteady Euler flows past a wall or through a nozzle
    10-15-2015Zhou Ping XinOn Global Well-Posedness of The Compressible Navier-Stokes Systems with Large Oscillations
    10-22-2015Xiangdi HuangOn Nash’s problem for compressible flows
    10-29-2015Pin YuShock formations for 3 dimensional wave equations
    11-05-2015No talk 
    11-12-2015Zhou Ping Xin (9:30am-10:30am) Nicolai Krylov (10:30am-11:30am)Nonlinear Asymptotic Stability of Lane-Emden Solutions for The Viscous Gaseous Star ProblemOn the existence of $\bf W^{2}_{p}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions
    11-19-2015Nicolai KrylovTo the theory of viscosity solutions for uniformly parabolic Isaacs equations
    11-26-2015ThanksgivingNo seminar
    12-4-2015John Loftin (@11:00am)Moduli of Equivariant Minimal Surfaces in CH^2$
    01-28-2016Xiaoli HanThe symplecitic and Lagrangian mean curvature flow 
    02-04-2016Pranav PanditCategorical Kähler Geometry
    02-11-2016Lydia BieriEinstein’s Equations, Energy and Gravitational Radiation
    02-18-2016Zuoqiang ShiLow dimensional manifold model for image processing
    02-25-2016Chun Peng WangSmooth Transonic Flows of Meyer Type in De Laval Nozzles
    03-03-2016Piotr ChruscielSingularities in general relativity
    03-10-2016Feimin HuangIsometric immersion of complete surface with slowly decaying negative Gauss curvature
    03-17-2016Spring BreakNo Talk
    03-24-2016Michael EichmairMinimal surfaces, isoperimetry, and non-negative scalar curvature in asymptotically flat manifolds
    03-31-2016Felix FinsterLorentzian spectral geometry and the fermionic signature operator
    04-07-2016(Room 232, Science Center)Stefano Bianchini, SISSAConcentration of entropy dissipation for scalar conservation laws
    04-14-2016Tai-peng TsaiStability of periodic waves of the 1D nonlinear Schr\”odinger equations
    04-21-2016Stefano Bianchini, SISSAQuadratic interaction functional for system of conservation laws
    04-28-2016Mihalis Dafermos, PrincetonThe linear stability of the Schwarzschild solution to gravitational perturbations
    05-05-2016Xu-Jia WangMonge-Ampere equations arising in geometric optics
    05-12-2016Stefano Bianchini
  • Special Seminar
    9:50 am-10:50 am
    11/01/2019-04/26/2016

    The seminar on geometric analysis will be held on Tuesdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule can be found below. Titles will be added as they are provided.

    DayNameTitle
    09-08-2015Binglong ChenOn the geometry of complete positively curved Kahler manifolds
    09-15-2015Hongwei XuMean Curvature Flow and Sphere Theorem
    09-22-2015Teng FeiSome new solutions to the Strominger system
    09-29-2015Xuqian FanThe Steklov eigenvalues on annuli
    10-06-2015Binglong ChenRicci flow and the moduli spaces of positive isotropic curvature metrics on four-manifolds
    10-13-2015Pengfei GuanIsometric embeddings of $(S^2,g)$ to general warped product space $(N^3,\bar g)$.
    10-20-2015Ovidiu SavinSmoothness of the eigenfunction for the Monge-Ampere equation
    10-27-2015Tom IlmanenFlow of curves by curvature in R^n
    11-03-2015Tom Hou (Caltech)Existence and stability of self-similar singularities for a 1D model of the 3D axisymmetric Euler equations
    11-10-2015Jerome Darbon (9:30am-10:30am) Adam Jacob (10:30am-11:30am)On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton-Jacobi Equations(1,1) forms with specified Lagrangian phase
    11-17-2015Ovidiu SavinExamples of singular minimizers in the calculus of variations
    11-24-2015Hongwei XuMean curvature flow meets Ricci flow:  Convergence and sphere theorems of sub manifolds arising from Yau rigidity theory
    12-01-2015Tom Ilmanen
    01-26-2016Mao ShengUniformization of p-adic curves
    02-02-2016Yi ZhangHodge Bundles on Smooth Compactifications of Siegel Varieties
    02-09-2016Valentino TosattiNon-Kahler Calabi-Yau manifolds
    02-16-2016Camillo De LellisApproaching Plateau’s problem with minimizing sequences of sets
    02-23-2016Junbin LiConstruction of black hole formation spacetimes
    03-01-2016Ben WeinkoveMonge-Ampere equations and metrics on complex manifolds
    03-08-2016Albert ChauSurvey on Kahler Ricci flow on non-negatively curved non-compact manifolds
    03-15-2016Spring Break 
    03-22-2016Richard Schoen (Standford)The geometry of eigenvalue extremal problems
    03-29-2016Piotr ChruscielMass of characteristic surfaces
    04-05-2016 (Room 232, Science Center)Niky Kamran, McGill UniversityNon-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets
    04-12-2016Connor Mooney, UT AustinFinite time blowup for parabolic systems in the plane
    04-19-2016 (Room 232, Science Center)Xu-Jia WangBoundary behaviour of solutions to singular elliptic equations
    04-26-2016Andre NevesA path to Yau’s conjecture
  • Seminars

    Seminars Colloquia & Seminar
    13/3/2018 Topology Seminar

    10:00 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/22/2018 Topology Seminar

    10:00 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/18/2019 General Relativity

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/24/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/10/18 Topology Seminar

    10:30 am-12:00 am
    11/01/2019-09/11/2018
  • Seminars
    10:30 am-11:42 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/26/2019 Topology

    10:30 am-12:40 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/16/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/11/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/13/2019 General Relativity

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/25/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/18/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars
    10:30 am-12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/20/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars
    10:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/9/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    11/1/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/30/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/2/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/1/2020 Quantum Matter seminar

    10:30 am-12:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-02-2016 Random Matrix & Probability Theory Seminar

    10:32 am
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    10:36 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-07-16 Mathematical Physics Seminar

    10:38 am
    11/01/2019

    No additional detail for this event.

  • Special Seminar

    Special Seminar
    11-04-16 Special Seminar

    10:42 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    10:43 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-09-2016 Random Matrix & Probability Theory Seminar

    10:44 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    10:46 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    10:56 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    10:57 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-14-16 Mathematical Physics Seminar

    10:58 am
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
  • General Relativity Seminar
  • Seminars

    Seminars Colloquia & Seminar
    02-09-2018 Mirror Symmetry Seminar

    11:00 am
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-16-2016 Random Matrix & Probability Theory Seminar

    11:00 am
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/19/2018 Mirror Symmetry Seminar

    11:00 am-11:00 pm
    11/01/2019
  • General Relativity Seminar
  • General Relativity Seminar
  • Seminars

    Seminars Colloquia & Seminar
    2-16-2018 Mirror Symmetry Seminar

    11:00 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2-23-2018 Mirror Symmetry Seminar

    11:00 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3-2-2018 Mirror Symmetry Seminar

    11:00 am-12:00 am
    11/01/2019-03/03/2018
  • General Relativity Seminar
  • Seminars

    Seminars Colloquia & Seminar
    4-13-2018 Mirror Symmetry Seminar

    11:00 am-12:00 am
    11/01/2019-04/14/2018
  • Member Seminar
    11:01 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-21-16 Mathematical Physics Seminar

    11:02 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:03 am-11:04 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    11:03 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:04 am
    11/01/2019

    The  CMSA Colloquium will take place every Wednesday from 4:30-5:30pm in CMSA Building, 20 Garden Street, G10.

    Spring 2020

    DateSpeakerTitle/Abstract
    1/29/2020David Yang (Harvard)

    Abstract: Data-intensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in data-intensive economies: first, states are key collectors and repositories of data; second, data is a non-rival input in innovation. We document the importance of state-collected data for innovation using comprehensive data on Chinese facial recognition AI firms and government contracts. Firms produce more commercial software and patents, particularly data-intensive ones, after receiving government public security contracts. Moreover, effects are largest when contracts provide more data. We then build a directed technical change model to study the state’s role in three applications: autocracies demanding AI for surveillance purposes, data-driven industrial policy, and data regulation due to privacy concerns. When the degree of non-rivalry is as strong as our empirical evidence suggests, the state’s collection and processing of data can shape the direction of innovation and growth of data-intensive economies.

    2/5/2020Scott Aaronson (UT Austin)

    Video

    Title: Gentle Measurement of Quantum States and Differential Privacy

    Abstract: I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography”
    of quantum states (that is, answering a large number of questions about a quantum state given few copies of it).

    Based on joint work with Guy Rothblum (arXiv:1904.08747)

    2/12/2020Scott Kominers (Harvard)Title: A Compact, Logical Approach to Large-Market Analysis

    Abstract: In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

    2/19/2020Peter Shor (MIT)Title: Quantum Money from Lattices

    Abstract: Quantum money is  a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.

    2/26/2020Daneil Wise (McGill)Title: The Cubical Route to Understanding Groups

    Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds and simultaneously dramatically extended our understanding of many infinite groups.
    3/4/2020

    4:45 – 5:45pm

    Salil Vadhan (Harvard)Title: Derandomizing Algorithms via Spectral Graph Theory

    Abstract: Randomization is a powerful tool for algorithms; it is often easier to design efficient algorithms if we allow the algorithms to “toss coins” and output a correct answer with high probability. However, a longstanding conjecture in theoretical computer science is that every randomized algorithm can be efficiently “derandomized” — converted into a deterministic algorithm (which always outputs the correct answer) with only a polynomial increase in running time and only a constant-factor increase in space (i.e. memory usage).

    In this talk, I will describe an approach to proving the space (as opposed to time) version of this conjecture via spectral graph theory. Specifically, I will explain how randomized space-bounded algorithms are described by random walks on directed graphs, and techniques in algorithmic spectral graph theory (e.g. solving Laplacian systems) have yielded deterministic space-efficient algorithms for approximating the behavior of such random walks on undirected graphs and Eulerian directed graphs (where every vertex has the same in-degree as out-degree). If these algorithms can be extended to general directed graphs, then the aforementioned conjecture about derandomizing space-efficient algorithms will be resolved.

    3/11/2020

    Postponed

    Jose Scheinkman

    (Columbia)

    This colloquium will be rescheduled at a later date. 

    Title: Menu Costs and the Volatility of Inflation

    Abstract: We present a state-dependent equilibrium pricing model that generates inflation rate fluctuations from idiosyncratic shocks to the cost of price changes of individual firms.  A firm’s nominal price increase lowers other firms’ relative prices, thereby inducing further nominal price increases. We first study a mean-field limit where the equilibrium is characterized by a variational inequality and exhibits a constant rate of inflation. We use the limit model to show that in the presence of a large but finite number n of firms the snowball effect of repricing causes fluctuations to the aggregate price level  and these fluctuations converge to zero slowly as n grows. The fluctuations caused by this mechanism are larger when the density of firms at the repricing threshold is high, and the density at the threshold is high when the trend inflation level is high. However a calibration to US data shows that this mechanism is quantitatively important even at modest levels of trend inflation and  can account for the positive relationship between inflation level and volatility that has been observed empirically.

    3/12/2020

    4:00 – 5:00pm

    Daniel Forger (University of Michigan)This meeting will be taking place virtually on Zoom.

    Title: Math, Music and the Mind; Mathematical analysis of the performed Trio Sonatas of J. S. Bach

    Abstract: I will describe a collaborative project with the University of Michigan Organ Department to perfectly digitize many performances of difficult organ works (the Trio Sonatas by J.S. Bach) by students and faculty at many skill levels. We use these digitizations, and direct representations of the score to ask how music should encoded in the mind. Our results challenge the modern mathematical theory of music encoding, e.g., based on orbifolds, and reveal surprising new mathematical patterns in Bach’s music. We also discover ways in which biophysical limits of neuronal computation may limit performance.

    Daniel Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan. He is also a visiting scholar at Harvard’s NSF-Simons Center and an Associate of the American Guild of Organists.

    3/25/2020Cancelled
    4/1/2020Mauricio Santillana (Harvard)This meeting will be taking place virtually on Zoom.

    Title: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring

    Abstract: I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.

    4/8/2020Juven Wang (CMSA)This meeting will be taking place virtually on Zoom.

    Title: Quantum Matter Adventure to Fundamental Physics and Mathematics (Continued)

    Abstract: In 1956, Parity violation in Weak Interactions is confirmed in particle physics. The maximal parity violation now is a Standard Model physics textbook statement, but it goes without any down-to-earth explanation for long. Why? We will see how the recent physics development in Quantum Matter may guide us to give an adventurous story and possibly a new elementary
    explanation.  We will see how the topology and cobordism in mathematics may come into play of anomalies and non-perturbative interactions in
    fundamental physics. Perhaps some of you (geometers,  string theorists, etc.) can team up with me to understand the “boundary conditions” of the Standard Model and Beyond

    4/15/2020
    Lars Andersson (Max-Planck Institute for Gravitational Physics)
    This meeting will be taking place virtually on Zoom.

    Title: Stability of spacetimes with supersymmetric compactifications

    Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and Shing-Tung Yau.

    4/22/2020William Minicozzi (MIT)This meeting will be taking place virtually on Zoom.

    Title: Mean curvature flow in high codimension

    Abstract: I will talk about joint work with Toby Colding on higher codimension mean curvature flow.  Some of the ideas come from function theory on manifolds with Ricci curvature bounds.

    4/29/2020Gerhard Huisken (Tübingen University / MFO)This meeting will be taking place virtually on Zoom.

    Title: Mean curvature flow of mean-convex embedded 2-surfaces in 3-manifolds

    Abstract: The lecture describes joint work with Simon Brendle on the deformation of embedded surfaces with positive mean curvature in Riemannian 3-manifolds in direction of their mean curvature vector. It is described how to find long-time solutions of this flow, possibly including singularities that are overcome by surgery, leading to a comprehensive description of embedded mean-convex surfaces and the regions they bound in a 3-manifold. The flow can be used to sweep out the region between space-like infinity and the outermost horizon in asymptotically flat 3-manifolds arising in General Relativity. (Joint with Simon Brendle.)

    5/6/2020Lydia Bieri (UMich)This meeting will be taking place virtually on Zoom.

    Title: Energy, Mass and Radiation in General Spacetimes

    Abstract: In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. Isolated gravitating systems such as binary stars, black holes or galaxies can be described in GR by asymptotically flat (AF) solutions of these equations. These are solutions that look like flat Minkowski space outside of spatially compact regions. There are well-defined notions for energy and mass for such systems. The energy-matter content as well as the dynamics of such a system dictate the decay rates at which the solution tends to the flat one at infinity. Interesting questions occur for very general AF systems of slow decay. We are also interested in spacetimes with pure radiation. In this talk, I will review what is known for these systems. Then we will concentrate on spacetimes with pure radiation. In particular, we will compare the situations of incoming radiation and outgoing radiation under various circumstances and what we can read off from future null infinity.

    5/13/2020Mikhail Lukin (Harvard)

    Video

    This meeting will be taking place virtually on Zoom.

    Title: Exploring New Frontiers of Quantum Science with Programmable Atom Arrays

    Abstract: We will discuss recent work at a new scientific interface between  many-body physics and quantum information science. Specifically, we will  describe the advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Within this system we performed quantum simulations of one dimensional spin models, discovered a new type of non-equilibrium quantum dynamics associated with the so-called many body scars and created large-scale entangled states. We will also describe the most recent developments that now allow the control over 200 atoms in two-dimensional arrays.   Ongoing efforts  to study exotic many-body phenomena and to realize and test quantum optimization algorithms within such systems will be discussed.

    5/20/2020This meeting will be taking place virtually on Zoom.

    Fall 2019

    DateSpeakerTitle/Abstract
    9/18/2019Bill Helton (UC San Diego)Title:  A taste of noncommutative convex algebraic geometry

    Abstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example,

    ◦ A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials.

    ◦ A convex NC semialgebraic set has a linear matrix inequality representation.

    ◦ The natural Nullstellensatz are falling into place.

    The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019.

    9/25/2019Pavel Etingof (MIT)

     

    Title: Double affine Hecke algebras

    Abstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications.

    10/2/2019Spiro Karigiannis (University of Waterloo)Title: Cohomologies on almost complex manifolds and their applications

    Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.

    10/9/2019Hans Lindblad (Johns Hopkins University)Title:  Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition

     

    Abstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition  satisfy the preserved wave coordinate condition.

     

    Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times.

    John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas  lainerman came up with the ‘null condition’, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition.

    Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition.

    Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to afraction and has now been used to prove global existence also with matter fields.

    Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equationsbackwards to obtain global solutions with given data at infinity.

    10/16/2019Aram Harrow (MIT)

    Video

    Title: Monogamy of entanglement and convex geometry

    Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems.

    10/23/2019No talk
    10/30/2019Nima Arkani-Hamed (IAS)

    Video

    Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity
    11/6/2019Kevin Costello (Perimeter Institute)

    Video

    Title: A unified perspective on integrability

     

    Abstract: Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics.   I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu.

    11/13/2019Heather  Harrington (University of Oxford)Title:  Algebra, Geometry and Topology of ERK Enzyme Kinetics

    Abstract: In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

    11/20/2019Xi Yin (Harvard)

    Video

    Title: An Introduction to the Non-Perturbative Bootstrap

    Abstract: I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap

    11/25/2019

    Monday

    Madhu Sudan (Harvard)
    Abstract: The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits.

    In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction.

    Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard).

    12/4/2019Xiao-Gang Wen (MIT)
    Video
    Title: Emergence of graviton-like excitations from a lattice model

    Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases.

    2018-2019

    DateSpeakerTitle/Abstract
    9/26/2018Xiao-Gang Wen (MIT)Title: A classification of low dimensional topological orders and fully extended TQFTs

    Abstract: In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1-dimension, there is no non-trivial topological orders. In 2-dimensions, the topological orders are classified by modular tensor category theory. In 3-dimensions, the topological orders are classified by a simple class of braided fusion 2-categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs.

    10/03/2018Richard Schoen (Stanford)Title: Perspectives on the scalar curvature

    Abstract: This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied.

    10/10/2018Justin Solomon (MIT)Title: Correspondence and Optimal Transport for Geometric Data Processing

    Abstract: Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make large-scale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometrically-structured data.

    10/17/2018Jeremy England (MIT)Title: Wisdom of the Jumble

    Abstract: There are certain, specific behaviors that are particularly distinctive of life. For example, living things self-replicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of life-like phenomena in a wide range of messy systems made of many interacting components.

    In this talk I will discuss some of the recent insights we have gleaned from studying emergent fine-tuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more life-like ways of computing that have the potential to either be cheaper or more powerful than existing means.

    10/31/2018Moon Duchin (Tufts)Title: Exploring the (massive) space of graph partitions

    Abstract: The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts).  I’ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics.

    11/14/2018Dusa McDuff (Columbia)Title: The virtual fundamental class in symplectic geometry

    Abstract: Essential to many constructions and applications of symplectic  geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well  understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so  that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there  are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a  construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim.

    11/19/2018Xiaoqin Wang (Johns Hopkins)Title: Computational Principles of Auditory Cortex

    Abstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication.

    11/28/2018Robert Haslhofer (University of Toronto)Title: Recent progress on mean curvature flow

    Abstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanen’s multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits.

    12/5/2018Robert McCann (University of Toronto)Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity

    Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of  probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics.

    Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf

    12/12/2018Zhiwei Yun (MIT)Title: Shtukas: what and why

    Abstract: This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them.

    1/30/2019Richard Freeman (Harvard)Title:  Innovation in Cell Phones in the US and China: Who Improves Technology Faster?

    Abstract:  Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps.  Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones.  Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality.  The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being.

    2/7/2019

    *Thursday*

    Ulrich Mueller (Princeton)Title: Inference for the Mean

    Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.

    2/13/2019Christian Santangelo (UMass Amherst)Title: 4D printing with folding forms

    Abstract: 4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target three-dimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our group’s efforts to understand and design structures that can fold from an initially flat sheet to target three-dimensional shapes. After reviewing the state-of-the-art in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome.

    2/20/2019Michael Woodford (Columbia)Title: Optimally Imprecise Memory and Biased Forecasts

    Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings.

    [authors: Rava Azeredo da Silveira (ENS) and Michael Woodford (Columbia)]

    2/27/2019

    2:30pm

    Ian Martin (LSE)Title: Sentiment and Speculation in a Market with Heterogeneous Beliefs

    Abstract: We present a dynamic model featuring risk-averse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so “the market” is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou]

    3/6/2019

    2:30pm

    Philippe Sosoe (Cornell)Title:  A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation

    Abstract:  In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS’s result, and discuss a sharp transition in the construction of the Gibbs-type invariant measures considered by these authors.  (Joint work with Tadahiro Oh and Leonardo Tolomeo)

    3/13/2019

    5:15pm

    Greg Galloway (University of Miami)Title:  On the geometry and topology of initial data sets in General Relativity

    Abstract:  A theme of long standing interest (to the speaker!)  concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness).  Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple.  The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces,  which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack.

    3/20/2019Sonia Jaffe (Microsoft)Title:  Quality Externalities on Platforms:  The Case of Airbnb

    Abstract:  We explore quality externalities on platforms:  when buyers have limited information, a seller’s quality affects whether her buyers return to the platform, thereby impacting other sellers’ future business.  We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller’s customers to return to the platform.  We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higher-GRP sellers, platforms may be able to increase overall seller surplus.  (Joint work with Peter Coles, Steven Levitt, and Igor Popov.)

    3/27/2019

    5:15pm

    Tatyana Sharpee (Salk Institute for Biological Studies)Title: Hyperbolic geometry of the olfactory space.

    Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their co-occurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical tree-like networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

    4/3/2019

    2:30pm

    Sarah Moshary (Chicago Booth)Title:  Deregulation through Direct Democracy:  Lessons from Liquor

    Abstract:  This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool.

    4/10/2019

    2:30pm

    Pietro Veronesi (Chicago Booth)Title: Inequality Aversion, Populism, and the Backlash Against Globalization

    Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model.

    Paper

    Online Appendix

    4/17/2019Yi-Zhuang You (UCSD)Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

    Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

    .

    [1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103

    [2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804

    [3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223

    4/24/2019Shengwu Li (Harvard)
    Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.
    Date…………SpeakerTitle
    02-09-2018 *Friday       Fan Chung

    (UCSD)

    Sequences: random, structured or something in between

    There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns;

    testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems.

    02-14-2018Zhengwei Liu

    (Harvard Physics)

    A new program on quantum subgroups

    Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing.

    02-21-2018Don Rubin

    (Harvard)

    Essential concepts of causal inference — a remarkable history

    Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis.

    02-26-2018 *MondayTom Hou

    (Caltech)

    Computer-assisted analysis of singularity formation of a regularized 3D Euler equation

    Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate self-similar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate self-similar solution, which implies the existence of the finite time blow-up of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu.

    03-07-2018Richard Kenyon

    (Brown)

    Harmonic functions and the chromatic polynomial

    Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam.

    03-14-2018
    03-21-2018
    03-28-2018Andrea Montanari (Stanford)A Mean Field View of the Landscape of Two-Layers Neural Networks

    Abstract: Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD).  Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties?

    We consider a simple case, namely two-layers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to `average-out’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well.
    [Based on joint work with Song Mei and Phan-Minh Nguyen]

    03-30-2018
    04-04-2018Ramesh Narayan 

    (Harvard)

    Black Holes and Naked Singularities

    Abstract: Black Hole solutions in General Relativity contain Event Horizons and
    Singularities. Astrophysicists have discovered two populations of
    black hole candidates in the Universe: stellar-mass objects with
    masses in the range 5 to 30 solar masses, and supermassive objects
    with masses in the range million to several billion solar
    masses. There is considerable evidence that these objects have Event
    Horizons. It thus appears that astronomical black hole candidates are
    true Black Holes. Direct evidence for Singularities is much harder to
    obtain since, at least in the case of Black Holes, the Singularities
    are hidden inside the Event Horizon. However, General Relativity also
    permits Naked Singularities which are visible to external
    observers. Toy Naked Singularity models have been constructed, and
    some observational features of accretion flows in these spacetimes
    have been worked out.

    04-11-2018Pablo Parrilo

    (MIT)

    Graph Structure in Polynomial Systems: Chordal Networks

    Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).

    04-18-2018Washington Taylor

    (MIT)

    On the fibration structure of known Calabi-Yau threefolds

    Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds.

    04-25-2018 Xi Yin

    (Harvard)

    How we can learn what we need to know about M-theory

    Abstract: M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory.

    05-02-2018
    05-09-2018

    2016-2017

    DateNameTitle/Abstract
    01-25-17Sam Gershman, Harvard Center for Brain Science, Department of Psychology

    Title: Spectral graph theory of cognitive maps

    Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory.

    02-01-17Sean Eddy, Harvard Department of Molecular and Cellular Biology

    Sean_Eddy

    Title: Biological sequence homology searches: the future of deciphering the past 

    Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK.

    02-08-17Matthew Headrick, Brandeis University

    matthew_headrick

    Title: Quantum entanglement, classical gravity, and convex programming: New connections

    Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differential-geometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way.

    02-15-17Masahito Yamazaki, IMPU

    Masahito Yamazaki

     Title: Geometry of 3-manifolds and Complex Chern-Simons Theory

    Abstract: The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras.

    Video

    02-22-17Steven Rayan, University of Saskatchewan

    Title: Higgs bundles and the Hitchin system

    Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics.  As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence.  From this point of view, the Hitchin map and spectral curves emerge.  We’ll use these to form an impression of what the moduli space “looks like”.  I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry.

    Video

    03-01-17Jun Liu, Harvard University

    Jun liu

    Title: Expansion of biological pathways by integrative Genomics

    Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays.

    Based on the joint work with Yang Li and the Vamsi Mootha lab.

    Video

    03-08-17Gabor Lippner, Northeastern University

    ---

    Title: Evolution of cooperation in structured populations

    Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics.  Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies.  It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution.

    In this talk I will present new results about the model where the population is represented by an interaction network.  We study the likelihood of a random mutation spreading through the entire population.  The main question is to understand how the network influences this likelihood.  After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks.
    03-15-17 Spring Break: No session
    03-22-17Gunther Uhlmann, University of Washington

    guntherUhlman

    Abstract We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of
    waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others.
    The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.
    We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.
    03-29-17Leslie Greengard, Courant InstituteLeslie_GreengardTitle: Inverse problems in acoustic scattering and cryo-electron microscopy

    Abstract: A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy.

    NOTE: This talk will begin at 4:00pm

    04-05-17Gongjie Li, Harvard University

    GongjieLi

    Title: Unveiling the Origin of Planetary Systems by Dynamical and Statistical Approaches

    Abstract: The unexpected diversity of observed extrasolar planetary systems has posed new challenges to our classical understanding of planetary formation. A lot of these challenges can be addressed by a deeper understanding of the dynamics in planetary systems, which will also allow us to construct more accurate planetary formation theories consistent with observations. In this talk, I will first explain the origin of counter orbiting planets using a new dynamical mechanism I discovered, which also has wide implications in other astrophysical systems, such as the enhancement of tidal disruption rates near supermassive black hole binaries. In addition, I will discuss the architectural properties of circumbinary planetary systems from selection biases using statistical methods, and infer the origin of such systems.

    Video

    04-12-17Shlomo Razamat, Israel Institute of Technology

    ShlomoRazamat

    Title: Complicated four-dimensional physics and simple mathematics

    Abstract: We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index,  of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of Ruijsenaars-Schneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven.

    Video

    04-19-17Cumrun Vafa, Harvard University

    CumrunVafa

    Title: String Swampland

    Abstract: In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a no-go theorem for non-supersymmetric AdS/CFT holography.

    04-27-17Mehran Kardar, MIT

    MehranKardar

    Title: Levitation by Casimir forces in and out of equilibrium

    Abstract: Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw’s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint.

    Note: This talk will begin at 3:00pm

    05-02-17Simona Cocco, Laboratoire de Physique Statistique de l’ENSTitle: Reverse modeling of protein sequence data: from graphical models to structural and functional predictions

    Body: A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing
    similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models
    have led to substantial progress in protein structural and functional
    predictions.

    Note:  This talk will begin at 4:00pm

    05-03-17Xue-Mei Li, University of WarwickTitle: Perturbation to conservation law and stochastic averaging

    Abstract: A deterministic or random system with a conservation law is often used to
    approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces.

    Note: This talk will be held in the Science Center, Room 507

    05-10-17
    05-17-17Kwok Wai Chan, Chinese University of Hong KongTitle: Scattering diagrams from asymptotic analysis on Maurer-Cartan equations

    Abstract:  In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on Maurer-Cartan equations. In this talk, I will explain some results which implement part of Fukaya’s program. More precisely, I will show how semi-classical limits of Maurer-Cartan solutions give rise naturally to consistent scattering diagrams, which are known to encode Gromov-Witten data on the mirror side and have played an important role in the works of Kontsevich-Soibelman and Gross-Siebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015).

    05-24-17 NO COLLOQUIUM
    05-31-17Peter Michor, University of Vienna

     Title: Geometry of shape spaces and diffeomorphism groups and some of their uses

    Abstract: This talk is devoted to shape spaces, Riemannian metrics on them, their geodesics and distance functions, and some of their uses, mainly in computational anatomy. The simplest Riemannian metrics have vanishing geodesic distance, so one has to use, for example, higher order Sobolev metrics on shape spaces. These have curvature, which complicates statistics on these spaces.

    DateNameTitle
    09-09-16

    Bong Lian, Brandeis

    portrait

    Title: Riemann-Hilbert Problem and Period Integrals

    Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems.

    09-14-16Sze-Man Ngai, Georgia Southern UniversityngaiTitle: The multifractal formalism and spectral asymptotics of self-similar measures with overlaps

    Abstract: Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum.  The asymptotic behavior of the eigenvalue counting function for the associated  Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results.

    09-21-16Prof. L. Mahadevan, Harvard SEAS

    Mahadevan_200x300

    Title: “Morphogenesis: Biology, Physics and Mathematics”

    Abstract:  A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology.  Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains.  I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology.

    09-28-16Hong Liu, MIT

    liu_hong

    Title: A new theory of fluctuating hydrodynamics

    Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate  for capturing  fluctuations.  In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure.

    We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular,  the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations.

    Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anti-commuting variables and the theory exhibits an emergent supersymmetry.

    10-05-16

    Alexander LogunovTel-Aviv University

    alex

    Title: Zeroes of harmonic functions and Laplace eigenfunctions

     Abs: Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete.

    10-12-16 Conan Nai Chung Leung, CUHK

    conan_profile

    Title:  Coisotropic A-branes and their SYZ transform

    Abstract: “Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit.”

    10-19-16Vaughan Jones, UC Berkeley

    vj6

    Title: Are the Thompson groups any good as a model for Diff(S^1)?

    Abstract. The Thompson groups are by definition groups of piecewise linear
    diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can
    be conjugated to a group of smooth diffeomorphisms. That’s the good news.
    The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any
    procedure analogous to the constructions of the central extension of Diff(S^1)?
    I will define all the players in this game, explain this question in detail,and present some failed attempts to answer it.

     10-26-16

    Henry Cohn, Microsoft

    ????????????????????????????????????

    Sums of squares, correlation functions, and exceptional geometric structures

    Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding.  How can we understand and prove their optimality?  In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems.

    11-02-16

    Christian Borgs, Microsoft

    Borgs

    Title:  Graphon processes and limits of   sparse graph sequences

    Abstract:  The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for so-called exchangeable random graphs.   Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection.  While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model.  

    In this talk I describe a new model, where the underlying probability space is replaced by a sigma-finite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits.  The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life.

    11-09-16

    TIME CHANGE: 4PM

    Norden E. HuangNational Central University, (Taiwan)

    member1_clip_image003

    Title: On Holo-Hilbert Spectral Analysis

    Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation.

    11-16-16Tristan Collins, Harvard University

    image

    TIME CHANGE: 3:30PM

    Title: Restricted volumes and finite time singularities of the Kahler-Ricci flow

    Abstract:  I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow.  This is joint work with Valentino Tosatti.

    11-22-16 TUESDAY

    TIME CHANGE: 4-5PM

    Xiangfeng Gu, Stonybrook

    Title: Differential Geometric Methods for Engineering Applications

    Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation.

    11-30-16

    TIME CHANGE: 4:20PM

    Sharad Ramanathan, Harvard MCB & SEAS

    Ramanathan.Sharad_200x300

    Title: Finding co-ordinate systems to monitor the development of mammalian embryos
     12-07-16

    Valentino Tosatti, Northwestern

    Title: Metric limits of hyperkahler manifolds

    Abstract: I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang.

     12-14-16

    2015-2016

    DateNameTitle
    09-02-2015Madhu SudanRobust low-degree testing
    09-09-2015Mithat Unsal
    What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
    09-16-2015Subir SachdevBekenstein-Hawking entropy and strange metals
    09-23-2015Felix FinsterLinear hyperbolic equations in a rotating black hole geometry
    09-30-2015Leslie ValiantHolographic Algorithms
    10-07-2015Christopher RoganExploring the Frontier of Size and Energy with the Large Hadron Collider: sub-atomic particles, the Higgs Boson and beyond
    10-14-2015Boaz Barak, Harvard SEASConvexity, Bayesianism, and the quest towards Optimal Algorithms
    10-21-2015Zhouping XinEntropy and Uniqueness of Weak Solutions to The Multi-Dimensional Compressible Euler Systems
    10-28-2015Cristopher MooreStatistical inference, statistical physics, and the community detection problem
    11-04-2015Tom HouBlowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations
    11-11-2015Stan Osher, UCLAOvercoming the curse of dimensionality for certain Hamilton-Jacobi (HJ) equations arising in control theory and elsewhere
    11-18-2015Xiaole Shirley LiuInference of transcriptional regulation in cancers
    11-25-2015ThanksgivingNo seminar
    12-02-2015Scott KominersGeneralized Matching Market Design: Theory and Practice
    12-09-2015Matthew HolmanDynamical Chaos in Kepler Planetary Systems
    01-27-2016Conan LeungSome modern aspects of Morse theory 
    02-03-2016Camillo De LellisFrom Nash to Onsager, funny coincidences across differential geometry and the theory of turbulence
    02-10-2016Chun Peng Wang
    02-17-2016Samuel Kou, Harvard StatisticsBig data, Google and disease detection: the statistical story
    02-24-2016Dan Xie, Harvard CMSASingularity theory and supersymmetric field theory
    03-02-2016Lydia BieriMathematical General Relativity
    03-09-2016Piotr ChruscielThe mathematics of gravitation
    03-16-2016Spring BreakNo Talk
    03-23-2016Richard Freeman, Harvard EconomicsPulling Apart of Wages and Productivity: why “identical” workers have increasingly different pay and productivity.
    03-30-2016David Garfinkel, Oakland UniversityGravitational Wave Memory
    04-04-2016 (Hall A, Science Center)Xianfeng David Gu, Stony Brook UniversityA Discrete Variational Approach for Solving Monge-Ampere Equation
    04-06-2016Lars Hernquist, HarvardNext Generation Cosmological Simulations: Galaxy Assembly and Evolution
    04-13-2016Jun Zhang, Univ. of Michigan-Ann ArborKahler and Para-Kahler Structure in Information Geometry
    04-20-2016Sijue Wu, Univ. of MichiganOn two dimensional gravity water waves with angled crests
    04-27-2016Paul Seidel, MITTopological quantum field theory and the Gauss-Manin connection
    05-04-2016Hirosi Ooguri, CaltechString Theory And Its Applications in Mathematics and Physics
    05-11-2016      (4pm – 5pm)Juerg Froehlich, ETH and IASImplications of the Chiral Anomaly – From the Quantum Hall Effect to Topological Insulators and Out to Space
  • Colloquium
    11:05 am-11:06 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:07 am-11:08 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:08 am-11:09 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-22-2016 Random Matrix & Probability Theory Seminar

    11:12 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-07-2016 Random Matrix & Probability Theory Seminar

    11:16 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12-05-16 Mathematical Physics Seminar

    11:17 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:21 am-11:22 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    11:21 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-14-2016 Random Matrix & Probability Theory Seminar

    11:22 am
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    11:24 am
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    11:25 am
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Learning from health data in the million genome era
    11:26 am
    11/01/2019

    On November 12019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system.

    Speakers: 

    • Heidi Rehm, Ph.D.
      Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform.
    • Saiju Pyarajan, Ph.D.
      Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS
    • Tianxi Cai, Sci.D
      John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health
    • Susan Redline, M.D., M.P.H
      Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center
    • Avinash Sahu, Ph.D.
      Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health
    • Peter J. Park, Ph.D.
      Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School
    • David Roberson
      Community Engagement Manager, Seven Bridges

    Registration & Schedule

  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 Quantum Field Theory Seminar

    11:30 am-12:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    01-30-2017 Mathematical Physics Seminar

    11:30 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    11:32 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    02-06-2017 Mathematical Physics Seminar

    11:33 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    02-13-2017, Mathematical Physics Seminar

    11:34 am
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    11:35 am
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Spacetime and Quantum Mechanics Master Class Workshop
    11:36 am
    11/01/2019-10/30/2019
    Space-Time-poster-5

    As part of the program on Spacetime and Quantum Mechanics, Total Positivity and Motives, the CMSA will host a “Master Class Workshop”  on October 28-30, 2019. Each day of the workshop will feature an intensive full day of pedagogical lectures, with the aim of bringing actively interested but non-expert physicists and mathematicians up to speed on the featured topics.

    Everyone is welcome to attend the lectures.

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

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

    Photos of the event

    Organizers:

  • Member Seminar
    11:37 am
    11/01/2019

    Hansol Hong, Harvard

    Title: Homological Mirror Functors

    Abstract: I will first give a brief introduction to mirror symmetry, which intertwines symplectic geometry and complex geometry of a pair of Kahler manifolds, and explain mirror construction using formal deformation of a Lagrangian submanifold.  We will see that counting of holomorphic discs bounding Lagrangian naturally gives rise to a mirror space (Landau-Ginzburg model) and  a functor from Fukaya category to its mirror matrix factorization category. I will mainly focus on one specific example to give a concrete description of the construction.

  • Colloquium
    11:39 am-11:40 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:40 am-11:41 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    11:42 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:43 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:45 am
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/24/2019 Quantum Matter Seminar

    11:50 am-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/31/2019 Condensed Matter Seminar

    11:50 am-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/10/2019 Condensed Matter Seminar

    11:50 am-1:00 pm
    11/01/2019
  • CMSA EVENT: Quantum Information Workshop
    11:52 am-11:53 am
    11/01/2019
    Asset-6-600x338

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

    The CMSA will host a workshop on Quantum Information. This workshop will be held virtually using Zoom.

    The workshop on Quantum information is organized by Mikhail LukinHorng-Tzer Yau, and Norman Yao.

    More information to follow.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-12-2017 Random Matrix & Probability Theory Seminar

    11:56 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:56 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:58 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-22-2017 Random Matrix & Probability Theory Seminar

    11:58 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    11:59 am
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    5/6/2019 Math Physics

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars
    12:00 pm-1:30 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/19/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12/3/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/8/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/29/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/26/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/25/2019 Fluid Dynamics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 Condensed Matter Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/5/2018 Math Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/7/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/22/2019 Math Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/29/2018 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/15/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/9/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    1/28/2018 Mathematical Physics Seminar

    12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2/4/2019 Math Physics Seminar

    12:00 pm-2:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/25/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • General Relativity Seminar
    12:00 pm-1:00 pm
    11/01/2019

    The Seminar on General Relativity will take place every Wednesday from 12pm – 1pm in CMSA Building, 20 Garden Street, G10.

    The list of speakers is below and will be updated as details are confirmed.

    DateNameTitle
    04-06-2016Mihalis Dafermos (Princeton)The black hole stability problem: the inside story
    04-13-2016Felix Finster, University of RegensburgLinear stability of Kerr black holes
    04-20-2016Paul Chesler, Harvard PhysicsNumerical relativity in asymptotically anti-de Sitter spacetime
    04-27-2016Andy Strominger (Harvard Physics) & Mihalis Dafermos (Princeton University)The Scattering Problem in General Relativity
    05-04-2016Robert Penna, MITBMS invariance and the membrane paradigm
    05-11-2016Piotr T. Chruściel, University of ViennaGluing things in general relativity
    05-18-2016Achilleas Porfyriadis, Harvard PhysicsGravitational waves from the Kerr/CFT correspondence
    05-25-2016Scott Hughes, MITThe gravitational-wave event GW150914: What we learned, and how we learned it
  • Seminars

    Seminars Colloquia & Seminar
    3/4/2019 Mathematical Physics Seminar

    12:00 pm-2:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    1-5-2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Quantum Matter Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/28/2019 Math Physics

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/16/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-2-2018 Mathematical Physics Seminar

    12:00 pm-1:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2/25/2019 Math Physics Seminar

    12:00 pm-2:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/1/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2/11/2019 Mathematical Physics Seminar

    12:00 pm-2:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3/19/2018 Mathematical Physics Seminar

    12:00 pm-1:30 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-26-2018 Math Physics Seminar

    12:00 pm-1:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Condensed Matter Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/30/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-22-2017 Random Matrix & Probability Theory Seminar

    12:01 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:03 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Cosmic Road to New Physics
    12:04 pm
    11/01/2019
    The colourful star cluster NGC 3532

    The CMSA will host a 3-day workshop on cosmological signatures of fundamental physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

    The next decade will see a wealth of new cosmological data, which can lead to new insights for fundamental physics. This upcoming data will span the entire history of the cosmos, from the era prior to big-bang nucleosynthesis to the inner Galactic structure today, including the intervening eras of recombination and cosmic dawn. Often, beyond-standard-model (BSM) physics will leave imprints in more than one of these eras. Thus, it is timely to gather experts in BSM physics across the entire cosmic history to exchange ideas and develop joint and powerful probes of new physics. For this program, it will be crucial to have an overlap of particle physicists, astrophysicists and cosmologists. There are a number of tools and techniques being actively developed across these disciplines. The workshop aims to provide a platform for efficient exchange of these new ideas.

    The first day we will discuss sub-Galactic probes, including Gaia data and gravitational waves. The second day we will cover cosmological probes, such as the cosmic microwave background and the 21-cm line. The third day we will discuss early Universe probes, such as inflation and phase transitions. Every day the meeting will begin with a pedagogical blackboard talk plus an overview talk, followed by about 4 talks on more specific topics.

    Organizers:

    Scientific Advisory:

    Speakers: 

    CosmicRoad_Poster

  • Colloquium
    12:05 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:06 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:08 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:09 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar
    12:10 pm-1:10 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

     

    Speaker: Man-Wai Cheung

    Title: Compactification for cluster varieties without frozen variables of finite type

    Abstract: Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev–Borisov construction.

  • CMSA EVENT: 2019 Ding Shum Lecture
    12:11 pm
    11/01/2019
    DingShum-2019

    DSC_0468-e1568985499370

    On October 22, 2019, the CMSA will be hosting our third annual Ding Shum lecture. This year’s lecture will be a talk on “Election Security” by Ronald L. Rivest (MIT). The lecture will take place from 4:30-5:30pm in Science Center, Hall A.

    Ronald L. Rivest is an Institute Professor at the Massachusetts Institute of Technology. He is a member of the Electrical Engineering and Computer Science Department and the Computer Science and Artificial Intelligence Laboratory (CSAIL) and a founder of the Cryptography and Information Security research group within CSAIL. His research has been in the areas of algorithms, machine learning, cryptography, and election security, for which he has received multiple awards, including: the ACM Turing Award (with Adleman and Shamir), the BBVA Frontiers of Knowledge Award, National Inventor’s Hall of Fame membership, and the Marconi Prize.

    Prof. Rivest is also well-known as a co-author of the textbook “Introduction to Algorithms” (with Cormen, Leiserson, and Stein), and as a co-inventor of the RSA public-key cryptosystem (with Adleman and Shamir). He is a co-founder of RSA and of Verisign.He has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), in charge of the Security subcommittee. He is a member of the CalTech/MIT Voting Technology Project, on the Board of Verified Voting, and an advisor to the Electronic Privacy Information Center. Additionally, he has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), as a member of the CalTech/MIT Voting Technology Project, and as an advisor to the Electronic Privacy Information Center.

    Last year featured Eric Maskin, who spoke on “How to Improve Presidential Elections: the Mathematics of Voting.” The first Ding Shum lecture took place on October 10, 2017, featuring Leslie Valiant on “Learning as a Theory of Everything.”

    This event is made possible by the generous funding of Ding Lei and Harry Shum.

    DingShum-2019

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-1-2017 Random Matrix & Probability Seminar

    12:11 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Special Lecture Series on Donaldson-Thomas and Gromov-Witten Theories
    12:11 pm
    11/01/2019-04/19/2017

    From March 8 to April 19, the Center of Mathematical Sciences and Applications will be hosting a special lecture series on Donaldson-Thomas and Gromov-Witten Theories. Artan Sheshmani (QGM Aarhus and CMSA Harvard) will give eight talks on the topic on Wednesdays and Fridays from 9:00-10:30 am, which will be recorded and promptly available on CMSA’s Youtube Channel.

  • Colloquium
    12:12 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:13 pm-12:14 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2-27-2017 Mathematical Physics Seminar

    12:14 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-7-2017 Social Science Applications Forum

    12:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/13/2019 Special Seminar

    12:15 pm-1:05 pm
    11/01/2019
  • Colloquium
    12:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-8-2017 CMSA Special Lecture Series

    12:16 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Noncommutative Analysis, Computational Complexity, and Quantum Information
    12:19 pm
    11/01/2019-10/18/2019
    Noncommutative-Analysis-Poster-3

    On October 16-18, 2019 the CMSA will be hosting a workshop on Noncommutative Analysis, Computational Complexity, and Quantum Information.

    This workshop will focus on  linking three different rapidly developing areas: noncommutative real algebraic geometry (RAG), theory of computation and quantum information theory. This mix of overlapping but independently developing topics should lead to a stimulating flow of tools and important problems into several disciplines.  Given the different communities there will be an emphasis on tutorials and making the lectures broadly understandable.

    The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by Boaz Barak, Bill Helton, Pablo Parrilo, Tselil Schramm.

    Please register here

    Speakers:

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

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-8-2017 Random Matrix & Probability Theory Seminar

    12:21 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-6-2017 Mathematical Physics Seminar

    12:24 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    12:25 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-10-2017 Special Lecture Series

    12:27 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
    12:28 pm
    11/01/2019-05/05/2019
    1 Oxford Street, Cambridge MA 02138
    Differential Geometry, Calabi-Yau theory and General Relativity

    Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau

    On May 2-5, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the  Science Center, Lecture Hall C. 

    Organizers:

    • Horng-Tzer Yau (Harvard)
    • Wilfried Schmid (Harvard)
    • Clifford Taubes (Harvard)
    • Cumrun Vafa (Harvard)

    Speakers:

    • Lydia Bieri, University of Michigan
    • Tristan Collins, MIT
    • Simon Donaldson, Imperial College
    • Fan Chung Graham, UC San Diego
    • Nigel Hitchin, Oxford University
    • Jun Li, Stanford University
    • Kefeng Liu, UCLA
    • Chiu-Chu Melissa Liu, Columbia University
    • Alina Marian, Northeastern University
    • Xenia de la Ossa, Oxford University
    • Duong H. Phong, Columbia University
    • Richard Schoen, UC Irvine
    • Andrew Strominger, Harvard University
    • Nike Sun, MIT
    • Clifford Taubes, Harvard University
    • Chuu-Lian Terng, UC Irvine
    • Valentino Tosatti, Northwestern University
    • Karen Uhlenbeck, University of Texas
    • Cumrun Vafa, Harvard University
    • Mu Tao Wang, Columbia University
    • Edward Witten, IAS
    • Stephen Yau, Tsinghua University, P.R. China
  • Seminars

    Seminars Colloquia & Seminar
    3-21-2017 Social Science Applications Forum

    12:28 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:30 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-20-2017 Mathematical Physics Seminar

    12:30 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-5-2017 Random Matrix & Probability Theory Seminar

    12:31 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:32 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Conference on Algebraic Geometry, Representation theory and Mathematical Physics
    12:33 pm
    11/01/2019-05/01/2019

    From April 29 to May 1, 2019 the CMSA will be hosting a Conference on Algebraic Geometry, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.  

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

    List of registrants

    Videos

    Speakers: 

     

    Monday, April 29

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amWei Zhang, MITTitle: The arithmetic fundamental lemma for diagonal cycles

    Abstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization, the arithmetic Gan-Gross-Prasad conjecture, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions.  The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.

    10:00 – 10:30amBreak
    10:30 – 11:30amYuri Tschinkel, NYUTitle: Equivariant birational geometry and modular symbols

    Abstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).

    11:30 – 1:30pmLunch
    1:30 – 2:30pmAlexander Efimov, MoscowTitle: Torsionness for regulators of canonical extensions

    Abstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.

    2:30 – 3:00pmBreak
    3:00 – 4:00pmAmin Gholampour, MarylandTitle: Euler Characteristics of punctual quot schemes on threefolds

    Abstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F, n) and Quot(G,n), where Quot(-,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.

    4:00 – 4:30pmBreak
    4:30 – 5:30pmMaksym Fedorchuck, BCTitle:  Stability of one-parameter families of weighted hypersurfaces

    Abstract:  We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space.  The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions, and, if time permits, examples where this machinery can be used to produce birational models with good properties.  Joint work with Hamid Ahmadinezhad and Igor Krylov.

     

    Tuesday, April 30

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amBrendan Hassett, BrownTitle: Rationality for geometrically rational threefolds

    Abstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure, like smooth complete intersections of two quadrics.  (joint with Tschinkel)

    10:00 – 10:30amBreak
    10:30 – 11:30amDennis Gaitsgory, HarvardTitle: The Fundamental Local Equivalence in quantum geometric Langlands

    Abstract: The Fundamental Local Equivalence is statement that relates the q-twisted  Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its  dual is combinatorial, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra, which in itself is a geometric device that concisely encodes the root data.

    11:30 – 1:00pmLunch
    1:00- 2:00pmAndrei Negut, MITTitle: AGT relations in geometric representation theory

    Abstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces, and the goal is to connect them with the W-algebra of type gl_n.

    2:00 – 2:15pmBreak
    2:15 – 3:15pmDan Abramovich, BrownTitle: Resolution in characteristic 0 using weighted blowing up

    Abstract: Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved.

    Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop.

    We show that there is a functorial way to resolve varieties using \emph{weighted} blowings up, in the stack-theoretic sense. To an embedded variety $X \subset Y$ one functorially assigns an invariant $(a_1,\ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , \ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.

    This is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.

    3:15 – 3:30pmBreak
    3:30 – 4:30pmFedor Bogomolov, NYUTitle: On the base of a Lagrangian fibration for a compact hyperkahler manifold.

    Abstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of  Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.

    4:30 – 4:45pmBreak
    4:45 – 5:45pmDawei Chen, BCTitle: Volumes and intersection theory on moduli spaces of Abelian differentials

    Abstract: Computing volumes of moduli spaces has significance in many fields. For instance, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

     

    Wednesday, May 1

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amPavel Etingof, MITTitle: Short star-products for filtered quantizations

    Abstract: PDF

    This is joint work with Eric Rains and Douglas Stryker.

    10:00 – 10:30amBreak
    10:30 – 11:30amRoman Bezrukavnikov, MITTitle: Stability conditions and representation theory

    Abstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)
    and its relation to modular Lie algebra representations. I will also address a potential generalization of that picture
    to modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.

    11:30 – 11:45amBreak
    11:45 – 12:45pmQile Chen, BCTitle: Counting curves in critical locus via logarithmic compactification

    Abstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles, the non-compactness of the R-maps moduli makes such powerful torus action useless.

    In this talk, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action.

    This is a joint work with Felix Janda and Yongbin Ruan.

    12:45 – 2:30pmLunch
    2:30 – 3:30pmSi Li, TsinghuaTitle: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry

    Abstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.

    3:30 – 4:00pmBreak
    4:00 – 5:00pmLudmil Katzarkov, MoscowTitle: PDE’s non commutative  motives and HMS.

    Abstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir.  Geometry will be discussed.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-29-2017 Random Matrix & Probability Theory Seminar

    12:35 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-24-2017 Random Matrix & Probability Theory Seminar

    12:37 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-30-2017 CMSA Special Seminar

    12:38 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    03-27-2017 Mathematical Physics Seminar

    12:40 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:41 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-5-2017 Special Lecture Series

    12:42 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-7-2017 Special Lecture Series

    12:43 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:43 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-12-2017 Special Lecture Series

    12:44 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:45 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-14-2017 Special Lecture Series

    12:46 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-3-2017 Mathematical Physics Seminar

    12:50 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    12:51 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-12-2017 Social Science Applications Forum

    12:53 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Workshop on Mirror Symmetry and Stability
    12:55 pm
    11/01/2019-03/20/2019
    HMS-2019-1

    This three-day workshop will take place at Harvard University on March 18-20, 2019 in Science Center room 507. The main topic will be stability conditions in homological mirror symmetry. This workshop is funded by the Simons Collaboration in Homological Mirror Symmetry.

    Organizers: Denis Auroux, Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau, Bong Lian, Shing-Tung Yau, Jingyu Zhao

    Speakers:

    Dylan Allegretti (Sheffield)
    Tristan Collins (MIT)
    Naoki Koseki (Tokyo)
    Chunyi Li (Warwick)
    Jason Lo (CSU Northridge)
    Emanuele Macrì (NEU & IHES)
    Genki Ouchi (Riken iTHEMS)
    Pranav Pandit (ICTS)
    Laura Pertusi (Edinburgh)
    Jacopo Stoppa (SISSA)
    Alex Takeda (UC Berkeley)
    Xiaolei Zhao (UC Santa Barbara)

    More details will be added later.

    Visit the event page for more information. 

     

    HMS-2019-1

  • Colloquium
    12:55 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:57 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Simons Collaboration Workshop, April 5-7, 2018
    1:00 pm-6:00 pm
    11/01/2019-04/07/2018
    banner-image-1

    The CMSA will be hosting a three-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 5-7, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

    We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

    Confirmed Speakers:

  • Seminars

    Seminars Colloquia & Seminar
    4-11-2017 Social Science Applications Forum

    1:00 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    Combinatorics & Complexity Seminar, Fridays

    1:00 pm-4:00 pm
    11/01/2019

    The seminar on Combinatorics and Complexity will be held every Friday from 1:00-4:00pm in CMSA Building, 20 Garden Street, Room G10.

    The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

    Additional information on CMSA’s Combinatorics and Complexity program can be found here.

     

    DateNameTitle/Abstract
    09-08-17TBA
    09-15-2017TBA
    09-22-17TBA
    09-29-17TBA
    10-06-17 TBA
    10-13-2017TBA
    10-20-2017TBA
    10-27-2017TBA
    11-03-2017TBA
    11-10-2017TBA
    11-17-2017TBA
    11-24-2017TBA
    12-01-2017TBA
    12-08-2017 TBA
  • CMSA EVENT: Second Annual STAR Lab Conference
    1:01 pm-1:02 pm
    11/01/2019

    The second annual STAR Lab conference is running 10/29/-10/30/2015 at the Harvard Business School.  This event is co-sponsored by the Center of Mathematical Sciences and Applications.

    For more information, please consult the event’s website.

  • Colloquium
    1:02 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:07 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-10-2017 Mathematical Physics Seminar

    1:07 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-21-2015 Mathematical Physics Seminar

    1:09 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    1:10 pm-3:00 pm
    11/01/2019
  • Colloquium
    1:10 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    08-31-2015 Mathematical Physics Seminar

    1:10 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:11 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-01-2015 Differential Geometry Seminar

    1:12 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-12-2017 Random Matrix & Probability Theory Seminar

    1:12 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:13 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-01-2015 Evolution Equation Seminar

    1:13 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-14-2015 Mathematical Physics Seminar

    1:14 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-17-2017 Mathematical Physics Seminar

    1:14 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-18-2017 Social Science Applications Forum

    1:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-08-2015 Geometric Analysis Seminar

    1:16 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-06-2015 Geometric Analysis Seminar

    1:17 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:18 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-08-2015 Evolution Equations Seminar

    1:18 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:20 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:21 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    1:21 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-13-2015 Geometric Analysis Seminar

    1:22 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-19-2017 Random Matrix & Probability Theory Seminar

    1:22 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-10-2015 Evolution Equations Seminar

    1:23 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: 2016 Big Data Conference & Workshop
    1:24 pm
    11/01/2019-08/23/2016
    1 Oxford Street, Cambridge MA 02138

    ! LOCATION CHANGE: The conference will be in Science Center Hall C on Tuesday, Aug.23, 2016.

    The Center of Mathematical Sciences and Applications will be hosting a workshop on Big Data from August 12 – 21, 2016 followed by a two-day conference on Big Data from August 22 – 23, 2016.

    Big Data Conference features many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the second conference on Big Data the Center will host as part of our annual events. The 2015 conference was a huge success.

    The conference will be hosted at Harvard Science Center Hall A (Monday, Aug.22) & Hall C (Tuesday, Aug.23): 1 Oxford Street, Cambridge, MA 02138.

    The 2016 Big Data conference is sponsored by the Center of Mathematical Sciences and Applications at Harvard University and the Alfred P. Sloan Foundation.

    Conference Speakers:

    1. Jörn Boehnke, Harvard CMSA
    2. Joan Bruna, UC Berkeley [Video]
    3. Tamara Broderick, MIT [Video]
    4. Justin Chen, MIT [Video]
    5. Yiling Chen, Harvard University [Video]
    6. Amir Farbin, UT Arlington [Video]
    7. Doug Finkbeiner, Harvard University [Video]
    8. Andrew Gelman, Columbia University [Video]
    9. Nina Holden, MIT [Video]
    10. Elchanan Mossel, MIT
    11. Alex Peysakhovich, Facebook
    12. Alexander Rakhlin, University of Pennsylvania [Video]
    13. Neal Wadhwa, MIT [Video]
    14. Jun Yin, University of Wisconsin
    15. Harry Zhou, Yale University [Video]

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

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

    Please click here for registration.

    Conference Schedule:

    August 22 – Day 1
    8:30amBreakfast
    8:55amOpening remarks
    9:00am – 9:50amYiling Chen, “Machine Learning with Strategic Data Sources” [Video]
    9:50am – 10:40amAndrew Gelman, “Taking Bayesian Inference Seriously” [Video]
    10:40am – 11:10amBreak
    11:10am – 12:00pmHarrison Zhou, “A General Framework for Bayes Structured Linear Models” [Video]
    12:00pm – 1:30pmLunch
    1:30pm – 2:20pmDouglas Finkbeiner, “Mapping the Milky Way in 3D with star colors” [Video]
    2:20pm – 3:10pmNina Holden, “Sparse exchangeable graphs and their limits” [Video]
    3:10pm – 3:40pmBreak
    3:40pm – 4:30pmAlex Peysakhovich, “How social science methods inform personalization on Facebook News Feed” [Video]
    4:30pm – 5:20pmAmir Farbin, “Deep Learning in High Energy Physics” [Video]
    August 23 – Day 2
    8:45amBreakfast
    9:00am – 9:50amJoan Bruna Estrach, “Addressing Computational and Statistical Gaps with Deep Networks” [Video]
    9:50am – 10:40amJustin Chen & Neal Wadhwa, “Smaller Than the Eye Can See: Big Engineering from Tiny Motions in Video” [Video]
    10:40am – 11:10amBreak
    11:10am – 12:00pmAlexander Rakhlin, “How to Predict When Estimation is Hard: Algorithms for Learning on Graphs” [Video]
    12:00pm – 1:30pmLunch
    1:30pm – 2:20pmTamara Broderick, “Fast Quantification of Uncertainty and Robustness with Variational Bayes” [Video]
    2:20pm – 3:10pmElchanan Mossel, “Phylogenetic Reconstruction – a Rigorous Model of Deep Learning”
    3:10pm – 3:40pmBreak
    3:40pm – 4:30pmJörn Boehnke, “Amazon’s Price and Sales-rank Data: What can one billion prices on 150 thousand products tell us about the economy?”

    Workshop Participants:

    Richard Freeman’s Group:

    1. Sen Chai, ESSEC
    2. Brock Mendel, Harvard University
    3. Raviv Muriciano-Goroff, Stanford University
    4. Sifan Zhou, CMSA

    Scott Kominer’s Group:

    1. Bradly Stadie, UC Berkeley
    2. Neal Wadhwa, MIT [Video]
    3. Justin Chen

    Christopher Rogan’s Group:

    1. Amir Farbin, UT Arlington [Video]
    2. Paul Jackson, University of Adelaide

    For more information about the workshops, please reach out directly to the individual group leaders.

    This event is sponsored by CMSA Harvard University and the Alfred P. Sloan Foundation.

  • Seminars

    Seminars Colloquia & Seminar
    10-01-2015 Evolution Equations Seminar

    1:25 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-15-2015 Geometric Analysis Seminar

    1:26 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-16-2015 Random Matrix & Probability Theory Seminar

    1:27 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-23-2015 Random Matrix & Probability Theory Seminar

    1:29 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    5-3-2017 Random Matrix & Probability Theory Seminar

    1:29 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    1:30 pm-3:00 pm
    11/01/2019
  • Special Seminar
    1:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    5-2-2017 Social Sciences Application Forum

    1:30 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11/28/2018 Hodge Lecture

    1:30 pm
    11/01/2019
  • Seminars
    1:30 pm-3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    1/23/2019 Hodge Seminar

    1:30 pm-3:00 pm
    11/01/2019
  • Special Seminar
    1:30 pm-2:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    12/5/2018 Hodge Seminar

    1:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    11/14/2018 Hodge Seminar

    1:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    11/21/2018 Hodge Seminar

    1:30 pm
    11/01/2019
  • Colloquium
    1:31 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-28-2015 Mathematical Physics Seminar

    1:31 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-24-2017 Mathematical Physics Seminar

    1:31 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    1:32 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:33 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Concluding Conference of the Special Program on Nonlinear Equations, April 8 – 10, 2016
    1:34 pm
    11/01/2019-04/10/2016

    The Center of Mathematical Sciences and Applications will be hosting a concluding conference on April 8-10, 2016 to accompany the year-long program on nonlinear equations. The conference will have 15 speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

    Speakers:

    1. Lydia Bieri (University of Michigan)
    2. Luis Caffarelli (University of Texas at Austin)
    3. Mihalis Dafermos (Princeton University)
    4. Camillo De Lellis (Universität Zürich)
    5. Pengfei Guan (McGill University)
    6. Slawomir Kolodziej (Jagiellonian University)
    7. Melissa Liu (Columbia University)
    8. Duong H. Phong (Columbia University)
    9. Richard Schoen (UC Irvine)
    10. Cliff Taubes (Harvard University)
    11. Blake Temple (UC Davis)
    12. Valentino Tosatti (Northwestern University)
    13. Tai-Peng Tsai (University of British Columbia)
    14. Mu-Tao Wang (Columbia University)
    15. Xu-jia Wang (Australian National University)

    Please click NLE Conference Schedule with Abstracts for a downloadable schedule with talk abstracts.

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

    Schedule:

    April 8 – Day 1
    8:30amBreakfast
    8:45amOpening remarks
    9:00am – 10:00amCamillo De Lellis, “A Nash Kuiper theorem for $C^{1,1:5}$ isometric immersions of disks
    10:00am – 10:15amBreak
    10:15am – 11:15amXu-Jia Wang, “Monge’s mass transport problem
    11:15am – 11:30amBreak
    11:30am – 12:30pmPeng-Fei Guan, “The Weyl isometric embedding problem in general $3$ d Riemannian manifolds
    12:30pm – 2:00pmLunch
    2:00pm – 3:00pmBlake Temple, “An instability in the Standard Model of Cosmology
    3:00pm – 3:15pmBreak
    3:15pm – 4:15pmLydia Bieri, “The Einstein Equations and Gravitational Radiation
    4:15pm – 4:30pmBreak
    4:30pm – 5:30pmValentino Tosatti, “Adiabatic limits of Ricci flat Kahler metrics
    April 9 – Day 2
    8:45amBreakfast
    9:00am – 10:00amD.H. Phong, “On Strominger systems and Fu-Yau equations”
    10:00am – 10:15amBreak
    10:15am – 11:15amSlawomir Kolodziej, “Stability of weak solutions of the complex Monge-Ampère equation on compact Hermitian manifolds”
    11:15am – 11:30amBreak
    11:30am – 12:30pmLuis Caffarelli, “Non local minimal surfaces and their interactions”
    12:30pm – 2:00pmLunch
    2:00pm – 3:00pmMihalis Dafermos, “The interior of dynamical vacuum black holes and the strong cosmic censorship conjecture in general relativity”
    3:00pm – 3:15pmBreak
    3:15pm – 4:15pmMu-Tao Wang, “The stability of Lagrangian curvature flows”
    4:15pm – 4:30pmBreak
    4:30pm – 5:30pmMelissa Liu, “Counting curves in a quintic threefold”
    April 10 – Day 3
    8:45amBreakfast
    9:00am – 10:00amRick Schoen, “Metrics of fixed area on high genus surfaces with largest first eigenvalue”
    10:00am – 10:15amBreak
    10:15am – 11:15amCliff Taubes, “The zero loci of Z/2 harmonic spinors in dimensions 2, 3 and 4”
    11:15am – 11:30amBreak
    11:30am – 12:30pmTai-Peng Tsai, “Forward Self-Similar and Discretely Self-Similar Solutions of the 3D incompressible Navier-Stokes Equations”

    * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    10-22-2015 Evolution Equations Seminar

    1:37 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/11/2017 Mathematical Physics Seminar

    1:38 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9-18-17 Mathematical Physics Seminar

    1:39 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-17-2015 Evolution Equations Seminar

    1:39 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    9-27-17 RM&PT Seminar

    1:41 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9-27-17 Mathematical Physics Seminar

    1:42 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-23-17 Mathematical Physics Seminar

    1:43 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    9/11/2019 Random Matrix

    1:45 pm-2:45 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-25-17 RMPT Seminars

    1:45 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:47 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-10-2017 RM & PT Seminar

    1:48 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:51 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-22-2015 Geometric Analysis Seminar

    1:52 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:52 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-30-2015 Random Matrix & Probability Theory Seminar

    1:53 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-13-2017 Mathematical Physics Seminar

    1:53 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:54 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-21-2015 Mathematical Physics Seminar

    1:54 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-15-17 RM & PT Seminar

    1:55 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-6-2017 RM & PT Seminar

    1:56 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:58 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    2/22/2019 Social Science Applications Forum

    2:00 pm
    11/01/2019
  • Math Science Lectures in Honor of Raoul Bott

    Math Science Lectures in Honor of Raoul Bott Event
    Math Science Lectures in Honor of Raoul Bott: Freddy Cachazo

    2:00 pm-5:00 pm
    11/01/2019-04/03/2018
    1 Oxford Street, Cambridge MA 02138
    Math Science Lectures in Honor of Raoul Bott

    DSC_0170-e1525711590120

    On April 2-3, the CMSA will be hosting two lectures by Freddy Cachazo (Perimeter Institute) on “Geometry and Combinatorics in Particle Interactions.”  This will be the first of the new annual Bott Math Science Lecture Series hosted by the CMSA.

    The lectures will take place from 4:30-5:30pm in Science Center, Hall D.

     

    Cachazo-e1519325938458

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-20-2017 RM & PT Seminar

    2:00 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02/26/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    Homological Mirror Symmetry Seminar

    2:00 pm-4:00 pm
    11/01/2019-09/15/2017

    The seminar series, Homological Mirror Symmetry, will be held on selected Thursdays from 2PM – 4pm in CMSA Building, 20 Garden Street, Room G10.

    The list of speakers is below and will be updated as details are confirmed.

    DateNameTitle
    09-15-16
    09-22-16Netanel Blaier, Brandeis  “Intro to HMS.”

    Abstract: This is the first talk of the seminar series. We survey the statement of Homological Mirror Symmetry (introduced by Kontsevich in 1994) and some known results, as well as briefly discussing its importance, and the connection to other formulations of Mirror Symmetry and the SYZ conjecture. Following that, we will begin to review the definition of the A-side (namely, the Fukaya category) in some depth. No background is assumed! Also, in the last half hour, we will divide papers and topics among participants.

    Lecture Slides

    09-29-16Netanel Blaier, Brandeisblaier4“Intro to HMS 2.”

    Abstract: In the second talk, we review (some) of the nitty-gritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of J-holomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya’s differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$-structures. We will try to demonstrate all concepts in the Morse theory ‘toy model’.

    Lecture Slides

    10-06-16

    Hansol Hong, CMSAhong

    Title: Homological mirror symmetry for elliptic curves

    Abstract:
    We survey the proof of homological mirror symmetry by Polishchuk and Zaslow. Some of more recent methods to prove HMS for elliptic curves will be discussed also,
    which use homological algebra techniques and formal deformation theory of Lagrangians etc.

    Notes

    Notes (Baris)

    10-13-16

    Yu-Wei Fan, Harvard

    s_yuwei_fan

    Title: Semi-flat mirror symmetry and Fourier-Mukai transform

    Abstract: We will review the semi-flat mirror symmetry setting in Strominger-Yau-Zaslow, and discuss the correspondence between special Lagrangian sections on the A-side and deformed Hermitian-Yang-Mills connections on the B-side using real Fourier-Mukai transform, following Leung-Yau-Zaslow.

     10-20-16

    Tim Large, MIT

    Title: “Symplectic cohomology and wrapped Fukaya categories”

    Abstract: While mirror symmetry was originally conjectured for compact manifolds, the phenomenon applies to non-compact manifolds as well. In the setting of Liouville domains, a class of open symplectic manifolds including affine varieties, cotangent bundles and Stein manifolds, there is an A-infinity category called the wrapped Fukaya category, which is easier to define and often more amenable to computation than the original Fukaya category. In this talk I will construct it, along with symplectic cohomology (its closed-string counterpart), and compute some examples. We will then discuss how compactifying a symplectic manifold corresponds, on the B-side of mirror symmetry, to turning on a Landau-Ginzburg potential.

    Notes

     10-27-16

    Philip Engel, Columbia

    picture

    Title: Mirror symmetry in the complement of an anticanonical divisor”

    According to the SYZ conjecture, the mirror of a Calabi-Yau variety can be constructed by dualizing the fibers of a special Lagrangian fibration. Following Auroux, we consider this rubric for an open Calabi-Yau variety X-D given as the complement of a normal crossings anticanonical divisor D in X. In this talk, we first define the moduli space of special Lagrangian submanfiolds L with a flat U(1) connection in X-D, and note that it locally has the structure of a Calabi-Yau variety. The Fukaya category of such Lagrangians is obstructed, and the degree 0 part of the obstruction on L defines a holomorphic function on the mirror. This “superpotential” depends on counts of holomorphic discs of Maslov index 2 bounded by L. We then restrict to the surface case, where there are codimension 1 “walls” consisting of Lagrangians which bound a disc of Maslov index 0. We examine how the superpotential changes when crossing a wall and discuss how one ought to “quantum correct” the complex structure on the moduli space to undo the discontinuity introduced by these discs.

    Notes

    11-03-16

    Yusuf Baris Kartal, MIT

    HMS for Del Pezzo surfaces

    I will present Auroux-Katzarkov-Orlov’s proof of one side of the homological mirror symmetry for Del Pezzo surfaces. Namely I will prove their derived categories are equivalent to the categories of vanishing cycles for certain LG-models together with B-fields. I plan to show how the general B-field corresponds to non-commutative Del Pezzo surfaces and time allowing may mention HMS for simple degenerations of Del Pezzo surfaces. The tools include exceptional collections( and mutations for degenerate case), explicit description of NC deformations, etc.

    11-10-16No seminar this week
     12-08-16

    Lino Amorim, Boston University

    Title: The Fukaya category of a compact toric manifold

    Abstract: In this talk I will discuss the Fukaya category of a toric manifold following the work of Fukaya-Oh-Ohta-Ono. I will start with an overview of the general structure of the Fukaya category of a compact symplectic manifold. Then I will consider toric manifolds in particular the Fano case and construct its mirror.

    Video

  • CMSA EVENT: Topological Insulators and Mathematical Science – Conference and Program
    2:00 pm-7:00 pm
    11/01/2019-09/17/2014

    The CMSA will be hosting a conference on the subject of topological insulators and mathematical science on September 15-17.  Seminars will take place each day from 2:00-7:00pm in Science Center Hall D, 1 Oxford Street, Cambridge, MA.

  • Seminars
    2:00 pm-4:00 pm
    11/01/2019

    References: 

    • D. Auroux, A beginner’s introduction to Fukaya categories. arXiv:1301.7056
    • I. Smith, A symplectic prolegomenon. arXiv:1401.0269
    • D. Auroux, “Topics in geometry: mirror symmetry”, Fall 2009 (MIT Math 18.969)
    • Nick Sheridan’s IAS and Jussieu lectures. 
    • Sheel Gantara “Topics in symplectic topology”, Spring 2016 (Stanford Math 257B)
  • Seminars

    Seminars Colloquia & Seminar
    1/8/2019 Topology Seminar

    2:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-29-17 RM & PT Seminar

    2:03 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Seminars

    Seminars Colloquia & Seminar
    09-24-2015 Evolution Equations Seminar

    2:03 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-28-2015 Special Random Matrix & Probability Theory Seminar

    2:05 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-18-2015 Random Matrix & Probability Theory Seminar

    2:07 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 RM&PT Seminar

    2:08 pm
    11/01/2019
  • Colloquium
    2:08 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:10 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-29-2017 Mathematical Physics Seminar

    2:11 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Colloquium
    2:11 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-29-2015 Geometric Analysis Seminar

    2:14 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:14 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-28-2015 CMSA Special Seminar

    2:15 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-05-2015 Mathematical Physics Seminar

    2:16 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-6-2017 RM & PT Seminar

    2:16 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-15-2015 Evolution Equations Seminar

    2:17 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12-6-2017 Mathematical Physics Seminar

    2:17 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-07-2015 Random Matrix & Probability Theory Seminar

    2:19 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:20 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-29-2015 Evolution Equations Seminar

    2:20 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-14-2015 Random Matrix & Probability Theory Seminar

    2:21 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    2:21 pm
    11/01/2019-03/06/2018

    During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th, from 1:00 to 3:00pm in room G10, CMSA Building.

    You can watch Prof. Sheshmani describe the series here.

    The Syllabus is as follows:

    Date………..TopicVideo/Audio
    1-25-2018Gromov-Witten invariants 

    Definition, examples via algebraic geometry I

    Video / Audio / Combined 


    *due to technical difficulties the audio and video are split for this lecture.

     2-01-2018Gromov-Witten invariants 

    Virtual Fundamental Class I (definition)

    Video Audio / Combined 


    *due to technical difficulties the audio and video are split for this lecture

    2-13-2018Gromov-Witten invariants 

    Virtual Fundamental Class II (computation in some cases)

     2-15-2018Computing GW invariants 

    Three level GW classes

    Genus zero invariants of the projective plane

     2-20-2018Quantum Cohomology 

    Small Quantum Cohomology (Definition and Properties) I

    2-22-2018Quantum Cohomology 

    Small Quantum Cohomology (Definition and Properties) II

    2-27-2018Quantum Cohomology 

    Big Quantum Cohomology I

     3-1-2018Quantum Cohomology 

    Big Quantum Cohomology II

    GW potential

    WDVV equation

    3-6-2018GW invariants via Quantum Cohomology 

    The Quintic threefold case

    The P^2 case

    GW invariants via Quantum Cohomology 

    Dubrovin (quantum) connection

    Nakajima varieties 

    -Algebraic and symplectic reduction

    Nakajima varieties 

    Quasi maps to Nakajima varieties

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) I

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) II

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) III

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) I

     
    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) II

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) III

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) IV

     
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-21-2015 Random Matrix & Probability Theory Seminar

    2:22 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:23 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:24 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:29 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-28-2015 Random Matrix & Probability Theory Seminar

    2:30 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11/31/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/18/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/3/2019 Colloquium

    2:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Social Science Applications Forum

    2:30 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/19/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/7/2019 Social Science Applications Forum

    2:30 pm-3:00 pm
    11/01/2019
  • Colloquium

    Colloquium Colloquia & Seminar
    4/10/2019 Colloquium

    2:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/12/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    11/01/2019
  • Colloquium

    Colloquium Colloquia & Seminar
    2/27/2019 Colloquium

    2:30 pm-4:00 pm
    11/01/2019
  • General Relativity Seminar
    2:30 pm-3:30 pm
    11/01/2019-04/26/2020
  • Colloquium
    2:30 pm-3:00 pm
    11/01/2019
  • Colloquium
    2:32 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-19-2015 Mathematical Physics Seminar

    2:33 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-20-2015 Geometric Analysis Seminar

    2:35 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-26-2015 Mathematical Physics Seminar

    2:36 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    01-26-2018 Mirror Symmetry Seminar

    2:37 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-02-2015 Mathematical Physics Seminar

    2:37 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-03-2015 Geometric Analysis Seminar

    2:39 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-04-2015 Random Matrix & Probability Theory Seminar

    2:40 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    1-29-2018 Mathematical Physics Seminar

    2:42 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    2:43 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    2:44 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    2-2-2018 Mirror Symmetry Seminar

    2:44 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    2:45 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:47 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    2:48 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-19-2015 Evolution Equations Seminar

    2:50 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-09-2015 CMSA Special Lecture

    2:51 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:54 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-09-2015 Mathematical Physics Seminar

    2:54 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    2:55 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:56 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-19-2015 Random Matrix and Probability Theory Seminar

    2:57 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:59 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-16-2015 Mathematical Physics Seminar

    2:59 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    2-27-2018 HMS Lecture

    3:00 pm-4:00 pm
    11/01/2019-03/01/2018
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12/5/2018 Random Matrix and Probability Theory Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/17/2019 Fluid Dynamics Seminar

    3:00 pm
    11/01/2019
  • CMSA EVENT: 2018 Ding Shum Lecture
    3:00 pm-4:00 pm
    11/01/2019
    ding-shum-2018

     

    Screen-Shot-2018-06-14-at-1.41.25-PM

    On October 24, 2018, the CMSA will be hosting our second annual Ding Shum lecture. This event was made possible by the generous funding of Ding Lei and Harry Shum. Last year featured Leslie Valiant, who spoke on “learning as a Theory of Everything.”

    This year will feature Eric Maskin, who will speak on “How to Improve Presidential Elections: the Mathematics of Voting.” This lecture will take place from 5:00-6:00pm in Science Center, Hall D. 

    Pictures of the event can be found here.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/24/2018 RM & PT Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/7/2018 Random Matrix and Probability Theory Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/14/2018 RM & PT Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/28/2018 Random Matrix and Probability Theory Seminar

    3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    1/31/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Special Seminar
    3:00 pm-4:30 pm
    11/01/2019-05/09/2019

    In the Spring 2019 Semester, the CMSA will be hosting a special lecture series on Derived algebraic/differential geometry run by Artan Sheshmani, with lectures given by Prof. Sheshmani and Dr. Dennis Borisov. The seminar will be held on Tuesdays and Thursdays from 3:00-4:30pm in CMSA, room G10.

    Click here for reference material

    Click here for a syllabus

    Schedule:

    Section 1: Basic setting of derived geometry

    The goal: To collect the minimum set of tools needed to do algebraic geometry in the derived context.

    2/05/2019Lecture 1: Model and с-categoriesVideo
    2/07/2019Lecture 2: Grothendieck topologies and homotopy descentVideo
    2/12/2019Lecture 3: Derived Artin stacksVideo 
    2/14/2019Lecture 4: Cotangent complexes

    Section 2: Loop spaces and differential forms

    The goal: This is the algebraic heart of the course – here we learn the homological techniques that are needed for shifted symplectic forms.

    2/19/2019Lecture 5: De Rham complexes and S1-equivariant schemes (loop spaces)Video
    2/21/2019Lecture 6: Chern characterVideo
    2/26/2019

    Room G02

    Lecture 7: Local structure of closed differential forms in the derived sense Part IVideo
    2/28/2019Lecture 8: Local structure of closed differential forms in the derived sense Part IIVideo
    3/05/2019Lecture 9: Cyclic homologyVideo

    Section 3: Shifted symplectic structures
    Goal: To see applications of the algebraic techniques from above in the geometric context of the actual moduli spaces.

    3/07/2019Lecture 10: Definition and existence resultsVideo
    3/12/2019Lecture 11: Lagrangians and Lagrangian fibrationsVideo
    3/14/2019

    Room G02

    Lecture 12: Lagrangians and Lagrangian fibrationsVideo
    3/26/2019Lecture 13: Intersections of LagrangiansVideo
    3/28/2019

    Room G02

    Lecture 14: Examples and applications 2 (Part I)Video
    4/02/2019Lecture 15: Examples and applications 2 (Part II)Video

    Section 4: Uhlenbeck–Yau construction and correspondence

    4/04/2019Lecture 16: Examples and applications 2 (Part III)Video
    4/09/2019

    Room G02

    Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)Video
  • Seminars

    Seminars Colloquia & Seminar
    2/7/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars
    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2/14/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2/20/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/6/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/8/2019 Special Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/20/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    Algebraic Geometry Seminar, Thursdays

    3:00 pm-4:00 pm
    11/01/2019

    This seminar will not be held in the Spring 2018 Semester.

    The Algebraic Geometry Seminar will be every Thursday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

    The schedule will be updated as details are confirmed.

     

     

    DateNameTitle/Abstract
    09-14-17 Yu-Wei Fan (Harvard Math)

    Entropy of an autoequivalence on Calami-Yau manifolds

    Abstract:  We will recall the notion of entropy of an autoequivalence on triangulated categories, and provide counterexamples of a conjecture by Kikuta-Takahashi.

    11-1-17

    *5:00pm, G10*

     Shamil Shakirov, Harvard Math

    Undulation invariants of plane curves

    Abstract: “One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem, described by Cayley and Salmon in 1852, is to determine whether or not a given plane curve of degree r > 3 has undulation points — the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r – 3)(3 r – 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries, and we conjecture a generalization for r = 5

    11-2-17

     

    Alexander Moll, IHES

    Hilbert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves

    ABSTRACT: By Grojnowski and Nakajima, Fock spaces are cohomology rings of Hilbert scheme of points in the plane.  On the other hand, by Pressley-Segal, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the Kähler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J.  First, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this Kähler structure.  Second, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = – e_1 e_2 that is invariant under e_2 <-> e_1.  As a corollary of Lehn’s theorem, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element.  Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin.  As time permits, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov’s BPS/CFT Correspondence.

    11-9-17  TBD  TBD
    11-16-17 TBD TBD
    11-23-17  TBD  TBD
    11-30-17  TBD  TBD
    12-7-17  TBD  TBD
    12-15-17  TBD  TBD
  • Seminars

    Seminars Colloquia & Seminar
    4/24/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Fluid Dynamics Seminar

    Fluid Dynamics Seminar
    10/9/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/03/2018 RMPT Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    5/22/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    5/15/2019 Fluid Dynamics

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    5/1/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Special Seminar
    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    Dmytro Shklyrov HMS Focused Lecture Series

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/4/2019 Special Seminar

    3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    11-17-2015 Geometric Analysis Seminar

    3:00 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    9/18/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    11-23-2015 Mathematical Physics Seminar

    3:01 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    Random Matrix & Probability Theory Seminar (2016-2017)

    3:01 pm
    11/01/2019-12/14/2017
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    DSC_0025-768x512

    The random matrix and probability theory will be every Wednesday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

  • CMSA EVENT: Working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017
    3:02 pm-3:03 pm
    11/01/2019-01/13/2017

    The Center of Mathematical Sciences and Applications will be hosting a working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Participants:

    Gerard Ben Arous, Courant Institute of Mathematical Sciences

    Alex Bloemendal, Broad Institute

    Arup Chakraburty, MIT

    Zhou Fan, Stanford University

    Alpha Lee, Harvard University

    Matthew R. McKay, Hong Kong University of Science and Technology (HKUST)

    David R. Nelson, Harvard University

    Nick Patterson, Broad Institute

    Marc Potters, Capital Fund management

    Yasser Roudi, IAS

    Tom Trogdon, UC Irvine

    Organizers:

    Michael Brenner, Lucy Colwell, Govind Menon, Horng-Tzer Yau

    Please click Program for a downloadable schedule with talk abstracts.

    Please note that breakfast & lunch will be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants should you need recommendations for dinner.

    Schedule:

    January 9 – Day 1
    9:30am – 10:00amBreakfast & Opening remarks
    10:00am – 11:00amMarc Potters, “Eigenvector overlaps and the estimation of large noisy matrices”
    11:00am – 12:00pmYasser Roudi
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 10 – Day 2
    8:30am – 9:00amBreakfast
    9:00am – 10:00amArup Chakraburty, “The mathematical analyses and biophysical reasons underlying why the prevalence of HIV strains and their relative fitness are simply correlated, and pose the challenge of building a general theory that encompasses other viruses where this is not true.”
    10:00am – 11:00amTom Trogdon, “On the average behavior of numerical algorithms”
    11:00am – 12:00pmDavid R. Nelson, “Non-Hermitian Localization in Neural Networks”
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 11 – Day 3
    8:30am – 9:00amBreakfast
    9:00am – 10:00amNick Patterson
    10:00am – 11:00amLucy Colwell
    11:00am – 12:00pmAlpha Lee
    12:00pm – 2:00pmLunch
    2:00pm-4:00pmAfternoon Discussion
    4:00pmGerard Ben Arous (Public Talk), “Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms
    January 12 – Day 4
    8:30am – 9:00amBreakfast
    9:00am – 10:00amGovind Menon
    10:00am – 11:00amAlex Bloemendal
    11:00am – 12:00pmZhou Fan, “Free probability, random matrices, and statistics”
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 13 – Day 5
    8:30am – 9:00amBreakfast
    9:00am – 12:00pmFree for Working
    12:00pm – 2:00pmLunch
    2:00pmFree for Working

    * This event is sponsored by CMSA Harvard University.

  • Colloquium
    3:03 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-24-2015 Geometric Analysis Seminar

    3:03 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-04-2016 Evolution Equations Seminar

    3:04 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    Hodge and Noether-Lefschetz Loci Seminar

    3:06 pm
    11/01/2019

    In the Fall 2018 Semester the CMSA will be hosting a seminar on Hodge and Noether-Lefschetz loci, with lectures given by Hossein Movasati (IMPA). The seminar will occur weekly on Wednesday at 1:30 in room G10 of the CMSA.

    The schedule below will be updated as talks are confirmed.

    DateTitle/Abstract
    11/7/2018

    Video

    Title: Hodge and Noether-Lefschetz loci

    Abstract: Hodge cycles are topological cycles which are conjecturally (the millennium Hodge conjecture) supported in algebraic cycles of a given smooth projective complex manifold. Their study in families leads to the notion of Hodge locus, which is also known as Noether-Lefschetz locus in the case of surfaces. The main aim of this mini course is to introduce a computational approach to the study of Hodge loci for hypersurfaces and near the Fermat hypersurface. This will ultimately lead to the verification of the variational Hodge conjecture for explicit examples of algebraic cycles inside hypersurfaces and also the verification of integral Hodge conjecture for examples of Fermat hypersurfaces. Both applications highly depend on computer calculations of rank of huge matrices. We also aim to review some classical results on this topic, such as Cattani-Deligne-Kaplan theorem on the algebraicity of the components of the hodge loci, Deligne’s absolute Hodge cycle theorem for abelian varieties etc.

    In the theoretical side another aim is to use the available tools in algebraic geometry and construct the moduli space of projective varieties enhanced with elements in their algebraic de Rham cohomology ring. These kind of moduli spaces have been useful in mathematical physics in order to describe the generating function of higher genus Gromov-Witten invariants, and it turns out that the Hodge loci in such moduli spaces are well-behaved, for instance, they are algebraic leaves of certain holomorphic foliations. Such foliations are constructed from the underlying Gauss-Manin connection. This lectures series involves many reading activities on related topics, and contributions by participants are most welcome.

    11/14/2018

    Video

    Title:  Integral Hodge conjecture for Fermat varieties

    Abstract: We describe an algorithm which verifies whether  linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this  confirms the integral Hodge conjecture for quartic and quintic Fermat fourfolds. Our algorithm is based on computation of the list of elementary divisors of both the lattice of linear algebraic cycles, and the lattice of Hodge cycles written in terms of  vanishing cycles, and observing that these two lists are the same. This is a joint work with E. Aljovin and R. Villaflor.

    11/21/2018

    Video

    Title:  Periods of algebraic cycles

    Abstract: The tangent space of the Hodge locus at a point can be described by the so called infinitesimal variation of Hodge structures and the cohomology class of Hodge cycles. For hypersurfaces of dimension $n$ and degree $d$ it turns out that one can describe it without any knowledge of cohomology theories and in a fashion which E. Picard in 1900’s wanted to study integrals/periods. The data of cohomology class is replaced with periods of Hodge cycles, and explicit computations of these periods, will give us a computer implementable description of the tangent space.  As an application of this we show that for examples of $n$ and $d$, the locus of hypersurfaces containing two linear cycles whose intersection is of low dimension, is a reduced component of the Hodge locus in the underlying parameter space.

    11/28/2018

    Video

    Title: Periods of Complete Intersection Algebraic Cycles

    Speaker: Roberto Villaflor

    Abstract: In order to compute periods of algebraic cycles inside even dimensional smooth degree d hypersurfaces of the projective space, we restrict ourselves to cycles supported in a complete intersection subvariety. When the description of the complete intersection is explicit, we can compute its periods, and furthermore its cohomological class. As an application, we can use this data to describe the Zariski tangent space of the corresponding Hodge locus, as the degree d part of some Artinian Gorenstein ideal of the homogeneous coordinate ring of the projective space. Using this description, we can show that for d>5, the locus of hypersurfaces containing two linear cycles, is a reduced component of the Hodge locus in the underlying parameter space.

    12/05/2018

    Room G02

    Title: Some explicit Hodge cycles

    Abstract: Explicit examples of Hodge cycles are due to D. Mumford and A. Weil in the case of CM abelian varieties. In this talk, I will describe few other examples for the Fermat variety. Effective verification of the Hodge conjecture for these cycles is not known.

    12/12/2018

    Video

    Title: A conjectural Hodge locus for cubic tenfold

    Abstract: In this talk we will consider the difference  of two linear algebraic cycles of dimension 5 inside a smooth cubic tenfold and such that the dimension of their intersection is 3. We will show some computer assisted evidences to the fact that the corresponding Hodge locus is bigger than the expected locus of algebraic deformations of the cubic tenfold together with its linear cycles. A similar discussion will be also presented for cubic six and eightfold,  for which we will prove that the corresponding second and third order infinitesimal Hodge loci are smooth. The main ingredient is a computer implementation of power series of periods of hypersurfaces.

    1/16/2019Title: Algebraic BCOV anomaly equation

    Abstract: We introduce the moduli space T of  non-rigid compact Calabi-Yau threefolds enhanced with differential forms and a Lie algebra of vector fields in T. This will be used in order to give a purely algebraic interpretation of topological string partition functions and the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation (joint work with M. Alim, E. Scheidegger, S.-T. Yau).  We will also define similar moduli spaces for even dimensional Calabi-Yau varieties, where we have the notion of Hodge locus.

    1/23/2019

    Video

    Title: A new model for modular curves

    Abstract: One of the non-trivial examples of a Hodge locus is the modular curve X_0(N), which is due to isogeny of elliptic curves (a Hodge/algebraic cycle in the product of two elliptic curves). After introducing the notion of enhanced moduli of elliptic curves, I will describe a new model for X_0(N) in the weighted projective space of dimension 4 and with weights (2,3,2,3,1). I will also introduce some elements in the defining ideal of such a model.

    The talk is based on the article arXiv:1808.01689.

    1/30/2019

    Video

    Title: Constant Yukawa couplings

    Abstract: In this talk I will first introduce algebraic Yukawa couplings for any moduli of enhanced Calabi-Yau n-folds. Then I will list many examples in support of the following conjecture. A moduli of Calabi-Yau n-folds is a quotient of a Hermitian symmetric domain (constructed from periods) by an arithmetic group if and only if the corresponding Yukawa couplings are constants.

    2/6/2019

    Video

    Title: Integrality properties of CY modular forms

    Abstract: The integrality of the coefficients of the mirror map is a central problem in the arithmetic of Calabi-Yau varieties and it has been investigated  by Lian-Yau (1996, 1998), Hosono-Lian-Yau (1996), Zudilin (2002), Kontsevich-Schwarz-Vologodsky (2006) Krattenthaler-Rivoal (2010). The central tool in most of these works has been the so called Dwork method.  In this talk we use this method and classify all hypergeometric differential equations with a maximal unipotent monodromy whose mirror map has integral coefficients.

    We also  give a computable condition on the parameters of a hypergeometric function which conjecturally computes all the primes which appear in the denominators of the coefficients of the mirror map. This is a joint work with Kh. Shokri.

    2/13/2019Title: Foliations and Hodge loci

    Abstract: In this talk I will introduce a holomorphic foliation in a larger parameter space attached to families of enhanced projective varieties. Irreducible components of the Hodge locus with constant periods are algebraic leaves of such a foliation. Under the hypothesis that these are all the algebraic leaves,  we get the fact that such algebraic leaves are defined over the algebraic closure of the base field and that Hodge classes are weak absolute in the sense of C. Voisin.

     

    References:

  • Seminars

    Seminars Colloquia & Seminar
    02-02-2016 Geometric Analysis Seminar

    3:06 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    3:06 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Data Analysis Workshop, April 4 – 8, 2016
    3:09 pm-3:10 pm
    11/01/2019-04/08/2016

    The Center of Mathematical Sciences and Applications will be hosting a 5-day workshop on Data Analysis and related areas on April 4 – 8, 2016.

    Workshop Locations:

    April 4 – 7 (Monday ~ Thursday)

    Room G10,
    20 Garden Street, Cambridge, MA 02138 

    April 8 (Friday)

    EPS Faculty Lounge, Room 409, 4th floor, Hoffman Lab
    20 Oxford Street, Cambridge, MA 02138

     Participants:

    • Peter Hubyers (Harvard University)
    • Eli Tziperman (Harvard University)
    • Andrew Rhines (University of Washington)
    • Karen McKinnon (UCAR)
    • Douglas MacMartin (Caltech)
    • Thomas Laepple (Alfred Wegener Institute)
    • Yossi Ashkenazy (Ben-Gurion University)
    • Marlene Kretschamer (Potsdam Institute for Climate Impact Research)
    • Natesh Pillai (Harvard University)
    • Judah Cohen (Atmospheric and Environmental Research)
    • Cristian Proistosescu (Harvard University)

    Please click Workshop Agenda for a downloadable agenda.

    * This event is sponsored by CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    02-11-2016 Evolution Equations Seminar

    3:09 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    3:09 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2-16-2018 RM & PT Seminar

    3:09 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Colloquium
    3:11 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-03-2016 Random Matrix & Probability Theory Seminar

    3:11 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    3:13 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 RMPT Seminar

    3:15 pm-4:15 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/9/2019 RM & PT Seminar

    3:15 pm-4:15 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/30/2019 Random Matrix and Probability Theory Seminar

    3:15 pm-4:15 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/16/2019 RM & PT Seminar

    3:15 pm
    11/01/2019
  • Colloquium
    3:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-16-2016 Geometric Analysis Seminar

    3:16 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-15-2016 Mathematical Physics Seminar

    3:17 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-18-2016 Evolution Equations Seminar

    3:19 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-22-2016 Mathematical Physics Seminar

    3:20 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-23-2016 Geometric Analysis Seminar

    3:22 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-24-2016 Random Matrix & Probability Theory

    3:23 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Mini-workshop on SYZ and Homological Mirror Symmetry
    3:23 pm
    11/01/2019-12/02/2016

    The Center of Mathematical Sciences and Applications will be hosting a 4-day workshop on SYZ and Homological Mirror Symmetry and related areas on November 28 – December 2, 2016 at Harvard CMSA Building: Room G10, 20 Garden Street, Cambridge, MA 02138.

    Organizers:

    Bong Lian (Brandeis University), Siu-Cheong Lau (Boston University), Shing-Tung Yau (Harvard University)

    Speakers:

    1. Conan Leung, Chinese University of Hong Kong
    2. Junwu Tu, University of Missouri
    3. Jingyu Zhao, Columbia University
    4. David Treumann, Boston College
    5. Hiro Lee Tanaka, Harvard University
    6. Fabian Haiden, Harvard University
    7. Hansol Hong, Harvard CMSA/Brandeis University
    8. Netanel Blaier, Harvard CMSA/Brandeis University
    9. Garret Alston, The University of Oklahoma

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

    Conference Schedule:

    Monday, November 28 – Day 1
    10:30am –11:30amHiro Lee Tanaka“Floer theory through spectra”
    Lunch
    1:00pm – 2:30pmFabian Haiden“Categorical Kahler Geometry”
     2:30pm-2:45pm Break
    2:45pm – 4:15pmFabian Haiden“Categorical Kahler Geometry”
    4:30pm – 5:15pmGarret Alston“Potential Functions of Non-exact fillings”
    Tuesday, November 29 – Day 2
    10:30am –11:30amConan Leung, “Remarks on SYZ”
    Lunch
    1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
     2:30pm-2:45pm Break
    2:45pm – 4:15pmHiro Lee Tanaka“Floer theory through spectra”
    4:30pm – 5:15pmHansol Hong, “Mirror Symmetry for punctured Riemann surfaces and gluing construction”
    Wednesday, November 30 – Day 3
    10:30am –11:30amJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
    Lunch
    1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
     2:30-2:45pm Break
    2:45pm – 4:15pmDavid Treumann, “Invariants of Lagrangians via microlocal sheaf theory”
    Thursday, December 1 – Day 4
    10:30am –11:30amDavid Treumann“Some examples in three dimensions”
    Lunch
    1:00pm – 2:30pmJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
     2:30-2:45pm Break
    2:45pm – 3:30pmNetanel Blaier, “The quantum Johnson homomorphism, and the symplectic mapping class group of 3-folds”

    * This event is sponsored by the Simons Foundation and CMSA Harvard University.

  • Colloquium
    3:25 pm
    11/01/2019

    During the Spring 2021 semester, and until further notice, all seminars will take place virtually.

    The 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually, using zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed.

    To learn how to attend, please fill out this form.

    Information on previous colloquia can be found here.

    Spring 2021:

    DateSpeakerTitle/Abstract
    1/27/2021Evelyn Tang (Max Planck Institute for Dynamics and Self-Organization)

    Slides

    Video

    Title: Topology protects chiral edge currents in stochastic systems

    Abstract: Living systems can exhibit time-scales much longer than those of the underlying components, as well as collective dynamical behavior. How such global behavior is subserved by stochastic constituents remains unclear. I will present two-dimensional stochastic networks that consist of out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. I will discuss the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, stochastic growth and shrinkage, and synchronization.

    2/3/2021André Luiz de Gouvêa (Northwestern)

    Video

    Title: The Brave Nu World

    Abstract: Neutrinos are the least understood of the fundamental particles that make up the so-called Standard Model of Particle Physics. Measuring neutrino properties and identifying how they inform our understanding of nature at the smallest distant scales is among the highest priorities of particle physics research today. I will discuss our current understanding of neutrinos, concentrating on the observation of neutrino oscillations and neutrino masses, along with all the open questions that came of these discoveries from the end of the 20th century.

    2/10/2021Mykhaylo Shkolnikov (Princeton)

    Video

    Title: Probabilistic approach to free boundary problems and applications

    Abstract: We will discuss a recently developed probabilistic approach to (singular) free boundary problems, such as the supercooled Stefan problem. The approach is based on a new notion of solution, referred to as probabilistic, which arises naturally in the context of large system limits of interacting particle systems. In the talk, I will give an example of how such interacting particle systems arise in applications (e.g., finance), then obtain a solution of a free boundary problem in the large system limit, and discuss how this solution can be analyzed mathematically (thereby answering natural questions about the systemic risk in financial systems and neural synchronization in the brain). The talk is based on recent and ongoing joint works with Sergey Nadtochiy, Francois Delarue, Jiacheng Zhang and Xiling Zhang

    2/17/2021
    9:00 – 10:00PM ET
    C. Seshadhri (UC Santa Cruz)

    Video

    Title: Studying the (in)effectiveness of low dimensional graph embeddings

    Abstract: Low dimensional graph embeddings are a fundamental and popular tool used for machine learning on graphs. Given a graph, the basic idea is to produce a low-dimensional vector for each vertex, such that “similarity” in geometric space corresponds to “proximity” in the graph. These vectors can then be used as features in a plethora of machine learning tasks, such as link prediction, community labeling, recommendations, etc. Despite many results emerging in this area over the past few years, there is less study on the core premise of these embeddings. Can such low-dimensional embeddings effectively capture the structure of real-world (such as social) networks? Contrary to common wisdom, we mathematically prove and empirically demonstrate that popular low-dimensional graph embeddings do not capture salient properties of real-world networks. We mathematically prove that common low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, which have been widely established to be empirically true for real-world networks. Empirically, we observe that the embeddings generated by popular methods fail to recreate the triangle structure of real-world networks, and do not perform well on certain community labeling tasks. (Joint work with Ashish Goel, Caleb Levy, Aneesh Sharma, and Andrew Stolman.)

    2/24/2021David Ben-Zvi (U Texas)

    Video

    Title: Electric-Magnetic Duality for Periods and L-functions

    Abstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory.
    A fundamental aspect of the Langlands correspondence — the relative Langlands program — studies the representation of L-functions of Galois representations as integrals of automorphic forms. However, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don’t seem to line up.
    We present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely, we rewrite the relative Langlands program as duality in the presence of supersymmetric boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.

    3/3/2021

    9:00pm ET

    Omer Tamuz (Caltech)Title: Monotone Additive Statistics

    Abstract: How should a random quantity be summarized by a single number? We study mappings from random variables to real numbers, focussing on those with the following two properties: (1) monotonicity with respect to first-order stochastic dominance, and (2) additivity for sums of independent random variables. This problem turns out to be connected to the following question: Under what conditions on the random variables X and Y does there exist an independent Z so that X + Z first-order stochastically dominates Y + Z?

    (Joint work with Tobias Fritz, Xiaosheng Mu, Luciano Pomatto and Philipp Strack.)

    3/10/2021

    9:00pm ET

    Piotr Indyk (MIT)Title: Learning-Based Sampling and Streaming

    Abstract: Classical algorithms typically provide “one size fits all” performance, and do not leverage properties or patterns in their inputs. A recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. In this talk I will present two examples of this type, in the context of streaming and sampling algorithms. In particular, I will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (ICLR’19), and (b) sampling algorithms for estimating the support size of a distribution (ICLR’21). Both algorithms use an ML-based predictor that, given a data item, estimates the number of times the item occurs in the input data set. (The talk will cover material from papers co-authored with T Eden, CY Hsu, D Katabi, S Narayanan, R Rubinfeld, S Silwal, T Wagner and A Vakilian.

    3/17/2021
    9:00pm ET
    Chiu-Chu Melissa Liu (Columbia)Title: Topological Recursion and Crepant Transformation Conjecture

    Abstract: The Crepant Transformation Conjecture (CTC), first proposed by Yongbin Ruan and later refined/generalized by others, relates Gromov-Witten (GW) invariants of K-equivalent smooth varieties or smooth Deligne-Mumford stacks. We will outline a proof of all-genus open and closed CTC for symplectic toric Calabi-Yau 3-orbifolds based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong. Our proof relies on the Remodeling Conjecture (proposed by Bouchard-Klemm-Marino-Pasquetti and proved in full generality by Fang, Zong and the speaker) relating open and closed GW invariants of a symplectic toric Calabi-Yau 3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin Topological Recursion.

    3/24/2021Weinan E (Princeton)

    Video

    Title: Machine Learning and PDEs

    Abstract: I will discuss two topics:
    (1) Machine learning-based algorithms and “regularity” theory for very high dimensional PDEs;
    (2) Formulating machine learning as PDE (more precisely, integral-differental equation) problems.

    3/31/2021Thore Graepel (DeepMind/UCL)

    Video

    Title: From AlphaGo to MuZero – Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model

    Abstract: Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a perfect simulator is available. However, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. MuZero learns a model that, when applied iteratively, predicts the quantities most directly relevant to planning: the reward, the action-selection policy, and the value function. When evaluated on 57 different Atari games – the canonical video game environment for testing AI techniques, in which model-based planning approaches have historically struggled – our new algorithm achieved a new state of the art. When evaluated on Go, chess and shogi, without any knowledge of the game rules, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.

    4/7/2021Kui Ren (Columbia)Title: Inversion via Optimization: Revisiting the Classical Least-Squares Formulation of Inverse Problems

    Abstract: The classical least-squares formulation of inverse problems has provided a successful framework for the computational solutions of those problems. In recent years, modifications and alternatives have been proposed to overcome some of the disadvantages of this classical formulation in dealing with new applications. This talk intends to provide an (likely biased) overview of the recent development in constructing new least-squares formulations for model and data-driven solutions of inverse problems.

    4/14/2021Siu-Cheong Lau (Boston U)Title: An algebro-geometric formulation of computing machines

    Abstract: Neural network in machine learning has obvious similarity with quiver representation theory.  The main gap between the two subjects is that network functions produced from two isomorphic quiver representations are not equal, due to the presence of non-linear activation functions which are not equivariant under the automorphism group.  This violates the important math/physics principle that isomorphic objects should produce the same results.  In this talk, I will introduce a general formulation using moduli spaces of framed modules of (noncommutative) algebra and fix this gap.  Metrics over the moduli space are crucial.  I will also explain uniformization between spherical, Euclidean and hyperbolic moduli.

    4/21/2021Vasco Carvalho (Cambridge)Title: The Economy as a Complex Production Network
    Abstract: A modern economy is an intricately linked web of specialized production units, each relying on the flow of inputs from their suppliers to produce their own output, which in turn is routed towards other downstream units. From this production network vantage point we: (i) present the theoretical foundations for the role of such input linkages as a shock propagation channel and as a mechanism for transforming micro-level shocks into macroeconomic, economy-wide fluctuations (ii) selectively survey both empirical and simulation-based studies that attempt to ascertain the relevance and quantitative bite of this argument and (time permitting) (iii) discuss a range of domains where this networked production view is currently being extended to.
    4/28/2021

    9:00 – 10:00pm ET

    Shamit Kachru (Stanford)

    Slides

    Title: K3 Metrics from String Theory

    Abstract: Calabi-Yau manifolds have played a central role in important developments in string theory and mathematical physics.  Famously, they admit Ricci flat metrics — but the proof of that fact is not constructive, and the metrics remain mysterious.  K3 is perhaps the simplest non-trivial compact Calabi-Yau space.  In this talk, I describe two different methods of constructing (smooth, Ricci flat) K3 metrics, and a string theory duality which relates them.  The duality re-sums infinite towers of disc instanton corrections via a purely classical infinite-dimensional hyperkahler quotient construction, which can be practically implemented.


    Fall 2020:

    DateSpeakerTitle/Abstract
    9/23/2020David Kazhdan (Hebrew University)Title: On Applications of Algebraic Combinatorics to Algebraic Geometry

    Abstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.

    10/7/2020

    10:00am

    Mariangela Lisanti (Princeton University)

    Video

    Title: Mapping the Milky Way’s Dark Matter Halo with Gaia

    Abstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium, as typically assumed, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments, which search for the interactions of these particles in terrestrial targets.

    10/14/2020Gil Kalai (Hebrew University and IDC Herzliya)

    Video

    Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers

    Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to
    a) My general argument “against” quantum computers,
    b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
    Relevant papers:
    Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.
    wordpress.com/2019/11/stat-quantum2.pdf

    Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.
    wordpress.com/2020/08/laws-blog2.pdf

    Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.
    wordpress.com/2019/09/main-pr.pdf

    10/21/2020Marta Lewicka (University of Pittsburgh)

    Video

    Title: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models

    Abstract: We propose results that relate the following two contexts:
    (i) Given a Riemann metric G on a thin plate, we study the question of what is its closest isometric immersion, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.
    (ii) We perform the full scaling analysis of E^h, in the context of dimension reduction as the plate’s thickness h goes to 0, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).
    For each n, we identify conditions for the validity of the corresponding scaling, in terms of the vanishing of Riemann curvatures of G up to appropriate orders, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth, swelling, shrinkage, plasticity, etc. Our results display the interaction of calculus of variations,
    geometry and mechanics of materials in the prediction of patterns and shape formation.

    10/28/2020Jonathan Heckman (University of Pennsylvania)

    Video

    Title: Top Down Approach to Quantum Fields

    Abstract: Quantum Field theory (QFT) is the common language of particle physicists, cosmologists, and condensed matter physicists. Even so, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory, highlighting in particular the special role of seemingly “exotic”  higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs, and are now using this to extra observables from strongly correlated systems in theories with more than four spacetime dimensions, as well as in spacetimes with four or fewer spacetime dimensions. Along the way, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems

    11/4/2020
    9:00pm ET
    Surya Ganguli (Stanford)

    Video

    Title: Weaving together machine learning, theoretical physics, and neuroscience through mathematics

    Abstract: An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning, theoretical physics, and neuroscience.  The unification of these fields will likely enable us to exploit the power of complex systems analysis, developed in theoretical physics and applied mathematics, to elucidate the design principles governing neural systems, both biological and artificial, and deploy these principles to develop better algorithms in machine learning.  We will give several vignettes in this direction, including:  (1) determining the best optimization problem to solve in order to perform regression in high dimensions;  (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) developing interpretable machine learning to derive and understand state of the art models of the retina; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) delineating fundamental theoretical limits on the energy, speed and accuracy with which non-equilibrium sensors can detect signals
    Selected References:
    M. Advani and S. Ganguli, Statistical mechanics of optimal convex inference in high dimensions, Physical Review X, 6, 031034, 2016.
    M. Advani and S. Ganguli, An equivalence between high dimensional Bayes optimal inference and M-estimation, NeurIPS, 2016.
    A.K. Lampinen and S. Ganguli, An analytic theory of generalization dynamics and transfer learning in deep linear networks, International Conference on Learning Representations (ICLR), 2019.
    H. Tanaka, A. Nayebi, N. Maheswaranathan, L.M. McIntosh, S. Baccus, S. Ganguli, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction, NeurIPS 2019.
    S. Deny, J. Lindsey, S. Ganguli, S. Ocko, The emergence of multiple retinal cell types through efficient coding of natural movies, Neural Information Processing Systems (NeurIPS) 2018.
    B. Sorscher, G. Mel, S. Ganguli, S. Ocko, A unified theory for the origin of grid cells through the lens of pattern formation, NeurIPS 2019.
    Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
    S.E. Harvey, S. Lahiri, and S. Ganguli, A universal energy accuracy tradeoff in nonequilibrium cellular sensing, https://arxiv.org/abs/2002.10567

    11/11/2020Kevin Buzzard (Imperial College London)

    Video

    Title: Teaching proofs to computers

    Abstract: A mathematical proof is a sequence of logical statements in a precise language, obeying some well-defined rules. In that sense it is very much like a computer program. Various computer tools have appeared over the last 50 years which take advantage of this analogy by turning the mathematical puzzle of constructing a proof of a theorem into a computer game. The newest tools are now capable of understanding some parts of modern research mathematics. In spite of this, these tools are not used in mathematics departments, perhaps because they are not yet capable of telling mathematicians *something new*.
    I will give an overview of the Lean theorem prover, showing what it can currently do. I will also talk about one of our goals: using Lean to make practical tools which will be helpful for future researchers in pure mathematics.

    11/18/2020Jose A. Scheinkman (Columbia)

    Video

    Title: Re-pricing avalanches

    Abstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive.  Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper, we show that a state-dependent  pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment.  These fluctuations, in turn, cause fluctuations  in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)

    11/25/2020

    10:45am

    Eric J. Heller (Harvard)

    Video

    Title: Branched Flow

    Abstract: In classical and quantum  phase space flow, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In  evolution under smooth, random, weakly deflecting  but persistent perturbations, a remarkable regime develops, called branched flow. Lying between the first cusp catastrophes at the outset, leading to fully chaotic  statistical flow much later, lies the visually beautiful regime of branched flow.  It applies to tsunami wave propagation, freak wave formation, light propagation, cosmic microwaves arriving from pulsars, electron flow in metals and devices, sound propagation in the atmosphere and oceans, the large scale structure of the universe, and much more. The mathematical structure of this flow is only partially understood, involving exponential instability coexisting with “accidental” stability. The flow is qualitatively universal, but this has not been quantified.  Many questions arise, including the scale(s) of the random medium,  and the time evolution of manifolds and “fuzzy” manifolds in phase space.  The classical-quantum (ray-wave)  correspondence in this flow is only partially understood.  This talk will be an introduction to the phenomenon, both visual and mathematical, emphasizing unanswered questions

    12/2/2020Douglas Arnold (U of Minnesota)

    Video

    Title: Preserving geometry in numerical discretization

    Abstract: An important design principle for numerical methods for differential equations is that the discretizations preserve key geometric, topological, and algebraic structures of the original differential system.  For ordinary differential equations, such geometric integrators were developed at the end of the last century, enabling stunning computations in celestial mechanics and other applications that would have been impossible without them.  Since then, structure-preserving discretizations have been developed for partial differential equations.  One of the prime examples has been the finite element exterior calculus or FEEC, in which the structures to preserve are related to Hilbert complexes underlying the PDEs, the de Rham complex being a canonical example.  FEEC has led to highly successful new numerical methods for problems in fluid mechanics, electromagnetism, and other applications which relate to the de Rham complex.  More recently, new tools have been developed which extend the applications of FEEC far beyond the de Rham complex, leading to progress in discretizations of problems from solid mechanics, materials science, and general relativity.

    12/9/2020Manuel Blum and Lenore Blum (Carnegie Mellon)

    Video

    Title: What can Theoretical Computer Science Contribute to the Discussion of Consciousness?

    Abstract: The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We study consciousness from the perspective of theoretical computer science. This is done by formalizing the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. We give a precise formal definition of a Conscious Turing Machine (CTM), also called Conscious AI, in the spirit of Alan Turing’s simple yet powerful definition of a computer. We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness.
    After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness, the range of related concepts that the model explains easily and naturally, and the extent of the theory’s agreement with scientific evidence

  • Seminars

    Seminars Colloquia & Seminar
    02-25-2016 Evolution Equations Seminar

    3:25 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-03-2016 Evolution Equations Seminar

    3:26 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-29-2016 Geometric Analysis Seminar

    3:27 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-5-2018 Mathematical Physics Seminar

    3:27 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Seminars

    Seminars Colloquia & Seminar
    04-07-2016 Evolution Equations Seminar

    3:28 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: JDG 2017 Conference, April 28 – May 2, 2017
    3:29 pm
    11/01/2019-05/02/2017

    In celebration of the Journal of Differential Geometry’s 50th anniversary, the Harvard Math Department will be hosting the Tenth Conference on Geometry and Topology (JDG 2017) from April 28 – May 2, 2017.

    Registration and additional information on the conference can be found at http://abel.harvard.edu/jdg/index.html.

    Confirmed Speakers

    * This event is co-sponsored by Lehigh University and partially supported by the National Science Foundation.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2-23-2018 RM & PT Seminar

    3:30 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Seminars

    Seminars Colloquia & Seminar
    4/4/2019 General Relativity Seminar

    3:30 pm-4:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    02-29-2016 Social Science Application Forum

    3:30 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/14/2019 General Relativity Seminar

    3:30 pm-4:30 pm
    11/01/2019
  • Colloquium
    3:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/15/2019 Spacetime Seminar

    3:30 pm-5:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/10/2019 Spacetime Seminar

    3:30 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/17/2018 RM & PT Seminar

    3:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    02-29-2016 Mathematical Physics Seminar

    3:31 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-01-2016 Geometric Analysis Seminar

    3:32 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-10-2016 Evolution Equations Seminar

    3:34 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Working Conference on Materials and Data Analysis, March 27-30, 2017
    3:34 pm
    11/01/2019-03/30/2017

    The Center of Mathematical Sciences and Applications will be hosting a 5-day working Conference on Materials and Data Analysis and related areas, March 27-30, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Photos of the event can be found on CMSA’s Blog.

     Participants:

    Organizers:

    * This event is sponsored by CMSA Harvard University.

    Schedule:

    Monday, March 27

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amKieron Burke, University of California, IrvineBackground in DFT and electronic structure calculations
    10:00am – 11:00amKieron Burke, University of California, Irvine

    The density functionals machines can learn

    11:00am – 12:00pmSadasivan Shankar, Harvard UniversityA few key principles for applying Machine Learning to Materials (or Complex Systems) — Scientific and Engineering Perspectives

    Tuesday, March 28

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amRyan Adams, HarvardTBA
    10:00am – 11:00amGábor Csányi, University of Cambridge

    Interatomic potentials using machine learning: accuracy, transferability and chemical diversity

    11:00am – 1:00pmLunch Break
    1:00pm – 2:00pmEvan Reed, Stanford UniversityTBA

     Wednesday, March 29 

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amPatrick Riley, GoogleThe Message Passing Neural Network framework and its application to molecular property prediction
    10:00am – 11:00amJörg Behler, University of GöttingenTBA
    11:00am – 12:00pmEkin Doğuş Çubuk, Stanford UniversTBA
    4:00pmLeslie Greengard, Courant InstituteInverse problems in acoustic scattering and cryo-electron microscopy

    CMSA Colloquium

    Thursday, March 30

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amMatthias Rupp, Fitz Haber Institute of the Max Planck SocietyTBA
    10:00am – 11:00amPetros Koumoutsakos, Radcliffe Institute for Advanced Study, HarvardTBA
    11:00am – 1:00pmLunch Break
    1:00pm – 2:00pmDennis Sheberla, Harvard UniversityRapid discovery of functional molecules by a high-throughput virtual screening
  • CMSA EVENT: Workshop on Discrete and Topological Models for Effective Field Theories, January 9-13, 2017
    3:35 pm-3:36 pm
    11/01/2019-01/13/2017

    The Center of Mathematical Sciences and Applications will be hosting a Workshop on “Discrete and Topological Models for Effective Field Theories,” January 9-13, 2017.  The workshop will be hosted in G02 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Titles, abstracts and schedule will be provided nearer to the event.

    Participants:

    Dan Freed, UT Austin

    Anton Kapustin, California Institute of Technology

    Alexei Y. Kitaev, California Institute of Technology

    Greg Moore, Rutgers University

    Constantin Teleman, University of Oxford

    Organizers:

    Mike Hopkins, Shing-Tung Yau

    * This event is sponsored by CMSA Harvard University.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-09-2016 Random Matrix & Probability Theory

    3:35 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-23-2016 Random Matrix & Probability Theory

    3:37 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    3:38 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Working Conference on Covariance Analysis in Biology, May 1-4, 2017
    3:40 pm-3:41 pm
    11/01/2019-05/02/2017

    The Center of Mathematical Sciences and Applications will be hosting a working Conference on Covariance Analysis in Biology, May 1-4, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    This event is open and free.  If you would like to attend, please register here to help us keep a headcount. A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Speakers:

    Orr Ashenberg, Fred Hutchinson Cancer Research Center

    John Barton, Massachusetts Institute of Technology

    Simona Cocco, Laboratoire de Physique Statistique de l’ENS

    Sean Eddy, Harvard University

    Efthimios Kaxiras, Harvard University

    Michael Laub, Massachusetts Institute of Technology

    Debora S. Marks, Harvard University

    Govind Menon, Brown University

    Rémi Monasson, Laboratoire de Physique Théorique de l’ENS

    Andrew Murray, Harvard University

    Ilya Nemenman, Emory College

    Chris Sander, Dana-Farber Cancer Institute, Harvard Medical School

    Dave Thirumalai, University of Texas at Austin

    Martin Weigt, IBPS, Université Pierre et Marie Curie

    Matthieu Wyart, EPFL

    More speakers will be confirmed soon.

     

    Schedule:

    (Please click here for a downloadable version of the schedule.)

    Please note that the schedule for both days is currently tentative and is subject to change.

    May 1, Monday

    TimeSpeakerTopic
    9:00-10:00amSean EddyTBA
    10:00-11:00amMike LaubTBA
    11:00am-12:00pmIlya NemenmanTBA
    May 2, Tuesday
    TimeSpeakerTopic
    9:00-10:00amOrr AshenbergTBA
    10:00-11:00amDebora MarksTBA
    11:00am-12:00pmMartin WeigtTBA
    4:30pm-5:30pmSimona CoccoCMSA Colloquia

     

    May 3, Wednesday
    TimeSpeakerTopic
    9:00-10:00amAndrew MurrayTBA
    10:00-11:00amMatthieu WyartTBA
    11:00am-12:00pmRémi MonassonTBA

     

    May 4, Thursday
    TimeSpeakerTopic
    9:00-10:00amDavid ThirumalaiTBA
    10:00-11:00amChris SanderTBA
    11:00am-12:00pmJohn BartonTBA

     

    Organizers:

    Michael Brenner, Lucy Colwell, Elena Rivas, Eugene Shakhnovich

    * This event is sponsored by CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    03-07-2016 Mathematical Physics Seminar

    3:41 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2-26-2018 Mathematical Physics Seminar

    3:42 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-11-2016 Random Matrix & Probability Theory

    3:42 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: A Celebration of Symplectic Geometry: 15 Years of JSG, June 5-6, 2017
    3:44 pm
    11/01/2019-05/04/2017

    In celebration of the Journal of Symplectic Geometry’s 15th anniversary, the Center of Mathematical Sciences and Applications will be hosting A Celebration of Symplectic Geometry: 15 Years of JSG on June 5-6, 2017.

    To register for this event, please click here.

    Confirmed speakers:

    The conference is co-organized by Denis Auroux and Victor Guillemin. Additional information on the conference will be announced closer to the event.

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

    Schedule:

    The schedule for both days is currently tentative and is subject to change. A pdf version of the schedule can also be downloaded here.

    June 5, Monday (Full day)

    TimeSpeakerTopic
    8:30am – 9:0amBreakfast
    9:00am – 10:00amJonathan WeitsmanTitle: On the geometric quantization of (some) Poisson manifolds
    10:30am – 11:30amEckhard MeinrenkenTitle: On Hamiltonian loop group spaces

    Abstract: Let G be a compact Lie group. We explain a construction of an LG-equivariant spinor module over any Hamiltonian loop group space with proper moment map. It may be regarded as its `canonical spin-c structure’. We show how to reduce to finite dimensions, resulting in actual spin-s structure on transversals, as well as twisted spin-c structures for the associated quasi-hamiltonian space. This is based on joint work with Yiannis Loizides and Yanli Song.

    11:30am – 1:30pmBreak
    1:30pm – 2:30pmAna Rita PiresTitle: Infinite staircases in symplectic embedding problems

    Abstract: McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with Cristofaro-Gardiner, Holm and Mandini.

    Video

    3:00pm – 4:00pmSobhan SeyfaddiniTitle: Rigidity of conjugacy classes in groups of area-preserving homeomorphisms

    Abstract: Motivated by understanding the algebraic structure of groups of area-preserving homeomorphims F. Beguin, S. Crvoisier, and F. Le Roux were lead to the following question: Can the conjugacy class of a Hamiltonian homeomorphism be dense? We will show that one can rule out existence of dense conjugacy classes by simply counting fixed points. This is joint work with Le Roux and Viterbo.

    4:30pm – 5:30pmRoger CasalsTitle: Differential Algebra of Cubic Graphs
    Abstract: In this talk we will associate a combinatorial dg-algebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations and examples. From there we study the Legendrian surfaces behind these constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.Video

    June 6, Tuesday (Full day)

    TimeSpeakerTopic
    8:30am – 9:00amBreakfast
    9:00am – 10:00amAlejandro UribeTitle: Semi-classical wave functions associated with isotropic submanifolds of phase space

    Abstract: After reviewing fundamental ideas on the quantum-classical correspondence, I will describe how to associate spaces of semi-classical wave functions to isotropic submanifolds of phase space satisfying a Bohr-Sommerfeld condition. Such functions have symbols that are symplectic spinors, and they satisfy a symbol calculus under the action of quantum observables. This is the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin, and it is joint work with Victor Guillemin and Zuoqin Wang. I will inlcude applications and open questions.

    Video

    10:30am – 11:30amAlisa KeatingTitle: Symplectomorphisms of exotic discs

    Abstract: It is a theorem of Gromov that the group of compactly supported symplectomorphisms of R^4, equipped with the standard symplectic form, is contractible. While nothing is known in higher dimensions for the standard symplectic form, we show that for some exotic symplectic forms on R^{4n}, for all but finitely n, there exist compactly supported symplectomorphisms that are smoothly non-trivial. The principal ingredients are constructions of Milnor and Munkres, a symplectic and contact version of the Gromoll filtration, and Borman, Eliashberg and Murphy’s work on existence of over-twisted contact structures. Joint work with Roger Casals and Ivan Smith.

    Video

    11:30am – 1:30pmBreak
    1:30pm – 2:30pmChen HeTitle: Morse theory on b-symplectic manifolds

    Abstract: b-symplectic (or log-symplectic) manifolds are Poisson manifolds equipped with symplectic forms of logarithmic singularity. Following Guillemin, Miranda, Pires and Scott’s introduction of Hamiltonian group actions on b-symplectic manifolds, we will survey those classical results of Hamiltonian geometry to the b-symplectic case.

    Video

    3:00pm – 4:00pmYael KarshonTitle: Geometric quantization with metaplectic-c structures

    Abstract: I will present a variant of the Kostant-Souriau geometric quantization procedure that uses metaplectic-c structures to incorporate the “half form correction” into the prequantization stage. This goes back to the late 1970s but it is not widely known and it has the potential to generalize and improve upon recent works on geometric quantization.

    Video


  • Seminars

    Seminars Colloquia & Seminar
    03-08-2016 Geometric Analysis Seminar

    3:44 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-21-2016 Mathematical Physics Seminar

    3:46 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-24-2016 Evolution Equations Seminar

    3:47 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: 2017 Big Data Conference
    3:47 pm
    11/01/2019-08/19/2017
    1 Oxford Street, Cambridge MA 02138

    The Center of Mathematical Sciences and Applications will be hosting a conference on Big Data from August 18 – 19, 2017, in Hall D of the Science Center at Harvard University.

    The Big Data Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the third conference on Big Data the Center will host as part of our annual events, and is co-organized by Richard Freeman, Scott Kominers, Jun Liu, Horng-Tzer Yau and Shing-Tung Yau.

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

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

    Confirmed Speakers:

     

    Following the conference, there will be a two-day workshop from August 20-21. The workshop is organized by Scott Kominers, and will feature:

    • Jörn Boehnke, Harvard University
    • Nikhil Naik, Harvard University
    • Bradly Stadie, Open AI, University of California, Berkeley

     

    Conference Schedule

    A PDF version of the schedule below can also be downloaded here.

    August 18, Friday (Full day)

    TimeSpeakerTopic
    8:30 am – 9:00 amBreakfast
    9:00 am – 9:40 amMohammad Akbarpour

    Video

    Title: Information aggregation in overlapping generations and the emergence of experts

    Abstract: We study a model of social learning with “overlapping generations”, where agents meet others and share data about an underlying state over time. We examine under what conditions the society will produce individuals with precise knowledge about the state of the world. There are two information sharing regimes in our model: Under the full information sharing technology, individuals exchange the information about their point estimates of an underlying state, as well as their sources (or the precision of their signals) and update their beliefs by taking a weighted average. Under the limited information sharing technology, agents only observe the information about the point estimates of those they meet, and update their beliefs by taking a weighted average, where weights can depend on the sequence of meetings, as well as the labels. Our main result shows that, unlike most social learning settings, using such linear learning rules do not guide the society (or even a fraction of its members) to learn the truth, and having access to, and exploiting knowledge of the precision of a source signal are essential for efficient social learning (joint with Amin Saberi & Ali Shameli).

    9:40 am – 10:20 amLucas Janson

    Video

    Title: Model-Free Knockoffs For High-Dimensional Controlled Variable Selection

    Abstract: Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new framework of model-free knockoffs, which reads from a different perspective the knockoff procedure (Barber and Candès, 2015) originally designed for controlling the false discovery rate in linear models. The key innovation of our method is to construct knockoff variables probabilistically instead of geometrically. This enables model-free knockoffs to deal with arbitrary (and unknown) conditional models and any dimensions, including when the dimensionality p exceeds the sample size n, while the original knockoffs procedure is constrained to homoscedastic linear models with n greater than or equal to p. Our approach requires the design matrix be random (independent and identically distributed rows) with a covariate distribution that is known, although we show our procedure to be robust to unknown/estimated distributions. As we require no knowledge/assumptions about the conditional distribution of the response, we effectively shift the burden of knowledge from the response to the covariates, in contrast to the canonical model-based approach which assumes a parametric model for the response but very little about the covariates. To our knowledge, no other procedure solves the controlled variable selection problem in such generality, but in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case-control study of Crohn’s disease in the United Kingdom, making twice as many discoveries as the original analysis of the same data.

    Slides

    10:20 am – 10:50 amBreak
    10:50 pm – 11:30 pmNoureddine El Karoui

    Video

    Title: Random matrices and high-dimensional statistics: beyond covariance matrices

    Abstract: Random matrices have played a central role in understanding very important statistical methods linked to covariance matrices (such as Principal Components Analysis, Canonical Correlation Analysis etc…) for several decades. In this talk, I’ll show that one can adopt a random-matrix-inspired point of view to understand the performance of other widely used tools in statistics, such as M-estimators, and very common methods such as the bootstrap. I will focus on the high-dimensional case, which captures well the situation of “moderately” difficult statistical problems, arguably one of the most relevant in practice. In this setting, I will show that random matrix ideas help upend conventional theoretical thinking (for instance about maximum likelihood methods) and highlight very serious practical problems with resampling methods.

    11:30 am – 12:10 pmNikhil Naik

    Video

    Title: Understanding Urban Change with Computer Vision and Street-level Imagery

    Abstract: Which neighborhoods experience physical improvements? In this work, we introduce a computer vision method to measure changes in the physical appearances of neighborhoods from time-series street-level imagery. We connect changes in the physical appearance of five US cities with economic and demographic data and find three factors that predict neighborhood improvement. First, neighborhoods that are densely populated by college-educated adults are more likely to experience physical improvements. Second, neighborhoods with better initial appearances experience, on average, larger positive improvements. Third, neighborhood improvement correlates positively with physical proximity to the central business district and to other physically attractive neighborhoods. Together, our results illustrate the value of using computer vision methods and street-level imagery to understand the physical dynamics of cities.

    (Joint work with Edward L. Glaeser, Cesar A. Hidalgo, Scott Duke Kominers, and Ramesh Raskar.)

    12:10 pm – 12:25 pmVideo #1

    Video #2

    Data Science Lightning Talks
    12:25 pm – 1:30 pmLunch
    1:30 pm – 2:10 pmTracy Ke

    Video

    Title: A new SVD approach to optimal topic estimation

    Abstract: In the probabilistic topic models, the quantity of interest—a low-rank matrix consisting of topic vectors—is hidden in the text corpus matrix, masked by noise, and Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank matrix and the singular vectors of the text corpus matrix are usually complicated and hard to spell out, so how to use SVD for learning topic models faces challenges.

    We overcome the challenge by revealing a surprising insight: there is a low-dimensional simplex structure which can be viewed as a bridge between the low-rank matrix of interest and the SVD of the text corpus matrix, and which allows us to conveniently reconstruct the former using the latter. Such an insight motivates a new SVD-based approach to learning topic models.

    For asymptotic analysis, we show that under a popular topic model (Hofmann, 1999), the convergence rate of the l1-error of our method matches that of the minimax lower bound, up to a multi-logarithmic term. In showing these results, we have derived new element-wise bounds on the singular vectors and several large deviation bounds for weakly dependent multinomial data. Our results on the convergence rate and asymptotical minimaxity are new. We have applied our method to two data sets, Associated Process (AP) and Statistics Literature Abstract (SLA), with encouraging results. In particular, there is a clear simplex structure associated with the SVD of the data matrices, which largely validates our discovery.

    2:10 pm – 2:50 pmAlbert-László Barabási

    Video

    Title: Taming Complexity: From Network Science to Controlling Networks

    Abstract: The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here we explore the controllability of an arbitrary complex network, identifying the set of driver nodes whose time-dependent control can guide the system’s entire dynamics. We apply these tools to several real networks, unveiling how the network topology determines its controllability. Virtually all technological and biological networks must be able to control their internal processes. Given that, issues related to control deeply shape the topology and the vulnerability of real systems. Consequently unveiling the control principles of real networks, the goal of our research, forces us to address series of fundamental questions pertaining to our understanding of complex systems.

     

    2:50 pm – 3:20 pmBreak
    3:20 pm – 4:00 pmMarena Lin

    Video

    Title: Optimizing climate variables for human impact studies

    Abstract: Estimates of the relationship between climate variability and socio-economic outcomes are often limited by the spatial resolution of the data. As studies aim to generalize the connection between climate and socio-economic outcomes across countries, the best available socio-economic data is at the national level (e.g. food production quantities, the incidence of warfare, averages of crime incidence, gender birth ratios). While these statistics may be trusted from government censuses, the appropriate metric for the corresponding climate or weather for a given year in a country is less obvious. For example, how do we estimate the temperatures in a country relevant to national food production and therefore food security? We demonstrate that high-resolution spatiotemporal satellite data for vegetation can be used to estimate the weather variables that may be most relevant to food security and related socio-economic outcomes. In particular, satellite proxies for vegetation over the African continent reflect the seasonal movement of the Intertropical Convergence Zone, a band of intense convection and rainfall. We also show that agricultural sensitivity to climate variability differs significantly between countries. This work is an example of the ways in which in-situ and satellite-based observations are invaluable to both estimates of future climate variability and to continued monitoring of the earth-human system. We discuss the current state of these records and potential challenges to their continuity.

    4:00 pm – 4:40 pmAlex Peysakhovich Title: Building a cooperator

    Abstract: A major goal of modern AI is to construct agents that can perform complex tasks. Much of this work deals with single agent decision problems. However, agents are rarely alone in the world. In this talk I will discuss how to combine ideas from deep reinforcement learning and game theory to construct artificial agents that can communicate, collaborate and cooperate in productive positive sum interactions.

    4:40 pm – 5:20 pmTze Leung Lai

    Video

    Title: Gradient boosting: Its role in big data analytics, underlying mathematical theory, and recent refinements

    Abstract: We begin with a review of the history of gradient boosting, dating back to the LMS algorithm of Widrow and Hoff in 1960 and culminating in Freund and Schapire’s AdaBoost and Friedman’s gradient boosting and stochastic gradient boosting algorithms in the period 1999-2002 that heralded the big data era. The role played by gradient boosting in big data analytics, particularly with respect to deep learning, is then discussed. We also present some recent work on the mathematical theory of gradient boosting, which has led to some refinements that greatly improves the convergence properties and prediction performance of the methodology.

    August 19, Saturday (Full day)

    TimeSpeakerTopic
    8:30 am – 9:00 amBreakfast
    9:00 am – 9:40 amNatesh Pillai

    Video

    Title: Accelerating MCMC algorithms for Computationally Intensive Models via Local Approximations

    Abstract: We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler’s exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this article: when the likelihood has some local regularity, the number of model evaluations per Markov chain Monte Carlo (MCMC) step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ordinary differential equation (ODE) and partial differential equation (PDE) inference problems, with both synthetic and real data.

    9:40 am – 10:20 amRavi Jagadeesan

    Video

    Title: Designs for estimating the treatment effect in networks with interference

    Abstract: In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring” on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide range of interference functions encountered in applications, we show both by theory and simulations that the classical Neymanian estimator for the direct effect has desirable properties for our designs. This further extends to settings where homophily is present in addition to interference.

    10:20 am – 10:50 amBreak
    10:50 am – 11:30 amAnnie Liang

    Video

    Title: The Theory is Predictive, but is it Complete? An Application to Human Generation of Randomness

    Abstract: When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? This question is difficult to answer, because in general we do not know how much “predictable variation” there is in the problem. In this paper, we consider approaches motivated by machine learning algorithms as a means of constructing a benchmark for the best attainable level of prediction.  We illustrate our methods on the task of predicting human-generated random sequences. Relative to a theoretical machine learning algorithm benchmark, we find that existing behavioral models explain roughly 15 percent of the predictable variation in this problem. This fraction is robust across several variations on the problem. We also consider a version of this approach for analyzing field data from domains in which human perception and generation of randomness has been used as a conceptual framework; these include sequential decision-making and repeated zero-sum games. In these domains, our framework for testing the completeness of theories provides a way of assessing their effectiveness over different contexts; we find that despite some differences, the existing theories are fairly stable across our field domains in their performance relative to the benchmark. Overall, our results indicate that (i) there is a significant amount of structure in this problem that existing models have yet to capture and (ii) there are rich domains in which machine learning may provide a viable approach to testing completeness (joint with Jon Kleinberg and Sendhil Mullainathan).

    11:30 am – 12:10 pmZak Stone

    Video

    Title: TensorFlow: Machine Learning for Everyone

    Abstract: We’ve witnessed extraordinary breakthroughs in machine learning over the past several years. What kinds of things are possible now that weren’t possible before? How are open-source platforms like TensorFlow and hardware platforms like GPUs and Cloud TPUs accelerating machine learning progress? If these tools are new to you, how should you get started? In this session, you’ll hear about all of this and more from Zak Stone, the Product Manager for TensorFlow on the Google Brain team.

    12:10 pm – 1:30 pmLunch
    1:30 pm – 2:10 pmJann Spiess

    Video

    Title: (Machine) Learning to Control in Experiments

    Abstract: Machine learning focuses on high-quality prediction rather than on (unbiased) parameter estimation, limiting its direct use in typical program evaluation applications. Still, many estimation tasks have implicit prediction components. In this talk, I discuss accounting for controls in treatment effect estimation as a prediction problem. In a canonical linear regression framework with high-dimensional controls, I argue that OLS is dominated by a natural shrinkage estimator even for unbiased estimation when treatment is random; suggest a generalization that relaxes some parametric assumptions; and contrast my results with that for another implicit prediction problem, namely the first stage of an instrumental variables regression.

    2:10 pm – 2:50 pmBradly StadieTitle: Learning to Learn Quickly: One-Shot Imitation and Meta Learning

    Abstract: Many reinforcement learning algorithms are bottlenecked by data collection costs and the brittleness of their solutions when faced with novel scenarios.
    We will discuss two techniques for overcoming these shortcomings. In one-shot imitation, we train a module that encodes a single demonstration of a desired behavior into a vector containing the essence of the demo. This vector can subsequently be utilized to recover the demonstrated behavior. In meta-learning, we optimize a policy under the objective of learning to learn new tasks quickly. We show meta-learning methods can be accelerated with the use of auxiliary objectives. Results are presented on grid worlds, robotics tasks, and video game playing tasks.

    2:50 pm – 3:20 pmBreak
    3:20 pm – 4:00 pmHau-Tieng Wu

    Video

    Title: When Medical Challenges Meet Modern Data Science

    Abstract: Adaptive acquisition of correct features from massive datasets is at the core of modern data analysis. One particular interest in medicine is the extraction of hidden dynamics from a single observed time series composed of multiple oscillatory signals, which could be viewed as a single-channel blind source separation problem. The mathematical and statistical problems are made challenging by the structure of the signal which consists of non-sinusoidal oscillations with time varying amplitude/frequency, and by the heteroscedastic nature of the noise. In this talk, I will discuss recent progress in solving this kind of problem by combining the cepstrum-based nonlinear time-frequency analysis and manifold learning technique. A particular solution will be given along with its theoretical properties. I will also discuss the application of this method to two medical problems – (1) the extraction of a fetal ECG signal from a single lead maternal abdominal ECG signal; (2) the simultaneous extraction of the instantaneous heart/respiratory rate from a PPG signal during exercise; (3) (optional depending on time) an application to atrial fibrillation signals. If time permits, the clinical trial results will be discussed.

    4:00 pm – 4:40 pmSifan Zhou

    Video

    Title: Citing People Like Me: Homophily, Knowledge Spillovers, and Continuing a Career in Science

    Abstract: Forward citation is widely used to measure the scientific merits of articles. This research studies millions of journal article citation records in life sciences from MEDLINE and finds that authors of the same gender, the same ethnicity, sharing common collaborators, working in the same institution, or being geographically close are more likely (and quickly) to cite each other than predicted by their proportion among authors working on the same research topics. This phenomenon reveals how social and geographic distances influence the quantity and speed of knowledge spillovers. Given the importance of forward citations in academic evaluation system, citation homophily potentially put authors from minority group at a disadvantage. I then show how it influences scientists’ chances to survive in the academia and continue publishing. Based on joint work with Richard Freeman.

     

    To view photos and video interviews from the conference, please visit the CMSA blog.

     

  • Seminars

    Seminars Colloquia & Seminar
    12-07-2015 Mathematical Physics Seminar

    3:49 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-22-2016 Geometric Analysis Seminar

    3:51 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/16/2019 Colloquium

    4:00 pm
    11/01/2019
  • Yip Lecture Series

    Yip Lecture Series Event
    Yip Annual Lecture

    4:00 pm-5:00 pm
    11/01/2019
    1 Oxford Street, Cambridge MA 02138

    On April 18, 2019 Harvard CMSA hosted the inaugural Yip lecture. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Peter Galison (Harvard Physics).

    The lecture was held from 4:00-5:00pm in Science Center, Hall A.

    Credit:Bronzwaer/Davelaar/Moscibrodzka/Falcke/Radboud University
  • Seminars
    4:00 pm-5:00 pm
    11/01/2019

  • Math Science Lectures in Honor of Raoul Bott

    Math Science Lectures in Honor of Raoul Bott Event
    Math Science Lectures in Honor of Raoul Bott: Mina Aganagic

    4:00 pm
    11/01/2019-04/10/2019
    1 Oxford Street, Cambridge MA 02138

    On April 9 and 10, 2019 the CMSA hosted two lectures by Mina Aganagic (UC Berkeley).  This was the second annual Math Science Lecture Series held in honor of Raoul Bott.

    The lectures took place in Science Center, Hall C

    “Two math lessons from string theory”

    Lecture 1:

     

     

     

     

     

    April 9, 2019

    Title: “Lesson on Integrability”

     

    Abstract: The quantum Knizhnik-Zamolodchikov (qKZ) equation is a difference generalization of the famous Knizhnik-Zamolodchikov (KZ) equation. The problem to explicitly capture the monodromy of the qKZ equation has been open for over 25 years. I will describe the solution to this problem, discovered jointly with Andrei Okounkov. The solution comes from the geometry of Nakajima quiver varieties and has a string theory origin.

    Part of the interest in the qKZ monodromy problem is that its solution leads to integrable lattice models, in parallel to how monodromy matrices of the KZ equation lead to knot invariants. Thus, our solution of the problem leads to a new, geometric approach, to integrable lattice models. There are two other approaches to integrable lattice models, due to Nekrasov and Shatashvili and to Costello, Witten and Yamazaki. I’ll describe joint work with Nikita Nekrasov which explains how string theory unifies the three approaches to integrable lattice models.

    Lecture 2:

     

     

     

     

     

    April 10, 2019

    Title: “Lesson on Knot Categorification”

     

    Abstract: An old problem is to find a unified approach to the knot categorification problem. The new string theory perspective on the qKZ equation I described in the first talk can be used to derive two geometric approaches to the problem.

    The first approach is based on a category of B-type branes on resolutions of slices in affine Grassmannians. The second is based on a category of A-branes in a Landau-Ginzburg theory. The relation between them is two dimensional (equivariant) mirror symmetry. String theory also predicts that a third approach to categorification, based on counting solutions to five dimensional Haydys-Witten equations, is equivalent to the first two.

    This talk is mostly based on joint work with Andrei Okounkov.

     

    Information about last year’s Math Science Bott lecture can be found here. 

    Aganagic

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    03-28-2016 Mathematical Physics Seminar

    4:08 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-06-2016 Random Matrix & Probability Theory

    4:10 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-30-2016 Random Matrix & Probability Theory Seminar

    4:11 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-14-2016 Evolution Equations Seminar

    4:13 pm
    11/01/2019

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  • Seminars

    Seminars Colloquia & Seminar
    04-12-2016 Geometric Analysis Seminar

    4:14 pm
    11/01/2019

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  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Special Seminar

    4:15 pm
    11/01/2019
  • Seminars

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    03-31-2016 Evolution Equations Seminar

    4:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    4:15 pm-5:15 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    Duality String Seminar, Thursdays

    4:15 pm-6:00 pm
    11/01/2019-10/12/2016

    The Duality String  Seminar is held every Thursday at 4:15pm in Jefferson Lab, 453.

    For details, please visit the website.

    * The Duality String Seminar is sponsored by the Center of Mathematical Sciences and Applications’ Cheng Yu-Tong Fund, for Research at the Interface of Mathematics and Physics.

  • Seminars

    Seminars Colloquia & Seminar
    04-04-2016 Mathematical Physics Seminar

    4:20 pm
    11/01/2019

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  • Seminars

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    04-05-2016 Geometric Analysis Seminar

    4:21 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

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    04-11-2016 Mathematical Physics Seminar

    4:22 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

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    04-07-2016 Evolution Equations Seminar

    4:24 pm
    11/01/2019

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  • Seminars

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    04-06-2016 Seminar on General Relativity

    4:25 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-11-2016 Random Matrix & Probability Theory Seminar

    4:28 pm
    11/01/2019

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  • Seminars

    Seminars Colloquia & Seminar
    04-13-2016 General Relativity Seminar

    4:29 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars
    4:30 pm-5:30 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2/14/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium

    Colloquium Colloquia & Seminar
    2/20/2019 Colloquium

    4:30 pm-5:00 pm
    11/01/2019
  • Colloquium

    Colloquium Colloquia & Seminar
    2/13/2019 Colloquium

    4:30 pm-5:00 pm
    11/01/2019
  • Seminars
    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars

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    1/30/2019 Colloquium

    4:30 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/4/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    11/01/2019
  • Seminars

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    10/3/2019 RM & PT Seminar

    4:30 pm-5:00 pm
    11/01/2019
  • Seminars

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    4/24/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Seminars

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    10/9/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Seminars
    4:30 pm-5:30 pm
    11/01/2019
  • Seminars

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    4/17/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Seminars

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    10/2/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars

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    9/25/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/18/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars

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    04-20-2016 General Relativity Seminar

    4:30 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/20/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3/28/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    04-18-2016 Social Science Application Forum

    4:31 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:33 pm
    11/01/2019

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  • Seminars

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    04-19-2016 Geometric Analysis Seminar

    4:33 pm
    11/01/2019

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  • Seminars

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    04-18-2016 Mathematical Physics Seminar

    4:34 pm
    11/01/2019

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    4:34 pm
    11/01/2019

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    04-21-2016 Evolution Equations Seminar

    4:35 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:36 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-20-2016 Random Matrix & Probability Theory Seminar

    4:37 pm
    11/01/2019

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  • Seminars

    Seminars Colloquia & Seminar
    04-26-2016 Geometric Analysis Seminar

    4:38 pm
    11/01/2019

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  • Colloquium
    4:39 pm
    11/01/2019

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  • Seminars

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    04-25-2016 Mathematical Physics Seminar

    4:39 pm
    11/01/2019

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  • Colloquium
    4:41 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-27-2016 Random Matrix & Probability Theory Seminar

    4:42 pm
    11/01/2019

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  • Seminars

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    04-27-2016 General Relativity Seminar

    4:44 pm
    11/01/2019

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  • Seminars

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    04-28-2016 CMSA Special Seminar

    4:45 pm
    11/01/2019

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    04-28-2016 Evolution Equations Seminar

    4:46 pm
    11/01/2019

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  • Seminars

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    05-04-2016 General Relativity Seminar

    4:48 pm
    11/01/2019

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  • Seminars

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    04-29-2016 CMSA Special Seminar

    4:49 pm
    11/01/2019

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  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    05-02-2016 Mathematical Physics Seminar

    4:50 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-05-2016 Evolution Equations Seminar

    4:51 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-25-2016 General Relativity Seminar

    4:52 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar
    4:54 pm
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
    4:58 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    5:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2018 HMS Focused Lecture Series

    5:00 pm
    11/01/2019

    As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester. The lectures will take place  on Tuesdays and Thursdays in the CMSA Building, 20 Garden Street, Room G10.

    The schedule will be updated below.

    DateSpeakerTitle/Abstract
    January 23, 25, 30 and February 1 

    3-5pm

    *Room G10*

    Ivan Losev 

    (Northeastern)

    Title: BGG category O: towards symplectic duality 

    Abstract: We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson, Ginzburg and Soergel on the Koszul duality for such categories, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting.

    Approximate (optimistic) plan of the lectures:

    1) Preliminaries and BGG category O.

    2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem.

    3) Localization theorem continued. Soergel modules.

    4) Koszul algebras and Koszul duality for categories O.

    Time permitting: other instances of Symplectic duality.

    Prerequisites:

    Semi-simple Lie algebras and their finite dimensional representation theory.

    Some  Algebraic geometry. No prior knowledge of category O/ Geometric

    Representation theory is assumed.

    Scanned from a Xerox Multifunction Device

    February 27, 

    and March 1

    3-5pm

    Colin Diemer 

    (IHES)

    Title: Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS. 

    Abstract: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau’s the role of the mirror map is well-appreciated. In these talks I’ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov, Kontsevich, Pantev), the interplay of the topology  of LG models with autoequivalence relations in the Calabi-Yau setting, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we’ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster).

    March 6 and 8 

    4-5pm

    Adam Jacob 

    (UC Davis)

    Title: The deformed Hermitian-Yang-Mills equation 

    Abstract: In this series I will discuss the deformed Hermitian-Yang-Mills equation, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible, and cover joint work with T.C. Collins and S.-T. Yau.

    March 6, 8, 13, 15 

    3-4pm

    Dmytro Shklyarov 

    (TU Chemnitz)

    Title: On categories of matrix factorizations and their homological invariants 

    Abstract: The talks will cover the following topics:

    1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements.

    2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the “classical” mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models.

    3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data, namely, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type, open varieties, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which, just as their non-equivariant cousins, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds.

    April 10 & 12 

    3-4pm

    Mauricio Romo 

    (IAS)

    Title: Gauged Linear Sigma Models, Supersymmetric Localization and Applications 

    Abstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with  CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs).

    Lecture notes

    April 17, 19, 26 

    3-5pm

    Andrew  Harder 

    (University of Miami)

    Title: Perverse sheaves of categories on surfaces 

    Abstract: Perverse sheaves of categories on a Riemann surface S are systems of categories and functors which are encoded by a graphs on S, and which satisfy conditions that resemble the classical characterization of perverse sheaves on a disc.

    I’ll review the basic ideas behind Kapranov and Schechtman’s notion of a perverse schober and generalize this to perverse sheaves of categories on a punctured Riemann surface. Then I will give several examples of perverse sheaves of categories in both algebraic geometry, symplectic geometry, and category theory. Finally, I will describe how one should be able to use related ideas to prove homological mirror symmetry for certain noncommutative deformations of projective 3-space.

     

    May 15, 17 

    1-3pm

    Charles Doran 

    (University of Alberta)

    Lecture One:
    Title: Picard-Fuchs uniformization and Calabi-Yau geometry
    Abstract:
    Part 1:  We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties, with emphasis on Calabi-Yau manifolds.  Specializing to the case of K3 surfaces, we explore general results on “Picard-Fuchs uniformization” of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces.  As an application, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces.
    Part 2:  We next consider families with one natural complex structure modulus, (e.g., elliptic curves, rank 19 K3 surfaces, b_1=4 Calabi-Yau threefolds, …), where the Picard-Fuchs equations are ODEs.  What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces?  Using Hodge theory and parabolic cohomology, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space.  In particular, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau.

     

    Lecture Two:
    Title: Calabi-Yau fibrations: construction and classification
    Abstract:

    Part 1:  Codimension one Calabi-Yau submanifolds induce fibrations, with the periods of the total space relating to those of the fibers and the structure of the fibration.  We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals.

    Part 2:  We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces.  The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces.  When the total space of the fibration is a Calabi-Yau threefold, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations.  The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1.

  • CMSA EVENT: Noga Alon Public Talk, 9-7-17
    5:00 pm-6:00 pm
    11/01/2019

    Noga Alon (Tel Aviv University) will be giving a public talk on September 7, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

    Title: Graph Coloring: Local and Global

    Abstract: Graph Coloring is arguably the most popular subject in Discrete Mathematics, and its combinatorial, algorithmic and computational aspects have been studied intensively. The most basic notion in the area, the chromatic number of a graph, is an inherently global property. This is demonstrated by the hardness of computation or approximation of this invariant as well as by the existence of graphs with arbitrarily high chromatic number and no short cycles. The investigation of these graphs had a profound impact on Graph Theory and Combinatorics. It combines combinatorial, probabilistic, algebraic and topological techniques with number theoretic tools. I will describe the rich history of the subject focusing on some recent results.

  • CMSA EVENT: 2017 Ding Shum Lecture
    5:00 pm-6:00 pm
    11/01/2019
    1 Oxford Street, Cambridge MA 02138

    Leslie Valiant will be giving the inaugural talk of the Ding Shum Lectures on Tuesday, October 10 at 5:00 pm in Science Center Hall D, Cambridge, MA.

    Learning as a Theory of Everything

    Abstract: We start from the hypothesis that all the information that resides in living organisms was initially acquired either through learning by an individual or through evolution. Then any unified theory of evolution and learning should be able to characterize the capabilities that humans and other living organisms can possess or acquire. Characterizing these capabilities would tell us about the nature of humans, and would also inform us about feasible targets for automation. With this purpose we review some background in the mathematical theory of learning. We go on to explain how Darwinian evolution can be formulated as a form of learning. We observe that our current mathematical understanding of learning is incomplete in certain important directions, and conclude by indicating one direction in which further progress would likely enable broader phenomena of intelligence and cognition to be realized than is possible at present.

     

  • CMSA EVENT: Jennifer Chayes Public Talk, 11-02-17
    5:00 pm-6:00 pm
    11/01/2019

    Jennifer Chayes (Microsoft Research) will be giving a public talk on November 02, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

    Title: Network Science: From the Online World to Cancer Genomics

    Abstract: Everywhere we turn these days, we find that networks can be used to describe relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage many human diseases. In this talk, I look quite generally at some of the models we are using to describe these networks, processes we are studying on the networks, algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. I’ll discuss in some detail particular applications to cancer genomics, applying network algorithms to suggest possible drug targets for certain kinds of cancer.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    05-11-2016 Random Matrix & Probability Theory Seminar

    5:00 pm
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
    5:02 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    06-01-2016 Random Matrix & Probability Theory Seminar

    5:03 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    06-08-2016 Random Matrix & Probability Theory Seminar

    5:04 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    07-12-2016 Chinese Economy Seminar

    5:06 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

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    07-19-2016 Chinese Economy Seminar

    5:07 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    08-02-2016 China Gazetteer Seminar

    5:08 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-12-2016 Mathematical Physics Seminar

    5:10 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-19-2016 Mathematical Physics Seminar

    5:11 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-21-2016 Random Matrix & Probability Theory Seminar

    5:13 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium

    Colloquium Colloquia & Seminar
    3/27/2019 Colloquium

    5:15 pm-6:15 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-23-2018 Math Physics

    5:15 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium

    Colloquium Colloquia & Seminar
    2/13/2019 Colloquium

    5:15 pm-6:15 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4-16-2018 Social Science Applications Forum

    5:16 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-20-2018 Social Science Applications Forum

    5:18 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-26-16 Mathematical Physics Seminar

    5:32 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-28-2016 Random Matrix & Probability Theory Seminar

    5:35 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    5:36 pm
    11/01/2019

    As part of the Program on Topological Aspects of Condensed Mattera weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

    DateSpeakerTitle/Abstract
    8/29/2018Zeng-Cheng GuTitle: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory

    Abstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.

    9/10/2018Dominic Else, MIT

    Video

    Title: Phases and topology in periodically driven (Floquet) systems

    Abstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.

    9/17/2018Adrian Po, MIT

    Video

    Title: A modern solution to the old problem of symmetries in band theory

    Abstract: There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants.

    9/24/2018Maxim MetlitskiTitle: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs

    Abstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.

    10/1/2018Cancelled
    10/9/2018

    Tuesday

    3:00-4:30pm

    Sagar VijayTitle: Fracton Phases of Matter

    Abstract:  Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped, point-like excitations (“fractons”) that are strictly immobile at zero temperature, and by degenerate ground-states that are locally indistinguishable.  Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions, and these states of matter are a gateway for exploring mechanisms for quantum information storage, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases, constructions of these states using well-studied two-dimensional topological phases, and a model in which the fracton excitations carry a protected internal degeneracy, which provides a natural generalization of non-Abelian anyons to three spatial dimensions.  I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.

    10/15/2018Ethan LakeTitle: A primer on higher symmetries

    Abstract: The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.

    10/22/2018

    Room G02

    Yin-Chen He, PerimeterTitle: Emergent QED3 and QCD3 in condensed matter system

    Abstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.

    10/29/2018Dominic Williamson, Yale

    Video

    Title: Symmetry and topological order in tensor networks

    Abstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.

    11/13/2018

    Tuesday

    3:00-4:30pm

    Jason Alicea, CaltechTitle: Time-crystalline topological superconductors
    11/19/2018X. G. Wen, MIT

    Video

    Title: A classification of 3+1D topological orders

    Abstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.

    12/3/2018

    *Room G02*

    Claudio Chamon, Boston UniversityTitle: Many-body scar states with topological properties in 1D, 2D, and 3D.

    Abstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies.

    12/10/2018

    Room G02

    Anders Sandvik, Boston University and Institute of Physics, CAS, BeijingTitle: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets

    Abstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.

    1/8/2019Lukasz Fidkowski, Univ. of Washington

    Video

    Title: Non-trivial quantum cellular automata in 3 dimensions

    Abstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom.  This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.

    3/18/2019Ari Turner, Technion

    Video

    Title:  Trapping Excitations at Phantasmagoric Wave Vectors

    Abstract:  This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this, and also introduce “finite fields”, which are the number systems one needs to define exponentials mod. 2.

    4/1/2019Yi-Zhuang You (UCSD)Title: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points

    Abstract: Noether’s theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s  theorem at the deconfined quantum critical point (DQCP), which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.

    4/8/2019Adam Nahum (Oxford)Title: Emergent statistical mechanics of entanglement in random unitary circuits

    Abstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.

    4/16/2019

    Lyman 425

    1:30pm

    Xie Chen (Calthech)Title: Foliated Fracton Order

    Abstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk, I will present a new framework, which we call the “foliated fracton order”, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models, but also points to the direction of search for interesting new features.

    4/24/2019

    10:30am

    Michael Freedman (Microsoft Station Q)

    Video

    Title: Quantum cellular automata in higher dimensions

    Abstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.

    4/26/2019

    10:30am

    Maissam Barkeshli (University of Maryland)

    Video

    Title: Relative anomalies in (2+1)D symmetry enriched topological states

    Abstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.

    5/3/2019Yuan-Ming Lu (Ohio State)Title: Spontaneous symmetry breaking from anyon condensation

    Abstract: In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

    5/9/2019

    10:30am

    Michael Zaletel (UC Berkeley)Title: Three-partite entanglement in CFTs and chiral topological orders

    Abstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement, multi-partite entanglement is far richer, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure, the “entanglement of purification,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders, and solicit the audience’s help in proving or disproving it.

    5/28/2019

    10:30am

    Masaki Oshikawa (U Tokyo)Title: Gauge invariance, polarization, and conductivity

     

    Abstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors, and also to general constraints on the electric conductivity.

    7/18/2019Eslam Khalaf (Harvard)

    Title: Dynamical correlations in anomalous disordered wires

    Abstract: In a (multichannel) disordered wire, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case, the classical dynamics are described by diffusion + drift, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.
    The problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.
    The mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.
  • Seminars

    Seminars Colloquia & Seminar
    Spacetime and Quantum Mechanics Seminar

    5:38 pm
    11/01/2019

    As part of the program on Spacetime and Quantum Mechanics, the CMSA will be hosting a weekly seminar on Thursdays at 2:30pm in room G10.

    DateSpeakerTitle/Abstract
    9/12/2019Pasha Pylyavskyy (University of Minnesota)Title: Vector-relation configurations and plabic graphs
    19/18/2019

    2:00pm

    G02

    Francis Brown (University of Oxford)Title: Amplitudes, Polylogs and Moduli Spaces
    9/19/2019Chuck Doran (University of Alberta)Title: Calabi-Yau geometry of the N-loop sunset Feynman integrals

    Abstract: I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals.

    Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli.

    These include: (1) an iterated fibration structure which allows one to “bootstrap” both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (“jump loci”) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via “creative telescoping”; and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties.

    Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev.

    9/26/2019Tomasz Taylor (Northeastern)Title: Celestial Amplitudes
    10/3/2019Simon Caron-Huot (McGill)Title: Poincare Duals of Feynman Integrals
    10/10/2019

    3:30pm

    Yutin Huang (National Taiwan University)Title: Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian
    10/15/2019

    Tuesday

    3:30pm

     

    Sergey Fomin (Univ. of Michigan)

     

    Title: “Morsifications and mutations” (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston). 
    10/18/2019

    Friday 

    G02

    Sebastian Franco (The City College of New York)Title: Graded quivers, generalized dimer models, and topic geometry
    10/31/2019Junjie Rao (Albert Einstein Institute)Title: All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
    11/1/2019

    SC 232

    1:30pm

    George Lusztig (MIT)Title: Total positivity in Springer fibres
    11/12/2019

    Tuesday

    G02

    3:30pm

     

    Pierpaolo Mastrolia (University of Padova)

    Title: Feynman Integrals and Intersection Theory
    11/14/2019

    G02

    Pierpaolo Mastrolia (University of Padova)Title: Feynman Integrals and Intersection Theory Pt. II
    11/21/2019Cristian Vergu (Niels Bohr Institute)Title: The Octagonal Alphabet
    11/26/2019Stephan Stieberger (IAS)Title: Strings on the Celestial Sphere
    12/4/2019Hadleigh Frost (Oxford)Title: BCJ numerators, $\mathcal{M}_{0,n}$, and ABHY

    Abstract: We relate the BCJ numerator Jacobi property to the classical fact that the top homology group of $\mathcal{M}_{0,n}$ is isomorphic to a component of the free Lie algebra. We describe ways to get BCJ numerators, and caution that the BCJ Jacobi property doesn’t imply the existence of what has been called a ‘kinematic algebra.’

     12/5/2019David Kosower (IAS)Title: From scattering amplitudes to classical observables
    12/10/2019Ramis Movassagh (MIT)Title: Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law

    Abstract: In recent years, there has been a surge of activities in proposing “exactly solvable” quantum spin chains with surprising high amount of ground state entanglement–exponentially more than the critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $\sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and ‘generic’ aspects of local spin chains.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-05-2016 Random Matrix & Probability Theory Seminar

    5:41 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/10/2018 Math-Physics Seminar

    5:41 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    5:42 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3/14/2019 Random Matrix and Probability Theory Seminar

    5:45 pm
    11/01/2019
  • Seminars
    5:48 pm
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
    5:52 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/17/2018 Math-Physics Seminar

    5:53 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/24/2018 Math-Physics Seminar

    5:55 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    5:56 pm
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
    5:59 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Workshop on Additive Combinatorics, Oct. 2-6, 2017
    6:00 pm-6:01 pm
    11/01/2019-10/06/2017

    The workshop on additive combinatorics will take place October 2-6, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    Additive combinatorics is a mathematical area bordering on number theory, discrete mathematics, harmonic analysis and ergodic theory. It has achieved a number of successes in pure mathematics in the last two decades in quite diverse directions, such as:

    • The first sensible bounds for Szemerédi’s theorem on progressions (Gowers);
    • Linear patterns in the primes (Green, Tao, Ziegler);
    • Construction of expanding sets in groups and expander graphs (Bourgain, Gamburd);
    • The Kakeya Problem in Euclidean harmonic analysis (Bourgain, Katz, Tao).

    Ideas and techniques from additive combinatorics have also had an impact in theoretical computer science, for example

    • Constructions of pseudorandom objects (eg. extractors and expanders);
    • Constructions of extremal objects (eg. BCH codes);
    • Property testing (eg. testing linearity);
    • Algebraic algorithms (eg. matrix multiplication).

    The main focus of this workshop will be to bring together researchers involved in additive combinatorics, with a particular inclination towards the links with theoretical computer science. Thus it is expected that a major focus will be additive combinatorics on the boolean cube (Z/2Z)^n , which is the object where the exchange of ideas between pure additive combinatorics and theoretical computer science is most fruitful. Another major focus will be the study of pseudorandom phenomena in additive combinatorics, which has been an important contributor to modern methods of generating provably good randomness through deterministic methods. Other likely topics of discussion include the status of major open problems (the polynomial Freiman-Ruzsa conjecture, inverse theorems for the Gowers norms with bounds, explicit correlation bounds against low degree polynomials) as well as the impact of new methods such as the introduction of algebraic techniques by Croot–Pach–Lev and Ellenberg–Gijswijt.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Ben GreenSwastik KoppartyRyan O’DonnellTamar Ziegler.

    Monday, October 2

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast 
    9:30-10:20amJacob FoxTower-type bounds for Roth’s theorem with popular differences

    Abstract: A famous theorem of Roth states that for any $\alpha > 0$ and $n$ sufficiently large in terms of $\alpha$, any subset of $\{1, \dots, n\}$ with density $\alpha$ contains a 3-term arithmetic progression. Green developed an arithmetic regularity lemma and used it to prove that not only is there one arithmetic progression, but in fact there is some integer $d > 0$ for which the density of 3-term arithmetic progressions with common difference $d$ is at least roughly what is expected in a random set with density $\alpha$. That is, for every $\epsilon > 0$, there is some $n(\epsilon)$ such that for all $n > n(\epsilon)$ and any subset $A$ of $\{1, \dots, n\}$ with density $\alpha$, there is some integer $d > 0$ for which the number of 3-term arithmetic progressions in $A$ with common difference $d$ is at least $(\alpha^3-\epsilon)n$. We prove that $n(\epsilon)$ grows as an exponential tower of 2’s of height on the order of $\log(1/\epsilon)$. We show that the same is true in any abelian group of odd order $n$. These results are the first applications of regularity lemmas for which the tower-type bounds are shown to be necessary.

    The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

    10:20-11:00amCoffee Break 
    11:00-11:50amYufei ZhaoTower-type bounds for Roth’s theorem with popular differences

    Abstract:  Continuation of first talk by Jacob Fox. The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

    12:00-1:30pmLunch 
    1:30-2:20pmJop BriëtLocally decodable codes and arithmetic progressions in random settings

    Abstract: This talk is about a common feature of special types of error correcting codes, so-called locally decodable codes (LDCs), and two problems on arithmetic progressions in random settings, random differences in Szemerédi’s theorem and upper tails for arithmetic progressions in a random set in particular. It turns out that all three can be studied in terms of the Gaussian width of a set of vectors given by a collection of certain polynomials. Using a matrix version of the Khintchine inequality and a lemma that turns such polynomials into matrices, we give an alternative proof for the best-known lower bounds on LDCs and improved versions of prior results due to Frantzikinakis et al. and Bhattacharya et al. on arithmetic progressions in the aforementioned random settings.

    Joint work with Sivakanth Gopi

    2:20-3:00pmCoffee Break 
    3:00-3:50pmFernando Shao

    Large deviations for arithmetic progressions

    Abstract: We determine the asymptotics of the log-probability that the number of k-term arithmetic progressions in a random subset of integers exceeds its expectation by a constant factor. This is the arithmetic analog of subgraph counts in a random graph. I will highlight some open problems in additive combinatorics that we encountered in our work, namely concerning the “complexity” of the dual functions of AP-counts.

    4:00-6:00pmWelcome Reception

    Tuesday, October 3

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amEmanuele ViolaInterleaved group products

    Authors: Timothy Gowers and Emanuele Viola

    Abstract: Let G be the special linear group SL(2,q). We show that if (a1,a2) and (b1,b2) are sampled uniformly from large subsets A and B of G^2 then their interleaved product a1 b1 a2 b2 is nearly uniform over G. This extends a result of Gowers (2008) which corresponds to the independent case where A and B are product sets. We obtain a number of other results. For example, we show that if X is a probability distribution on G^m such that any two coordinates are uniform in G^2, then a pointwise product of s independent copies of X is nearly uniform in G^m, where s depends on m only. Similar statements can be made for other groups as well.

    These results have applications in computer science, which is the area where they were first sought by Miles and Viola (2013).

    10:20-11:00amCoffee Break
    11:00-11:50amVsevolod LevOn Isoperimetric Stability

    Abstract: We show that a non-empty subset of an abelian group with a small edge boundary must be large; in particular, if $A$ and $S$ are finite, non-empty subsets of an abelian group such that $S$ is independent, and the edge boundary of $A$ with respect to $S$ does not exceed $(1-c)|S||A|$ with a real $c\in(0,1]$, then $|A|\ge4^{(1-1/d)c|S|}$, where $d$ is the smallest order of an element of $S$. Here the constant $4$ is best possible.

    As a corollary, we derive an upper bound for the size of the largest independent subset of the set of popular differences of a finite subset of an abelian group. For groups of exponent $2$ and $3$, our bound translates into a sharp estimate for the additive  dimension of the popular difference set.

    We also prove, as an auxiliary result, the following estimate of possible independent interest: if $A\subseteq{\mathbb Z}^n$ is a finite, non-empty downset, then, denoting by $w(z)$ the number of non-zero components of the vector $z\in\mathbb{Z}^n$, we have   $$ \frac1{|A|} \sum_{a\in A} w(a) \le \frac12\, \log_2 |A|. $$

    12:00-1:30pmLunch
    1:30-2:20pmElena GrigorescuNP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem

    Abstract: I will discuss the complexity of decoding Reed-Solomon codes, and some results establishing NP-hardness for asymptotically smaller decoding radii than the maximum likelihood decoding radius. These results follow from the study of a generalization of the classical Subset Sum problem to higher moments, which may be of independent interest. I will further discuss a connection with the Prouhet-Tarry-Escott problem studied in Number Theory, which turns out to capture a main barrier in extending our techniques to smaller radii.

    Joint work with Venkata Gandikota and Badih Ghazi.

    2:20-3:00pmCoffee Break
    3:00-3:50pmSean PrendivillePartition regularity of certain non-linear Diophantine equations.

    Abstract:  We survey some results in additive Ramsey theory which remain valid when variables are restricted to sparse sets of arithmetic interest, in particular the partition regularity of a class of non-linear Diophantine equations in many variables.

    Wednesday, October 4

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast 
    9:30-10:20amOlof SisaskBounds on capsets via properties of spectra

    Abstract: A capset in F_3^n is a subset A containing no three distinct elements x, y, z satisfying x+z=2y. Determining how large capsets can be has been a longstanding problem in additive combinatorics, particularly motivated by the corresponding question for subsets of {1,2,…,N}. While the problem in the former setting has seen spectacular progress recently through the polynomial method of Croot–Lev–Pach and Ellenberg–Gijswijt, such progress has not been forthcoming in the setting of the integers. Motivated by an attempt to make progress in this setting, we shall revisit the approach to bounding the sizes of capsets using Fourier analysis, and in particular the properties of large spectra. This will be a two part talk, in which many of the ideas will be outlined in the first talk, modulo the proof of a structural result for sets with large additive energy. This structural result will be discussed in the second talk, by Thomas Bloom, together with ideas on how one might hope to achieve Behrend-style bounds using this method.

    Joint work with Thomas Bloom.

    10:20-11:00amCoffee Break 
    11:00-11:50amThomas BloomBounds on capsets via properties of spectra

    This is a continuation of the previous talk by Olof Sisask.

    12:00-1:30pmLunch 
    1:30-2:20pmHamed HatamiPolynomial method and graph bootstrap percolation

    Abstract: We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori and multidimensional grids (in particular hypercubes). The former answers a question of Morrison and Noel, and the latter provides an alternative and simpler proof for one of their main results. This is based on a joint work with Lianna Hambardzumyan and Yingjie Qian.

    2:20-3:00pmCoffee Break
    3:00-3:50pmArnab BhattacharyyaAlgorithmic Polynomial Decomposition

    Abstract: Fix a prime p. Given a positive integer k, a vector of positive integers D = (D_1, …, D_k) and a function G: F_p^k → F_p, we say a function P: F_p^n → F_p admits a (k, D, G)-decomposition if there exist polynomials P_1, …, P_k: F_p^n -> F_p with each deg(P_i) <= D_i such that for all x in F_p^n, P(x) = G(P_1(x), …, P_k(x)). For instance, an n-variate polynomial of total degree d factors nontrivially exactly when it has a (2, (d-1, d-1), prod)-decomposition where prod(a,b) = ab.

    When show that for any fixed k, D, G, and fixed bound d, we can decide whether a given polynomial P(x_1, …, x_n) of degree d admits a (k,D,G)-decomposition and if so, find a witnessing decomposition, in poly(n) time. Our approach is based on higher-order Fourier analysis. We will also discuss improved analyses and algorithms for special classes of decompositions.

    Joint work with Pooya Hatami, Chetan Gupta and Madhur Tulsiani.

    Thursday, October 5

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amMadhur TulsianiHigher-order Fourier analysis and approximate decoding of Reed-Muller codes

     Abstract: Decomposition theorems proved by Gowers and Wolf provide an appropriate notion of “Fourier transform” for higher-order Fourier analysis. I will discuss some questions and techniques that arise from trying to develop polynomial time algorithms for computing these decompositions.

    I will discuss constructive proofs of these decompositions based on boosting, which reduce the problem of computing these decompositions to a certain kind of approximate decoding problem for codes. I will also discuss some earlier and recent works on this decoding problem.

    Based on joint works with Arnab Bhattacharyya, Eli Ben-Sasson, Pooya Hatami, Noga Ron-Zewi and Julia Wolf.

    10:20-11:00amCoffee Break
    11:00-11:50amJulia WolfStable arithmetic regularity

    The arithmetic regularity lemma in the finite-field model, proved by Green in 2005, states that given a subset A of a finite-dimensional vector space over a prime field, there exists a subspace H of bounded codimension such that A is Fourier-uniform with respect to almost all cosets of H. It is known that in general, the growth of the codimension of H is required to be of tower type depending on the degree of uniformity, and that one must allow for a small number of non-uniform cosets.

    Our main result is that, under a natural model-theoretic assumption of stability, the tower-type bound and non-uniform cosets in the arithmetic regularity lemma are not necessary.  Specifically, we prove an arithmetic regularity lemma for k-stable subsets in which the bound on the codimension of the subspace is a polynomial (depending on k) in the degree of uniformity, and in which there are no non-uniform cosets.

    This is joint work with Caroline Terry.

    12:00-1:30pmLunch 
    1:30-2:20pmWill Sawin

    Constructions of Additive Matchings

    Abstract: I will explain my work, with Robert Kleinberg and David Speyer, constructing large tri-colored sum-free sets in vector spaces over finite fields, and how it shows that some additive combinatorics problems over finite fields are harder than corresponding problems over the integers. 

    2:20-3:00pmCoffee Break
    3:00-3:50pmMei-Chu ChangArithmetic progressions in multiplicative groups of finite fields

    Abstract:   Let G be a multiplicative subgroup of the prime field F_p of size |G|> p^{1-\kappa} and r an arbitrarily fixed positive integer. Assuming \kappa=\kappa(r)>0 and p large enough, it is shown that any proportional subset A of G contains non-trivial arithmetic progressions of length r.

    Friday, October 6

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amAsaf FerberOn a resilience version of the Littlewood-Offord problem

    Abstract:  In this talk we consider a resilience version of the classical Littlewood-Offord problem. That is, consider the sum X=a_1x_1+…a_nx_n, where the a_i-s are non-zero reals and x_i-s are i.i.d. random variables with     (x_1=1)= P(x_1=-1)=1/2. Motivated by some problems from random matrices, we consider the question: how many of the x_i-s  can we typically allow an adversary to change without making X=0? We solve this problem up to a constant factor and present a few interesting open problems.

    Joint with: Afonso Bandeira (NYU) and Matthew Kwan (ETH, Zurich).

    10:20-11:00amCoffee Break
    11:00-11:50amKaave HosseiniProtocols for XOR functions and Entropy decrement

    Abstract: Let f:F_2^n –> {0,1} be a function and suppose the matrix M defined by M(x,y) = f(x+y) is partitioned into k monochromatic rectangles.  We show that F_2^n can be partitioned into affine subspaces of co-dimension polylog(k) such that f is constant on each subspace. In other words, up to polynomial factors, deterministic communication complexity and parity decision tree complexity are equivalent.

    This relies on a novel technique of entropy decrement combined with Sanders’ Bogolyubov-Ruzsa lemma.

    Joint work with Hamed Hatami and Shachar Lovett

    12:00-1:30pmLunch
    1:30-2:20pmGuy Kindler

    From the Grassmann graph to Two-to-Two games

    Abstract: In this work we show a relation between the structure of the so called Grassmann graph over Z_2 and the Two-to-Two conjecture in computational complexity. Specifically, we present a structural conjecture concerning the Grassmann graph (together with an observation by Barak et. al., one can view this as a conjecture about the structure of non-expanding sets in that graph) which turns out to imply the Two-to-Two conjecture.

    The latter conjecture its the lesser-known and weaker sibling of the Unique-Games conjecture [Khot02], which states that unique games (a.k.a. one-to-one games) are hard to approximate. Indeed, if the Grassmann-Graph conjecture its true, it would also rule out some attempts to refute the Unique-Games conjecture, as these attempts provide potentially efficient algorithms to solve unique games, that would actually also solve two-to-two games if they work at all.

    These new connections between the structural properties of the Grassmann graph and complexity theoretic conjectures highlight the Grassmann graph as an interesting and worthy object of study. We may indicate some initial results towards analyzing its structure.

    This is joint work with Irit Dinur, Subhash Khot, Dror Minzer, and Muli Safra.

  • CMSA EVENT: Current Developments In Mathematics 2018
    6:00 pm-5:00 pm
    11/01/2019-11/17/2018
    CDM2018

    Current Developments in Mathematics 2018 Conference.

    Friday, Nov. 16, 2018 2:15 pm – 6:00 pm

    Saturday, Nov. 17, 2018  9:00 am – 5:00 pm

    Harvard University Science Center, Hall B

    Visit the conference page here 

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/01/2018 Math-Physics Seminar

    6:01 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Fluid turbulence and Singularities of the Euler/ Navier Stokes equations
    6:02 pm
    11/01/2019-03/15/2018
    Fluid turbulence

    The Workshop on Fluid turbulence and Singularities of the Euler/ Navier Stokes equations will take place on March 13-15, 2019. This is the first of two workshop organized by Michael Brenner, Shmuel Rubinstein, and Tom Hou. The second, Machine Learning for Multiscale Model Reduction, will take place on March 27-29, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

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

    List of registrants

    Speakers: 

  • General Relativity Seminar
    6:03 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/08/2018 Math-Physics Seminar

    6:04 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:05 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Blockchain Conference
    6:05 pm
    11/01/2019-01/25/2018
    Blockchain

    On January 24-25, 2019 the Center of Mathematical Sciences will be hosting a conference on distributed-ledger (blockchain) technology. The conference is intended to cover a broad range of topics, from abstract mathematical aspects (cryptography, game theory, graph theory, theoretical computer science) to concrete applications (in accounting, government, economics, finance, management, medicine). The talks will take place in Science Center, Hall D.

    https://youtu.be/FyKCCutxMYo

    List of registrants

    Photos

    Speakers: 

  • Special Seminar
    6:06 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Workshop on Algebraic Methods in Combinatorics
    6:07 pm
    11/01/2019-11/17/2017

    The workshop on Algebraic Methods in Combinatorics will take place November 13-17, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    The main focus of the workshop is the application of algebraic method to study problems in combinatorics.  In recent years there has been a large number of results in which the use of algebraic technique has resulted in significant improvements to long standing open problems. Such problems include the finite field Kakeya problem, the distinct distance problem of Erdos and, more recently, the cap-set problem. The workshop will include talks on all of the above mentioned problem as well as on recent development in related areas combining combinatorics and algebra.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Zeev DvirLarry Guth, and Shubhangi Saraf.

    Click here for a list of registrants.

    Monday, Nov. 13

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Jozsef Solymosi

     

    On the unit distance problem

    Abstract: Erdos’ Unit Distances conjecture states that the maximum number of unit distances determined by n points in the plane is almost linear, it is O(n^{1+c}) where c goes to zero as n goes to infinity. In this talk I will survey the relevant results and propose some questions which would imply that the maximum number of unit distances is o(n^{4/3}). 

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

     

    Orit RazIntersection of linear subspaces in R^d and instances of the PIT problem 

    Abstract: In the talk I will tell about a new deterministic, strongly polynomial time algorithm which can be viewed in two ways. The first is as solving a derandomization problem, providing a deterministic algorithm to a new special case of the PIT (Polynomial Identity Testing) problem. The second is as computing the dimension of the span of a collection of flats in high dimensional space. The talk is based on a joint work with Avi Wigderson.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Andrew Hoon Suk

    Ramsey numbers: combinatorial and geometric

    Abstract:  In this talk, I will discuss several results on determining the tower growth rate of Ramsey numbers arising in combinatorics and in geometry.  These results are joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Janos Pach, and Benny Sudakov.

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Josh Zahl

    Cutting curves into segments and incidence geometry

    4:00-6:00pmWelcome Reception

    Tuesday, Nov. 14

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Péter Pál Pach

    Polynomials, rank and cap sets

    AbstractIn this talk we will look at a new variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like $\mathbb{Z}_4^n$ and $\mathbb{F}_q^n$ are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets and mention further applications of the method.

    10:30-11:00amCoffee Break
    11:00-12:00pmJordan Ellenberg

    The Degeneration Method

    Abstract:  In algebraic geometry, a very popular way to study (nice, innocent, nonsingular) varieties is to degenerate them to (weird-looking, badly singular, nonreduced) varieties (which are actually not even varieties but schemes.)  I will talk about some results in combinatorics using this approach (joint with Daniel Erman) and some ideas for future applications of the method.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Larry GuthThe polynomial method in Fourier analysis

    Abstract: This will be a survey talk about how the polynomial method helps to understand problems in Fourier analysis.  We will review some applications of the polynomial method to problems in combinatorial geometry.  Then we’ll discuss some problems in Fourier analysis, explain the analogy with combinatorial problems, and discuss how to adapt the polynomial method to the Fourier analysis setting.

     

    2:30-3:00pm

    Coffee Break
    3:00-4:00pmOpen Problem

    Wednesday, Nov. 15

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

     

    Avi Wigderson

    The “rank method” in arithmetic complexity: Lower bounds and barriers to lower bounds

    Abstract: Why is it so hard to find a hard function? No one has a clue! In despair, we turn to excuses called barriers. A barrier is a collection of lower bound techniques, encompassing as much as possible from those in use, together with a  proof that these techniques cannot prove any lower bound better than the state-of-art (which is often pathetic, and always very far from what we expect for complexity of random functions).

    In the setting of  Boolean computation of Boolean functions (where P vs. NP is the central open problem),  there are several famous barriers which provide satisfactory excuses, and point to directions in which techniques may be strengthened.

    In the setting of Arithmetic computation of polynomials and tensors (where  VP vs. VNP is the central open problem) we have no satisfactory barriers, despite some recent interesting  attempts.

    This talk will describe a new barrier for the Rank Method in arithmetic complexity, which encompass most lower bounds in this field. It also encompass most lower bounds on tensor rank in algebraic geometry (where the the rank method is called Flattening).

    I will describe the rank method, explain how it is used to prove lower bounds, and then explain its limits via the new barrier result. As an example, it shows that while the best lower bound on the tensor rank of any explicit 3-dimensional tensor of side n (which is achieved by a rank method) is 2n, no rank method can prove a lower bound which exceeds 8n

    (despite the fact that a random such tensor has rank quadratic in n).

    No special background knowledge is assumed. The audience is expected to come up with new lower bounds, or else, with new excuses for their absence.

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Venkat Guruswami

    Subspace evasion, list decoding, and dimension expanders

     Abstract: A subspace design is a collection of subspaces of F^n (F = finite field) most of which are disjoint from every low-dimensional subspace of F^n. This notion was put forth in the context of algebraic list decoding where it enabled the construction of optimal redundancy list-decodable codes over small alphabets as well as for error-correction in the rank-metric. Explicit subspace designs with near-optimal parameters have been constructed over large fields based on polynomials with structured roots. (Over small fields, a construction via cyclotomic function fields with slightly worse parameters is known.) Both the analysis of the list decoding algorithm as well as the subspace designs crucially rely on the *polynomial method*.

    Subspace designs have since enabled progress on linear-algebraic analogs of Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In particular, they yield an explicit construction of constant-degree dimension expanders over large fields. While constructions of such dimension expanders are known over any field, they are based on a reduction to a highly non-trivial form of vertex expanders called monotone expanders. In contrast, the subspace design approach is simpler and works entirely within the linear-algebraic realm. Further, in recent (ongoing) work, their combination with rank-metric codes yields dimension expanders with expansion proportional to the degree.

    This talk will survey these developments revolving around subspace designs, their motivation, construction, analysis, and connections.

    (Based on several joint works whose co-authors include Chaoping Xing, Swastik Kopparty, Michael Forbes, Nicolas Resch, and Chen Yuan.)

    12:00-1:30pmLunch
    1:30-2:30pm

     

    David Conlon

    Finite reflection groups and graph norms

    Abstract: For any given graph $H$, we may define a natural corresponding functional $\|.\|_H$. We then say that $H$ is norming if $\|.\|_H$ is a semi-norm. A similar notion $\|.\|_{r(H)}$ is defined by $\| f \|_{r(H)} := \| | f | \|_H$ and $H$ is said to be weakly norming if $\|.\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. Using results from the theory of finite reflection groups, we identify a much larger class of weakly norming graphs. This result includes all previous examples of weakly norming graphs and adds many more. We also discuss several applications of our results. In particular, we define and compare a number of generalisations of Gowers’ octahedral norms and we prove some new instances of Sidorenko’s conjecture. Joint work with Joonkyung Lee.

     

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Laszlo Miklós Lovasz

    Removal lemmas for triangles and k-cycles.

    Abstract: Let p be a fixed prime. A k-cycle in F_p^n is an ordered k-tuple of points that sum to zero; we also call a 3-cycle a triangle. Let N=p^n, (the size of F_p^n). Green proved an arithmetic removal lemma which says that for every k, epsilon>0 and prime p, there is a delta>0 such that if we have a collection of k sets in F_p^n, and the number of k-cycles in their cross product is at most a delta fraction of all possible k-cycles in F_p^n, then we can delete epsilon times N elements from the sets and remove all k-cycles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in particular, asked whether a polynomial bound holds. Despite considerable attention, prior to our work, the best known bound for any k, due to Fox, showed that 1/delta can be taken to be an exponential tower of twos of height logarithmic in 1/epsilon (for a fixed k).

    In this talk, we will discuss recent work on Green’s problem. For triangles, we prove an essentially tight bound for Green’s arithmetic triangle removal lemma in F_p^n, using the recent breakthroughs with the polynomial method. For k-cycles, we also prove a polynomial bound, however, the question of the optimal exponent is still open.

    The triangle case is joint work with Jacob Fox, and the k-cycle case with Jacob Fox and Lisa Sauermann.

    Thursday, Nov. 16

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Janos PachLet’s talk about multiple crossings

    Abstract: Let k>1 be a fixed integer. It is conjectured that any graph on n vertices that can be drawn in the plane without k pairwise crossing edges has O(n) edges. Two edges of a hypergraph cross each other if neither of them contains the other, they have a nonempty intersection, and their union is not the whole vertex set. It is conjectured that any hypergraph on n vertices that contains no k pairwise crossing edges has at most O(n) edges. We discuss the relationship between the above conjectures and explain some partial answers, including a recent result of Kupavskii, Tomon, and the speaker, improving a 40 years old bound of Lomonosov.

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Misha Rudnev

    Few products, many sums

    Abstract: This is what I like calling “weak Erd\H os-Szemer\’edi conjecture”, still wide open over the reals and in positive characteristic. The talk will focus on some recent progress, largely based on the ideas of I. D. Shkredov over the past 5-6 years of how to use linear algebra to get the best out of the Szemer\’edi-Trotter theorem for its sum-product applications. One of the new results is strengthening (modulo the log term hidden in the $\lesssim$ symbol) the textbook Elekes inequality

    $$

    |A|^{10} \ll |A-A|^4|AA|^4

    $$

    to

    $$|A|^{10}\lesssim |A-A|^3|AA|^5.$$

    The other is the bound 

    $$E(H) \lesssim |H|^{2+\frac{9}{20}}$$ for additive energy of sufficiently small multiplicative subgroups in $\mathbb F_p$.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Adam Sheffer

    Geometric Energies: Between Discrete Geometry and Additive Combinatorics

    Abstract: We will discuss the rise of geometric variants of the concept of Additive energy. In recent years such variants are becoming more common in the study of Discrete Geometry problems. We will survey this development and then focus on a recent work with Cosmin Pohoata. This work studies geometric variants of additive higher moment energies, and uses those to derive new bounds for several problems in Discrete Geometry.  

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Boris Bukh

    Ranks of matrices with few distinct entries

    Abstract: Many applications of linear algebra method to combinatorics rely on the bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these application. I will also present a classification of sets L for which no low-rank matrix with entries in L exists.

    Friday, Nov. 17

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Benny Sudakov

    Submodular minimization and set-systems with restricted intersections

    AbstractSubmodular function minimization is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint types under which it remains efficiently solvable. The arguably most relevant non-trivial constraint class for which polynomial algorithms are known are parity constraints, i.e., optimizing submodular function only over sets of odd (or even) cardinality. Parity constraints capture classical combinatorial optimization problems like the odd-cut problem, and they are a key tool in a recent technique to efficiently solve integer programs with a constraint matrix whose subdeter-minants are bounded by two in absolute value.

    We show that efficient submodular function minimization is possible even for a significantly larger class than parity constraints, i.e., over all sets (of any given lattice) of cardinality r mod m, as long as m is a constant prime power. To obtain our results, we combine tools from Combinatorial Optimization, Combinatorics, and Number Theory. In particular, we establish an interesting connection between the correctness of a natural algorithm, and the non-existence of set systems with specific intersection properties.

    Joint work with M. Nagele and R. Zenklusen

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Robert Kleinberg 

    Explicit sum-of-squares lower bounds via the polynomial method

    AbstractThe sum-of-squares (a.k.a. Positivstellensatz) proof system is a powerful method for refuting systems of multivariate polynomial inequalities, i.e. proving that they have no solutions. These refutations themselves involve sum-of-squares (sos) polynomials, and while any unsatisfiable system of inequalities has a sum-of-squares refutation, the sos polynomials involved might have arbitrarily high degree. However, if a system admits a refutation where all polynomials involved have degree at most d, then the refutation can be found by an algorithm with running time polynomial in N^d, where N is the combined number of variables and inequalities in the system.

    Low-degree sum-of-squares refutations appear throughout mathematics. For example, the above proof search algorithm captures as a special case many a priori unrelated algorithms from theoretical computer science; one example is Goemans and Williamson’s algorithm to approximate the maximum cut in a graph. Specialized to extremal graph theory, they become equivalent to flag algebras. They have also seen practical use in robotics and optimal control.

    Therefore, it is of interest to identify “hard” systems of low-degree polynomial inequalities that have no solutions but also have no low-degree sum-of-squares refutations. Until recently, the only known examples were either not explicit (i.e., known to exist by non-constructive means such as the probabilistic method) or not robust (i.e., a system is constructed which is not refutable by degree d sos polynomials, but becomes refutable when perturbed by an amount tending to zero with d). We present a new family of instances derived from the cap-set problem, and we show a super-constant lower bound on the degree of its sum-of-squares refutations. Our instances are both explicit and robust.

    This is joint work with Sam Hopkins.

    12:00-1:30pmLunch

     

  • Special Seminar
    6:10 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:11 pm-6:12 pm
    11/01/2019-10/25/2016

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/10/2018 RM & PT Seminar

    6:11 pm
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
    6:12 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-03-16 Mathematical Physics Seminar

    6:13 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/15/2018 Topology Seminar

    6:14 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/15/2018 Math Physics Seminar

    6:15 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-12-2016 Random Matrix & Probability Theory Seminar

    6:16 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:17 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-24-2016 Random Matrix & Probability Theory Seminar

    6:18 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/30/2018 RM & PT Seminar

    6:19 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:19 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:20 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-19-2016 Random Matrix & Probability Theory Seminar

    6:22 pm
    11/01/2019

    No additional detail for this event.

  • Member Seminar
    6:24 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/22/2018 Mathematical Physics Seminar

    6:24 pm
    11/01/2019
  • Member Seminar
    6:26 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-26-2016 Random Matrix & Probability Theory Seminar

    6:27 pm
    11/01/2019

    No additional detail for this event.

  • Member Seminar
    6:29 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-24-16 Mathematical Physics Seminar

    6:30 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    6:32 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    6:34 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:36 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-19-2016 Random Matrix & Probability Theory Seminar

    6:37 pm
    11/01/2019

    No additional detail for this event.

  • Member Seminar
    6:40 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-17-16 Mathematical Physics Seminar

    6:41 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-26-2016 Random Matrix & Probability Theory Seminar

    6:46 pm
    11/01/2019

    No additional detail for this event.

  • Member Seminar
    6:52 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-24-16 Mathematical Physics Seminar

    6:53 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    6:54 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    6:59 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    7:00 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    7:03 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-31-16 Mathematical Physics Seminar

    7:05 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12/10/2018 Mathematical Physics Seminar

    8:42 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    12/10/2018 Topology Seminar

    8:43 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    12/12/2018 Hodge Seminar

    8:43 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar
    8:45 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    1/16/2019 Hodge Seminar

    8:46 pm
    11/01/2019

    No additional detail for this event.

  • Fluid Dynamics Seminar

    Fluid Dynamics Seminar
    4/3/2019 Fluid Dynamics Seminar

    8:54 pm
    11/01/2019

    No additional detail for this event.

  • Program
    9:39 pm
    11/01/2019-12/18/2014

    arge random matrices provide some of the simplest models for large, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a rigorous understanding of universality in the case of orthogonal, Hermitian, or symplectic matrices with independent entries, resolving a conjecture of Wigner-Dyson-Mehta dating back 50 years. These new developments have exploited techniques from a wide range of mathematical areas in addition to probability, including combinatorics, partial differential equations, and hydrodynamic limits. It is hoped that these new techniques will be useful in the analysis of universal behaviour in matrix ensembles with more complicated structure such as random regular graph models, or 2D matrix ensembles, as well as more physically relevant systems such as band matrices and random Schroedinger-type Hamiltonians. For some of these models, results in the direction of universality have already been obtained.

    Here is a partial list of the mathematicians who are participating in this program

  • Program
    9:44 pm
    11/01/2019-12/28/2013

    During Academic year 2018-19, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines.

    As part of the Program, the CMSA will be hosting two workshops:

    .

    Additionally, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

    Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program
    NameTentative Visiting Dates

    Jason Alicea

    11/12/2018-11/16/2018
    Maissam Barkeshli4/22/2019 – 4/26/2019
    Xie Chen4/15-17/2019 4/19-21/2019 4/24-30/2019

    Lukasz Fidkowski

    1/7/2019-1/11/2019

    Zhengcheng Gu

    8/15/2018-8/30/2018 & 5/9/2019-5/19/2019

    Yin Chen He

    10/14/2018-10/27/2018
    Anton Kapustin8/26/2018-8/30/2018 & 3/28/2019-4/5/2019

    Michael Levin

    3/11/2019-3/15/2019
    Yuan-Ming Lu4/29/2019-6/01/2019

    Adam Nahum

    4/2/2019- 4/19/2019

    Masaki Oshikawa

    4/22/2019-5/22/2019
    Chong Wang 10/22/2018-11/16/2018

    Juven Wang

    4/1/2019-4/16/2019
    Cenke Xu 8/26/2018-10/1/2018

    Yi-Zhuang You

    4/1/2019-4/19/2019

    Mike Zaletel

    5/1/2019-5/10/2019
  • Program
    9:45 pm-9:46 pm
    11/01/2019-12/31/2010

    During Academic year 2018-19, the CMSA will be hosting a Program on Mathematical Biology.

    Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape.

    In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. And in mathematics and computation, there has been a revolution in terms of posing and solving problems at the intersection of computational geometry, statistics and inference.  So, how far are we from realizing a descriptive, predictive and controllable theory of biological shape?

    In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems

    The CMSA will be hosting three workshops as part of this program. The Workshop on Morphometrics, Morphogenesis and Mathematics will take place on October 22-26. 

    A workshop on Morphogenesis: Geometry and Physics will take place on December 3-6, 2018.

    A workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

  • Program
    9:48 pm
    11/01/2019-12/31/2010

    Recent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during fall 2019, with between 20-30 participants. They will also invite 10-20 longer-term visitors throughout the semester. Additionally, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10.

    Organizers:

    .

    Workshops:

     

    Here is a partial list of the mathematicians and physicists who have indicated that they will attend part or all of this special program as a visitor:

  • Program
    9:49 pm
    11/01/2019-12/23/2010

    The Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry, Symplectic geometry, Arithmetic geometry, Quantum topology and mathematical aspects of high energy physics, specially string theory with the goal of proving the homological mirror symmetry conjecture (HMS) in full generality and explore its applications. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model). We are happy to announce that the Simons Foundation has agreed to renew funding for the HMS collaboration program for three additional years.

    A brief induction of the Brandeis-Harvard CMSA HMS/SYZ research agenda and team members are as follow:


    Directors:


    Shing-Tung Yau (Harvard University)

    Born in Canton, China, in 1949, S.-T. Yau grew up in Hong Kong, and studied in the Chinese University of Hong Kong from 1966 to 1969. He did his PhD at UC Berkeley from 1969 to 1971, as a student of S.S. Chern. He spent a year as a postdoc at the Institute for Advanced Study in Princeton, and a year as assistant professor at SUNY at Stony Brook. He joined the faculty at Stanford in 1973. On a Sloan Fellowship, he spent a semester at the Courant Institute in 1975. He visited UCLA the following year, and was offered a professorship at UC Berkeley in 1977. He was there for a year, before returning to Stanford. He was a plenary speaker at the 1978 ICM in Helsinki. The following year, he became a faculty member at the IAS in Princeton. He moved to UCSD in 1984. Yau came to Harvard in 1987, and was appointed the Higgins Professor of Mathematics in 1997. He has been at Harvard ever since. Yau has received numerous prestigious awards and honors throughout his career. He was named a California Scientist of the Year in 1979. In 1981, he received a Oswald Veblen Prize in Geometry and a John J. Carty Award for the Advancement of Science, and was elected a member of the US National Academy of Sciences. In 1982, he received a Fields Medal for “his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex MongeAmpre equations”. He was named Science Digest, America’s 100 Brightest Scientists under 40, in 1984. In 1991, he received a Humboldt Research Award from the Alexander von Humboldt Foundation in Germany. He was awarded a Crafoord Prize in 1994, a US National Medal of Science in 1997, and a China International Scientific and Technological Cooperation Award, for “his outstanding contribution to PRC in aspects of making progress in sciences and technology, training researchers” in 2003. In 2010, he received a Wolf Prize in Mathematics, for “his work in geometric analysis and mathematical physics”. Yau has also received a number of research fellowships, which include a Sloan Fellowship in 1975-1976, a Guggenheim Fellowship in 1982, and a MacArthur Fellowship in 1984-1985. Yau’s research interests include differential and algebraic geometry, topology, and mathematical physics. As a graduate student, he started to work on geometry of manifolds with negative curvature. He later became interested in developing the subject of geometric analysis, and applying the theory of nonlinear partial differential equations to solve problems in geometry, topology, and physics. His work in this direction include constructions of minimal submanifolds, harmonic maps, and canonical metrics on manifolds. The most notable, and probably the most influential of this, was his solution of the Calabi conjecture on Ricci flat metrics, and the existence of Kahler-Einstein metrics. He has also succeeded in applying his theory to solve a number of outstanding conjectures in algebraic geometry, including Chern number inequalities, and the rigidity of complex structures of complex projective spaces. Yau’s solution to the Calabi conjecture has been remarkably influential in mathematical physics over the last 30 years, through the creation of the theory of Calabi-Yau manifolds, a theory central to mirror symmetry. He and a team of outstanding mathematicians trained by him, have developed many important tools and concepts in CY geometry and mirror symmetry, which have led to significant progress in deformation theory, and on outstanding problems in enumerative geometry. Lian, Yau and his postdocs have developed a systematic approach to study and compute period integrals of CY and general type manifolds. Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula of Candelas et al for worldsheet instantons on the quintic threefold. In the course of understanding mirror symmetry, Strominger, Yau, and Zaslow proposed a new geometric construction of mirror symmetry, now known as the SYZ construction. This has inspired a rapid development in CY geometry over the last two decades. In addition to CY geometry and mirror symmetry, Yau has done influential work on nonlinear partial differential equations, generalized geometry, Kahler geometry, and general relativity. His proof of positive mass conjecture is a widely regarded as a cornerstone in the classical theory of general relativity. In addition to publishing well over 350 research papers, Yau has trained more than 60 PhD students in a broad range of fields, and mentored dozens of postdoctoral fellows over the last 40 years.


    Professor Bong Lian (Brandeis University)

    BongBorn in Malaysia in 1962, Bong Lian completed his PhD in physics at Yale University under the direction of G. Zuckerman in 1991. He joined the permanent faculty at Brandeis University in 1995, and has remained there since. Between 1995 and 2013, he had had visiting research positions at numerous places, including the National University of Taiwan, Harvard University, and Tsinghua University. Lian received a J.S. Guggenheim Fellowship in 2003. He was awarded a Chern Prize at the ICCM in Taipei in 2013, for his “influential and fundamental contributions in mathematical physics, in particular in the theory of vertex algebras and mirror symmetry.” He has also been co-Director, since 2014, of the Tsinghua Mathcamp, a summer outreach program launched by him and Yau for mathematically talented teenagers in China. Since 2008, Lian has been the President of the International Science Foundation of Cambridge, a non-profit whose stated mission is “to provide financial and logistical support to scholars and universities, to promote basic research and education in mathematical sciences, especially in the Far East.” Over the last 20 years, he has mentored a number of postdocs and PhD students. His research has been supported by an NSF Focused Research Grant since 2009. Published in well over 60 papers over 25 years, Lian’s mathematical work lies in the interface between representation theory, Calabi-Yau geometry, and string theory. Beginning in the late 80’s, Lian, jointly with Zuckerman, developed the theory of semi-infinite cohomology and applied it to problems in string theory. In 1994, he constructed a new invariant (now known as the Lian- Zuckerman algebra) of a topological vertex algebra, and conjectured the first example of a G algebra in vertex algebra theory. The invariant has later inspired a new construction of quantum groups by I. Frenkel and A. Zeitlin, as semi-infinite cohomology of braided vertex algebras, and led to a more recent discovery of new relationships between Courant algebroids, A-algebras, operads, and deformation theory of BV algebras. In 2010, he and his students Linshaw and Song developed important applications of vertex algebras in equivariant topology. Lian’s work in CY geometry and mirror symmetry began in early 90’s. Using a characteristic p version of higher order Schwarzian equations, Lian and Yau gave an elementary proof that the instanton formula of Candelas et al implies Clemens’s divisibility conjecture for the quintic threefold, for infinitely many degrees. In 1996, Lian (jointly with Hosono and Yau) answered the so-called Large Complex Structure Limit problem in the affirmative in many important cases. Around the same year, they announced their hyperplane conjecture, which gives a general formula for period integrals for a large class of CY manifolds, extending the formula of Candelas et al. Soon after, Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula. In 2003, inspired by mirror symmetry, Lian (jointly with Hosono, Oguiso and Yau) discovered an explicit counting formula for Fourier-Mukai partners, and settled an old problem of Shioda on abelian and K3 surfaces. Between 2009 and 2014, Lian (jointly with Bloch, Chen, Huang, Song, Srinivas, Yau, and Zhu) developed an entirely new approach to study the so-called Riemann-Hilbert problem for period integrals of CY manifolds, and extended it to general type manifolds. The approach leads to an explicit description of differential systems for period integrals with many applications. In particular, he answered an old question in physics on the completeness of Picard-Fuchs systems, and constructed new differential zeros of hypergeometric functions.


    Denis Auroux (Harvard University)

    AurouxDenis Auroux’s research concerns symplectic geometry and its applications to mirror symmetry. While his early work primarily concerned the topology of symplectic 4-manifolds, over the past decade Auroux has obtained pioneering results on homological mirror symmetry outside of the Calabi-Yau setting (for Fano varieties, open Riemann surfaces, etc.), and developed an extension of the SYZ approach to non-Calabi-Yau spaces.After obtaining his PhD in 1999 from Ecole Polytechnique (France), Auroux was employed as Chargé de Recherche at CNRS and CLE Moore Instructor at MIT, before joining the faculty at MIT in 2002 (as Assistant Professor from 2002 to 2004, and as Associate Professor from 2004 to 2009, with tenure starting in 2006). He then moved to UC Berkeley as a Full Professor in 2009.
    Auroux has published over 30 peer-reviewed articles, including several in top journals, and given 260 invited presentations about his work. He received an Alfred P. Sloan Research Fellowship in 2005, was an invited speaker at the 2010 International Congress of Mathematicians, and in 2014 he was one of the two inaugural recipients of the Poincaré Chair at IHP. He has supervised 10 PhD dissertations, won teaching awards at MIT and Berkeley, and participated in the organization of over 20 workshops and conferences in symplectic geometry and mirror symmetry.




    Senior Personnel:

    Artan Sheshmani (Harvard CMSA)

    unnamedArtan Sheshmani’s research is focused on enumerative algebraic geometry and mathematical aspects of string theory. He is interested in applying techniques in algebraic geometry, such as, intersection theory, derived category theory, and derived algebraic geometry to construct and compute the deformation invariants of algebraic varieties, in particular Gromov-Witten (GW) or Donaldson-Thomas (DT) invariants. In the past Professor Sheshmani has worked on proving modularity property of certain DT invariants of K3-fibered threefolds (as well as their closely related Pandharipande-Thomas (PT) invariants), local surface threefolds, and general complete intersection Calabi-Yau threefolds. The modularity of DT/PT invariants in this context is predicted in a famous conjecture of  string theory called S-duality modularity conjecture, and his joint work has provided the proof to some cases of it, using degenerations, virtual localizations, as well as wallcrossing techniques. Recently, Sheshmani has focused on proving a series of dualities relating the various enumerative invariants over threefolds, notably the GW invariants and invariants that arise in topological gauge theory. In particular in his joint work with Gholampour, Gukov, Liu, Yau he studied DT gauge theory and its reductions to D=4 and D=2 which are equivalent to local theory of surfaces in Calabi-Yau threefolds. Moreover, in a recent joint work with Yau and Diaconescu, he has studied the construction and computation of DT invariants of Calabi-Yau fourfolds via a suitable derived categorical reduction of the theory to the DT theory of threefolds. Currently Sheshmani is interested in a wide range of problems in enumerative geometry of CY varieties in dimensions 3,4,5.

    Artan has received his PhD and Master’s degrees in pure mathematics under Sheldon Katz and Thomas Nevins from the University of Illinois at Urbana Champaign (USA) in 2011 and 2008 respectively. He holds a Master’s degree in Solid Mechanics (2004) and two Bachelor’s degrees, in Mechanical Engineering and Civil Engineering from the Sharif University of Technology, Tehran, Iran.  Artan has been a tenured Associate Professor of Mathematics with joint affiliation at Harvard CMSA and center for Quantum Geometry of Moduli Spaces (QGM), since 2016. Before that he has held visiting Associate Professor and visiting Assistant Professor positions at MIT.

    An Huang (Brandeis University)

    unnamedThe research of An Huang since 2011 has been focused on the interplay between algebraic geometry, the theory of special functions and mirror symmetry. With S. Bloch, B. Lian, V. Srinivas, S.-T. Yau, X. Zhu, he has developed the theory of tautological systems, and has applied it to settle several important problems concerning period integrals in relation to mirror symmetry. With B. Lian and X. Zhu, he has given a precise geometric interpretation of all solutions to GKZ systems associated to Calabi-Yau hypersurfaces in smooth Fano toric varieties. With B. Lian, S.-T. Yau, and C.-L. Yu, he has proved a conjecture of Vlasenko concerning an explicit formula for unit roots of the zeta functions of hypersurfaces, and has further related these roots to p-adic interpolations of complex period integrals. Beginning in 2018, with B. Stoica and S.-T. Yau, he has initiated the study of p-adic strings in curved spacetime, and showed that general relativity is a consequence of the self-consistency of quantum p-adic strings. One of the goals of this study is to understand p-adic A and B models.

    An Huang received his PhD in Mathematics from the University of California at Berkeley in 2011. He was a postdoctoral fellow at the Harvard University Mathematics Department, and joined Brandeis University as an Assistant Professor in Mathematics in 2016.



    Siu Cheong Lau (Boston University)
    unnamed

    The research interest of Siu Cheong Lau lies in SYZ mirror symmetry, symplectic and algebraic geometry.  His thesis work has successfully constructed the SYZ mirrors for all toric Calabi-Yau manifolds based on quantum corrections by open Gromov-Witten invariants and their wall-crossing phenomenon.  In collaboration with N.C. Leung, H.H. Tseng and K. Chan, he derived explicit formulas for the open Gromov-Witten invariants for semi-Fano toric manifolds which have an obstructed moduli theory.  It has a beautiful relation with mirror maps and Seidel representations.   Recently he works on a local-to-global approach to SYZ mirror symmetry.  In joint works with C.H. Cho and H. Hong, he developed a noncommutative local mirror construction for immersed Lagrangians, and a natural gluing method to construct global mirrors.  The construction has been realized in various types of geometries including orbifolds, focus-focus singularities and pair-of-pants decompositions of Riemann surfaces.

    Siu-Cheong Lau has received the Doctoral Thesis Gold Award (2012) and the Best Paper Silver Award (2017) at the International Congress of Chinese Mathematicians.  He was awarded the Simons Collaboration Grant in 2018.  He received a Certificate of Teaching Excellence from Harvard University in 2014.


    Affiliates:

    • Netanel Rubin-Blaier (Cambridge)
    • Kwokwai Chan (Chinese University of Hong Kong)
    • Mandy Cheung (Harvard University, BP)
    • Chuck Doran (University of Alberta)
    • Honsol Hong (Yonsei University)
    • Shinobu Hosono (Gakushuin University, Japan)
    • Conan Leung (Chinese University of Hong Kong)
    • Yu-shen Lin (Boston University)
    • Hossein Movassati (IMPA Brazil)
    • Arnav Tripathhy (Harvard University, BP)

     

    Postdocs:

    • Dennis Borisov
    • Tsung-Ju Lee
    • Dingxin Zhang
    • Jingyu Zhao
    • Yang Zhou

    Jobs:

    Postdoctoral Fellowship in Algebraic Geometry

    Postdoctoral Fellowship in Mathematical Sciences

     

    To learn about previous programming as part of the Simons Collaboration, click here.

  • More events
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-16-2018 Mathematical Physics Seminar
      12:00 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      1/27/2020 Math Physics Seminar
      12:00 am-1:00 pm
      11/01/2019
    • CMSA EVENT: Quantum Matter Workshop
      All day
      11/01/2019
      Layer-2-600x338

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

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

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

       

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

      Speakers:

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-9-2018 Math Physics Seminar
      12:00 am
      11/01/2019
    • Colloquium
      5:00 am
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Workshop on Quantum Information
      8:00 am-6:07 pm
      11/01/2019-04/24/2017
      banner-image-1

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

      Register for the event here.

      The following speakers are confirmed:

    • CMSA EVENT: From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
      8:30 am-5:20 pm
      11/01/2019-08/20/2018
      Mumford-3

      David_Mumford-1

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

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

      Speakers:

      Organizers:

       

      Publication:

      Pure and Applied Mathematics Quarterly

      Special Issue: In Honor of David Mumford

      Guest Editors: Ching-Li Chai, Amnon Neeman

       

    • CMSA EVENT: Big Data Conference 2018
      8:30 am-2:50 pm
      11/01/2019-08/24/2018
      1 Oxford Street, Cambridge MA 02138
      Big-Data-2018-1

       

      shutterstock_547250785-e1527881194717

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

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

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

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

      Please register here. 

      Confirmed Speakers: 

      Organizers: 

      • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
      • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
      • Richard Freeman, Herbert Ascherman Professor of Economics, Harvard University
      • Jun Liu, Professor of Statistics, Harvard University
      • Horng-Tzer Yau, Professor of Mathematics, Harvard University
    • CMSA EVENT: F-Theory Conference
      8:30 am-3:00 pm
      11/01/2019-09/30/2018

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

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

      Click here for videos of the talks. 

      Organizers:

      Speakers:

    • CMSA EVENT: Workshop on Foundations of Computational Science
      8:30 am-2:45 pm
      11/01/2019-08/31/2019
      AI-Poster-3

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

      Please register here. 

      Speakers:

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

    • CMSA EVENT: Workshop on Aspects of General Relativity
      8:30 am-3:30 pm
      11/01/2019-05/26/2017

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

      Speakers:

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

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

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

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

      Schedule:

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

      Organizers: Piotr T. Chruściel and Shing-Tung Yau

    • CMSA EVENT: Workshop on Morphometrics, Morphogenesis and Mathematics
      8:30 am-2:00 pm
      11/01/2019-10/24/2018

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

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

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

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

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

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

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

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

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

      Videos of the talks

      Confirmed Speakers:

    • CMSA EVENT: Morphogenesis: Geometry and Physics
      8:30 am-2:30 pm
      11/01/2019-12/05/2018

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

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

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

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

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

      Videos

      Please Register Here

      PDF of the Schedule

      Speakers:

    • CMSA EVENT: Geometric Analysis Approach to AI Workshop
      8:30 am-5:30 pm
      11/01/2019-01/21/2019
      Geo-Analysis-Poster-final-e1547584167900

      Geo-Analysis-1-e1543848888343

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

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

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

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

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

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

      Please register here

      Speakers: 

    • CMSA EVENT: 2019 Big Data Conference
      8:30 am-4:40 pm
      11/01/2019-08/20/2019
      1 Oxford Street, Cambridge MA 02138
      Big-Data-2019-Poster-5-2

      shutterstock_547250785-e1527881194717

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

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

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

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

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

    • CMSA EVENT: 2015 Conference on Big Data
      8:45 am-4:00 pm
      11/01/2019-10/26/2015
      1 Oxford Street, Cambridge MA 02138

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

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

       

      Registration for the conference is now closed.

      Please click here for a downloadable version of this schedule.

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

      Monday, August 24

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

      Tuesday, August 25

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

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

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

       Wednesday, August 26 

      TimeSpeakerTitle
      8:45amMeet and Greet
      9:00amAnkur MoitraBeyond Matrix Completion
      9:45amFlorent KrzakalaOptimal compressed sensing with spatial coupling and message passing
      10:30amBreak
      10:45amPiotr IndykFast Algorithms for Structured Sparsity
      11:30amGuido ImbensExact p-values for network inference
      12:15pmBreak for lunch
      2:00pmEdo AiroldiSome fundamental ideas for causal inference on large networks
      2:45pmRonitt RubinfeldSomething for almost nothing: sublinear time approximation algorithms
      3:30pmBreak
      3:45pmLenka ZdeborovaClustering of sparse networks:  Phase transitions and optimal algorithms
      4:30pmJelani NelsonDimensionality reductions via sparse matrices
    • CMSA EVENT: Workshop on Probabilistic and Extremal Combinatorics
      9:00 am-1:30 pm
      11/01/2019-02/09/2018

      The workshop on Probabilistic and Extremal Combinatorics will take place February 5-9, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      Extremal and Probabilistic Combinatorics are two of the most central branches of modern combinatorial theory. Extremal Combinatorics deals with problems of determining or estimating the maximum or minimum possible cardinality of a collection of finite objects satisfying certain requirements. Such problems are often related to other areas including Computer Science, Information Theory, Number Theory and Geometry. This branch of Combinatorics has developed spectacularly over the last few decades. Probabilistic Combinatorics can be described informally as a (very successful) hybrid between Combinatorics and Probability, whose main object of study is probability distributions on discrete structures.

      There are many points of interaction between these fields. There are deep similarities in methodology. Both subjects are mostly asymptotic in nature. Quite a few important results from Extremal Combinatorics have been proven applying probabilistic methods, and vice versa. Such emerging subjects as Extremal Problems in Random Graphs or the theory of graph limits stand explicitly at the intersection of the two fields and indicate their natural symbiosis.

      The symposia will focus on the interactions between the above areas. These topics include Extremal Problems for Graphs and Set Systems, Ramsey Theory, Combinatorial Number Theory, Combinatorial Geometry, Random Graphs, Probabilistic Methods and Graph Limits.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Benny Sudakov and David Conlon.  More details about this event, including participants, will be updated soon.

    • CMSA EVENT: Simons Collaboration on Homological Mirror Symmetry
      9:00 am-5:00 pm
      11/01/2019-05/08/2016

      The Center of Mathematical Sciences and Applications will be hosting a 3-day workshop on Homological Mirror Symmetry and related areas on May 6 – May 8, 2016 at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

      Organizers:

      D. Auroux, S.C. Lau, N.C. Leung, Bong Lian, C.C. Liu, S.T. Yau

      Speakers:

      1. Netanel Blaier (MIT)
      2. Kwokwai Chan (CUHK)
      3. Bohan Fang (Peking University)
      4. Amanda Francis (BYU)
      5. Hansol Hong (CUHK)
      6. Heather Lee (Purdue University)
      7. Si Li (Tsinghua University)
      8. Yu-Shen Lin (Stanford University)
      9. Alex Perry (Harvard University)
      10. Hiro Tanaka (Harvard University)
      11. Sara Tukachinsky (HUJ)
      12. Michael Viscardi (MIT)
      13. Eric Zaslow (Northwestern University)
      14. Jingyu Zhao (Columbia University)

      Please click here for the conference Main Website.

      Please click Simons Workshop Schedule with Abstract for a downloadable schedule with talk abstracts.

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

      Schedule:

      May 6 – Day 1
      9:00amBreakfast
      9:35amOpening remarks
      9:45am – 10:45amSi Li, “Quantum master equation, chiral algebra, and integrability”
      10:45am – 11:15amBreak
      11:15am – 12:15pmSara Tukachinsky, “Point like bounding chains and open WDVV
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmBohan Fang, “Mirror B model for toric Calabi Yau 3 folds
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmHiro Tanaka, “Toward Fukaya categories over arbitrary coefficients
      4:00pm – 4:15pmBreak
      4:15pm – 5:15pmHansol Hong, “Noncommutative mirror functors
      May 7 – Day 2
      9:00amBreakfast
      9:45am – 10:45amEric Zaslow, “Lagrangian fillings what does the sheaf say?
      10:45am – 11:15amBreak
      11:15am – 12:15pmAlex Perry, “Derived categories of Gushel Mukai varieties
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmAmanda Francis, “A Landau Ginzburg mirror theorem inspired by Borcea Voisin symmetry
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmHeather Lee, “Homological mirror symmetry for open Riemann surfaces from pair of pants decompositions
      4:00pm – 4:15pmBreak
      4:15pm – 5:15pmYu-Shen Lin, “Counting Holomorphic Discs via Tropical Discs on K3 Surfaces
      May 8 – Day 3
      9:00amBreakfast
      9:45am – 10:45amKwokwai Chan, “HMS for local CY manifolds via SYZ
      10:45am – 11:15amBreak
      11:15am – 12:15pmNetanel Blaier, “The quantum Johnson homomorphism, formality and symplectic isotopy
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmJingyu Zhao, “Periodic symplectic cohomology and the Hodge filtration
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmMichael Viscardi, “Equivariant quantum cohomology and the geometric Satake equivalence
      * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Simons Collaboration on Homological Mirror symmetry“.

      This event is sponsored by the Simons Foundation and CMSA Harvard University.

    • CMSA EVENT: Workshop on Geometry, Imaging, and Computing
      9:00 am-6:15 pm
      11/01/2019-03/26/2018
      GIC-Poster-2-e1520002551865

      On March 24-26, The Center of Mathematical Sciences and Applications will be hosting a workshop on Geometry, Imaging, and Computing, based off  the journal of the same name. The workshop will take place in CMSA building, G10.

      The organizing committee consists of Yang Wang (HKUST), Ronald Lui (CUHK), David Gu (Stony Brook), and Shing-Tung Yau (Harvard).

      Please click here to register for the event.

      Confirmed Speakers:

    • CMSA EVENT: Workshop on Optimization in Image Processing
      9:00 am-12:30 pm
      11/01/2019-06/30/2016

      The Center of Mathematical Sciences and Applications will be hosting a workshop on Optimization in Image Processing on June 27 – 30, 2016. This 4-day workshop aims to bring together researchers to exchange and stimulate ideas in imaging sciences, with a special focus on new approaches based on optimization methods. This is a cutting-edge topic with crucial impact in various areas of imaging science including inverse problems, image processing and computer vision. 16 speakers will participate in this event, which we think will be a very stimulating and exciting workshop. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Titles, abstracts and schedule will be provided nearer to the event.

      Speakers:

      1. Antonin Chambolle, CMAP, Ecole Polytechnique
      2. Raymond Chan, The Chinese University of Hong Kong
      3. Ke Chen, University of Liverpool
      4. Patrick Louis Combettes, Université Pierre et Marie Curie
      5. Mario Figueiredo, Instituto Superior Técnico
      6. Alfred Hero, University of Michigan
      7. Ronald Lok Ming Lui, The Chinese University of Hong Kong
      8. Mila Nikolova, Ecole Normale Superieure Cachan
      9. Shoham Sabach, Israel Institute of Technology
      10. Martin Benning, University of Cambridge
      11. Jin Keun Seo, Yonsei University
      12. Fiorella Sgallari, University of Bologna
      13. Gabriele Steidl, Kaiserslautern University of Technology
      14. Joachim Weickert, Saarland University
      15. Isao Yamada, Tokyo Institute of Technology
      16. Wotao Yin, UCLA

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

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

      Please click here for registration – Registration Deadline: June 7, 2016; Registration is capped at 70 participants.

      Schedule:

      June 27 – Day 1
      9:00amBreakfast
      9:20amOpening remarks
      9:30am – 10:20amJoachim Weickert, “FSI Schemes: Fast Semi-Iterative Methods for Diffusive or Variational Image Analysis Problems”
      10:20am – 10:50amBreak
      10:50am – 11:40pmPatrick Louis Combettes“Block-Iterative Asynchronous Variational Image Recovery”
      11:40am – 12:30pmIsao Yamada“Spicing up Convex Optimization for Certain Inverse Problems”
      12:30pm – 2:00pmLunch
      2:30pm – 3:20pmFiorella Sgallari, “Majorization-Minimization for Nonconvex Optimization”
      3:20pm – 3:50pmBreak
      3:50pm – 4:40pmShoham Sabach“A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Problems”
      June 28 – Day 2
      9:00amBreakfast
      9:30am – 10:20amAntonin Chambolle“Acceleration of alternating minimisations”
      10:20am – 10:50amBreak
      10:50am – 11:40amMario Figueiredo“ADMM in Image Restoration and Related Problems: Some History and Recent Advances”
      11:40am – 12:30pmKe Chen“Image Restoration and Registration Based on Total Fractional-Order Variation Regularization”
      12:30pm – 2:30pmLunch
      2:30pm – 4:40pmDiscussions
      June 29 – Day 3
      9:00amBreakfast
      9:30am – 10:20amAlfred Hero“Continuum relaxations for discrete optimization”
      10:20am – 10:50amBreak
      10:50am – 11:40amWotao Yin“Coordinate Update Algorithms for Computational Imaging and Machine Learning”
      11:40am – 12:30pmMila Nikolova“Limits on noise removal using log-likelihood and regularization”
      12:30pm – 2:30pmLunch
      2:30pm – 3:20pmMartin Benning, “Nonlinear spectral decompositions and the inverse scale space method”
      3:20pm – 3:50pmBreak
      3:50pm – 4:40pmRonald Ming Lui“TEMPO: Feature-endowed Teichmuller extremal mappings of point cloud for shape classification”
      June 30 – Day 4
      9:00amBreakfast
      9:30am – 10:20amJin Keun Seo“Mathematical methods for biomedical impedance imaging”
      10:20am – 10:50amBreak
      10:50am – 11:40amGabriele Steidl, “Iterative Multiplicative Filters for Data Labeling”
      11:40am – 12:30pmRaymond Chan, “Point-spread function reconstruction in ground-based astronomy”
      * This event is sponsored by CMSA Harvard University.

      Organizers: Raymond Chan and Shing-Tung Yau

    • CMSA EVENT: Machine Learning for Multiscale Model Reduction Workshop
      9:00 am-11:55 am
      11/01/2019-03/29/2019
      Machine-Learning-Poster

      The Machine Learning for Multiscale Model Reduction Workshop will take place on March 27-29, 2019. This is the second of two workshops organized by Michael BrennerShmuel Rubinstein, and Tom Hou.  The first, Fluid turbulence and Singularities of the Euler/ Navier Stokes equations, will take place on March 13-15, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

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

      List of registrants

      Speakers:

    • CMSA EVENT: Simons Collaboration Workshop, Jan. 10-13, 2018
      9:00 am-12:00 pm
      11/01/2019-01/13/2017
      banner-image-1

      The CMSA will be hosting a four-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on January 10-13, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

      We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

       

      Confirmed Participants:

    • CMSA EVENT: Mini-school on Nonlinear Equations, December 3-4, 2016
      9:00 am-5:00 pm
      11/01/2019-12/04/2016

      The Center of Mathematical Sciences and Applications will be hosting a Mini-school on Nonlinear Equations on December 3-4, 2016. The conference will have speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138.

      The mini-school will consist of lectures by experts in geometry and analysis detailing important developments in the theory of nonlinear equations and their applications from the last 20-30 years.  The mini-school is aimed at graduate students and young researchers working in geometry, analysis, physics and related fields.

      Please click here to register for this event.

      Speakers:

      1. Cliff Taubes (Harvard University)
      2. Valentino Tosatti (Northwestern University)
      3. Pengfei Guan (McGill University)
      4. Jared Speck (MIT)

      Schedule:

      December 3rd – Day 1
      9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
      10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
      12:15pm – 1:45pmLUNCH
      1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
      3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”
      December 4th – Day 2
      9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
      10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
      12:15pm – 1:45pmLUNCH
      1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
      3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”

      Please click Mini-School Program for a downloadable schedule with talk abstracts.

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

      * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

    • CMSA EVENT: Workshop on Coding and Information Theory
      9:00 am-3:30 pm
      11/01/2019-04/13/2018

      The workshop on coding and information theory will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

      Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory.  One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program.  Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities.  Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics.  All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      Click here for a list of registrants. 

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

    • CMSA EVENT: Topology and Dynamics in Quantum Matter Workshop
      9:15 am-3:25 pm
      11/01/2019-09/11/2019
      Topology-Poster

      On September 10-11, 2019, the CMSA will be hosting a second workshop on Topological Aspects of Condensed Matter.

      New ideas rooted in topology have recently had a major impact on condensed matter physics, and have led to new connections with high energy physics, mathematics and quantum information theory.  The aim of this program will be to deepen these connections and spark new progress by fostering discussion and new collaborations within and across disciplines.

      Topics include i) the classification of topological states  ii) topological orders in two and three dimensions including quantum spin liquids, quantum Hall states and fracton phases and iii)  interplay of symmetry and topology in quantum many body systems, including symmetry protected topological phases, symmetry fractionalization and anomalies iv) topological phenomena in quantum systems  driven far from equlibrium v) quantum field theory approaches to topological matter.

      This workshop is part of the CMSA’s program on Program on Topological Aspects of Condensed Matterand is the second of two workshops, in addition to a visitor program and seminars.

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

      Click here for a list of restaurants in the area. 

      Organizers: Michael Hermele (CU Boulder) and Ashvin Vishwanath (Harvard)

      Partial list of speakers:

      Videos of the lectures can be found in the Youtube playlist below. Links to talks are also available on the schedule below.

    • CMSA EVENT: Workshop on Invariance and Geometry in Sensation, Action and Cognition
      9:15 am-10:00 am
      11/01/2019-04/17/2019

      As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

      Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, it has traditionally not been an important part of biology, except in the context of aspects of structural biology. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use.

      This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines? The aim is to revisit these old neuro-cognitive problems using a series of modern lenses experimentally, theoretically and computationally, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models.

      In addition to talks, there will be a set of tutorial talks on the mathematical description of invariance (P.J. Olver), the computer vision aspects of invariant algorithms (S. Soatto), and the neuroscientific and cognitive aspects of invariance (TBA). The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by L. Mahadevan (Harvard), Talia Konkle (Harvard), Samuel Gershman (Harvard), and Vivek Jayaraman (HHMI).

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

      List of registrants

      Videos

      Tentative Speaker List:

      Schedule:

      Monday, April 15

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:15amWelcome and Introduction
      9:15 – 10:00amVivek JayaramanTitle: Insect cognition: Small tales of geometry & invariance

      Abstract: Decades of field and laboratory experiments have allowed ethologists to discover the remarkable sophistication of insect behavior. Over the past couple of decades, physiologists have been able to peek under the hood to uncover sophistication in insect brain dynamics as well. In my talk, I will describe phenomena that relate to the workshop’s theme of geometry and invariance. I will outline how studying insects —and flies in particular— may enable an understanding of the neural mechanisms underlying these intriguing phenomena.

      10:00 – 10:45amElizabeth TorresTitle: Connecting Cognition and Biophysical Motions Through Geometric Invariants and Motion Variability

      Abstract: In the 1930s Nikolai Bernstein defined the degrees of freedom (DoF) problem. He asked how the brain could control abundant DoF and produce consistent solutions, when the internal space of bodily configurations had much higher dimensions than the space defining the purpose(s) of our actions. His question opened two fundamental problems in the field of motor control. One relates to the uniqueness or consistency of a solution to the DoF problem, while the other refers to the characterization of the diverse patterns of variability that such solution produces.

      In this talk I present a general geometric solution to Bernstein’s DoF problem and provide empirical evidence for symmetries and invariances that this solution provides during the coordination of complex naturalistic actions. I further introduce fundamentally different patterns of variability that emerge in deliberate vs. spontaneous movements discovered in my lab while studying athletes and dancers performing interactive actions. I here reformulate the DoF problem from the standpoint of the social brain and recast it considering graph theory and network connectivity analyses amenable to study one of the most poignant developmental disorders of our times: Autism Spectrum Disorders.

      I offer a new unifying framework to recast dynamic and complex cognitive and social behaviors of the full organism and to characterize biophysical motion patterns during migration of induced pluripotent stem cell colonies on their way to become neurons.

      10:45 – 11:15amCoffee Break
      11:15 – 12:00pmPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

      Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical prerequisites will be kept to a bare minimum.

      12:00 – 12:45pmStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

      Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

      While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

      12:45 – 2:00pmLunch
      2:00 – 2:45pmAnitha PasupathyTitle: Invariant and non-invariant representations in mid-level ventral visual cortex

      My laboratory investigates how visual form is encoded in area V4, a critical mid-level stage of form processing in the macaque monkey. Our goal is to reveal how V4 representations underlie our ability to segment visual scenes and recognize objects. In my talk I will present results from two experiments that highlight the different strategies used by the visual to achieve these goals. First, most V4 neurons exhibit form tuning that is exquisitely invariant to size and position, properties likely important to support invariant object recognition. On the other hand, form tuning in a majority of neurons is also highly dependent on the interior fill. Interestingly, unlike primate V4 neurons, units in a convolutional neural network trained to recognize objects (AlexNet) overwhelmingly exhibit fill-outline invariance. I will argue that this divergence between real and artificial circuits reflects the importance of local contrast in parsing visual scenes and overall scene understanding.

      2:45 – 3:30pmJacob FeldmanTitle: Bayesian skeleton estimation for shape representation and perceptual organization

      Abstract: In this talk I will briefly summarize a framework in which shape representation and perceptual organization are reframed as probabilistic estimation problems. The approach centers around the goal of identifying the skeletal model that best “explains” a given shape. A Bayesian solution to this problem requires identifying a prior over shape skeletons, which penalizes complexity, and a likelihood model, which quantifies how well any particular skeleton model fits the data observed in the image. The maximum-posterior skeletal model thus constitutes the most “rational” interpretation of the image data consistent with the given assumptions. This approach can easily be extended and generalized in a number of ways, allowing a number of traditional problems in perceptual organization to be “probabilized.” I will briefly illustrate several such extensions, including (1) figure/ground and grouping (3) 3D shape and (2) shape similarity.

      3:30 – 4:00pmTea Break
      4:00 – 4:45pmMoira DillonTitle: Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development

      Abstract: Formal geometry lies at the foundation of millennia of human achievement in domains such as mathematics, science, and art. While formal geometry’s propositions rely on abstract entities like dimensionless points and infinitely long lines, the points and lines of our everyday world all have dimension and are finite. How, then, do we get to abstract geometric thought? In this talk, I will provide evidence that evolutionarily ancient and developmentally precocious sensitivities to the geometry of our everyday world form the foundation of, but also limit, our mathematical reasoning. I will also suggest that successful geometric reasoning may emerge through development when children abandon incorrect, axiomatic-based strategies and come to rely on dynamic simulations of physical entities. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations.

      4:45 – 5:30pmMichael McCloskeyTitle: Axes and Coordinate Systems in Representing Object Shape and Orientation

      Abstract: I describe a theoretical perspective in which a) object shape is represented in an object-centered reference frame constructed around orthogonal axes; and b) object orientation is represented by mapping the object-centered frame onto an extrinsic (egocentric or environment-centered) frame.  I first show that this perspective is motivated by, and sheds light on, object orientation errors observed in neurotypical children and adults, and in a remarkable case of impaired orientation perception. I then suggest that orientation errors can be used to address questions concerning how object axes are defined on the basis of object geometry—for example, what aspects of object geometry (e.g., elongation, symmetry, structural centrality of parts) play a role in defining an object principal axis?

      5:30 – 6:30pmReception

       

      Tuesday, April 16

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:45amPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

      Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical pre

      9:45 – 10:30amStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

      Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

      While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

      10:30 – 11:00amCoffee Break
      11:00 – 11:45amJeannette BohgTitle: On perceptual representations and how they interact with actions and physical representations

      Abstract: I will discuss the hypothesis that perception is active and shaped by our task and our expectations on how the world behaves upon physical interaction. Recent approaches in robotics follow this insight that perception is facilitated by physical interaction with the environment. First, interaction creates a rich sensory signal that would otherwise not be present. And second, knowledge of the regularity in the combined space of sensory data and action parameters facilitate the prediction and interpretation of the signal. In this talk, I will present two examples from our previous work where a predictive task facilitates autonomous robot manipulation by biasing the representation of the raw sensory data. I will present results on visual but also haptic data.

      11:45 – 12:30pmDagmar SternadTitle: Exploiting the Geometry of the Solution Space to Reduce Sensitivity to Neuromotor Noise

      Abstract: Control and coordination of skilled action is frequently examined in isolation as a neuromuscular problem. However, goal-directed actions are guided by information that creates solutions that are defined as a relation between the actor and the environment. We have developed a task-dynamic approach that starts with a physical model of the task and mathematical analysis of the solution spaces for the task. Based on this analysis we can trace how humans develop strategies that meet complex demands by exploiting the geometry of the solution space. Using three interactive tasks – throwing or bouncing a ball and transporting a “cup of coffee” – we show that humans develop skill by: 1) finding noise-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, and 3) optimizing predictability of the object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, attractors with few invariant types that overcome substantial delays and noise in the neuro-mechanical system.

      12:30 – 2:00pmLunch
      2:00 – 2:45pmSam OckoTitle: Emergent Elasticity in the Neural Code for Space

      Abstract: To navigate a novel environment, animals must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such internal maps, and how are these maps used to maintain representations of an animal’s position within an environment. We demonstrate analytically how a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent internal map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network during exploration. Moreover, we verify several experimentally testable predictions of our model, including: (1) systematic deformations of grid cells in irregular environments, (2) path-dependent shifts in grid cells towards the most recently encountered landmark, (3) a dynamical phase transition in which grid cells can break free of landmarks in altered virtual reality environments and (4) the creation of topological defects in grid cells. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

      2:45 – 3:30pmTatyana SharpeeTitle: Hyperbolic geometry of the olfactory space

      Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the production of a specific poison by a plant or bacteria will be accompanied by the emission of certain sets of volatile compounds. An animal can therefore judge the presence of poisons in the food by how the food smells. This perspective suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendrograms, and more generally between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

      3:30 – 4:00pmTea Break
      4:00 – 4:45pmEd ConnorTitle: Representation of solid geometry in object vision cortex

      Abstract: There is a fundamental tension in object vision between the 2D nature of retinal images and the 3D nature of physical reality. Studies of object processing in the ventral pathway of primate visual cortex have focused mainly on 2D image information. Our latest results, however, show that representations of 3D geometry predominate even in V4, the first object-specific stage in the ventral pathway. The majority of V4 neurons exhibit strong responses and clear selectivity for solid, 3D shape fragments. These responses are remarkably invariant across radically different image cues for 3D shape: shading, specularity, reflection, refraction, and binocular disparity (stereopsis). In V4 and in subsequent stages of the ventral pathway, solid shape geometry is represented in terms of surface fragments and medial axis fragments. Whole objects are represented by ensembles of neurons signaling the shapes and relative positions of their constituent parts. The neural tuning dimensionality of these representations includes principal surface curvatures and their orientations, surface normal orientation, medial axis orientation, axial curvature, axial topology, and position relative to object center of mass. Thus, the ventral pathway implements a rapid transformation of 2D image data into explicit representations 3D geometry, providing cognitive access to the detailed structure of physical reality.

      4:45 – 5:30pmL. MahadevanTitle: Simple aspects of geometry and probability in perception

      Abstract: Inspired by problems associated with noisy perception, I will discuss two questions: (i) how might we test people’s perception of probability in a geometric context ? (ii) can one construct invariant descriptions of 2D images using simple notions of probabilistic geometry? Along the way, I will highlight other questions that the intertwining of geometry and probability raises in a broader perceptual context.


      Wednesday, April 17

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:45amGily GinosarTitle: The 3D geometry of grid cells in flying bats

      Abstract: The medial entorhinal cortex (MEC) contains a variety of spatial cells, including grid cells and border cells. In 2D, grid cells fire when the animal passes near the vertices of a 2D spatial lattice (or grid), which is characterized by circular firing-fields separated by fixed distances, and 60 local angles – resulting in a hexagonal structure. Although many animals navigate in 3D space, no studies have examined the 3D volumetric firing of MEC neurons. Here we addressed this by training Egyptian fruit bats to fly in a large room (5.84.62.7m), while we wirelessly recorded single neurons in MEC. We found 3D border cells and 3D head-direction cells, as well as many neurons with multiple spherical firing-fields. 20% of the multi-field neurons were 3D grid cells, exhibiting a narrow distribution of characteristic distances between neighboring fields – but not a perfect 3D global lattice. The 3D grid cells formed a functional continuum with less structured multi-field neurons. Both 3D grid cells and multi-field cells exhibited an anatomical gradient of spatial scale along the dorso-ventral axis of MEC, with inter-field spacing increasing ventrally – similar to 2D grid cells in rodents. We modeled 3D grid cells and multi-field cells as emerging from pairwise-interactions between fields, using an energy potential that induces repulsion at short distances and attraction at long distances. Our analysis shows that the model explains the data significantly better than a random arrangement of fields. Interestingly, simulating the exact same model in 2D yielded a hexagonal-like structure, akin to grid cells in rodents. Together, the experimental data and preliminary modeling suggest that the global property of grid cells is multiple fields that repel each other with a characteristic distance-scale between adjacent fields – which in 2D yields a global hexagonal lattice while in 3D yields only local structure but no global lattice.

      Gily Ginosar 1 , Johnatan Aljadeff 2 , Yoram Burak 3 , Haim Sompolinsky 3 , Liora Las 1 , Nachum Ulanovsky 1

      (1) Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel

      (2) Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK

      (3) The Edmond and Lily Safra Center for Brain Sciences, and Racah Institute of Physics, The Hebrew

      University of Jerusalem, Jerusalem, 91904, Israel

      9:45 – 10:30amSandro RomaniTitle: Neural networks for 3D rotations

      Abstract: Studies in rodents, bats, and humans have uncovered the existence of neurons that encode the orientation of the head in 3D. Classical theories of the head-direction (HD) system in 2D rely on continuous attractor neural networks, where neurons with similar heading preference excite each other, while inhibiting other HD neurons. Local excitation and long-range inhibition promote the formation of a stable “bump” of activity that maintains a representation of heading. The extension of HD models to 3D is hindered by complications (i) 3D rotations are non-commutative (ii) the space described by all possible rotations of an object has a non-trivial topology. This topology is not captured by standard parametrizations such as Euler angles (e.g. yaw, pitch, roll). For instance, with these parametrizations, a small change of the orientation of the head could result in a dramatic change of neural representation. We used methods from the representation theory of groups to develop neural network models that exhibit patterns of persistent activity of neurons mapped continuously to the group of 3D rotations. I will further discuss how these networks can (i) integrate vestibular inputs to update the representation of heading, and (ii) be used to interpret “mental rotation” experiments in humans.

      This is joint work with Hervé Rouault (CENTURI) and Alon Rubin (Weizmann Institute of Science).

      10:30 – 11:00amCoffee Break
      11:00 – 11:45amSam GershmanTitle: The hippocampus as a predictive map

      Abstract: A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. I approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? I show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, I argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning.

      11:45 – 12:30pmLucia JacobsTitle: The adaptive geometry of a chemosensor: the origin and function of the vertebrate nose

      Abstract: A defining feature of a living organism, from prokaryotes to plants and animals, is the ability to orient to chemicals. The distribution of chemicals, whether in water, air or on land, is used by organisms to locate and exploit spatially distributed resources, such as nutrients and reproductive partners. In animals, the evolution of a nervous system coincided with the evolution of paired chemosensors. In contemporary insects, crustaceans, mollusks and vertebrates, including humans, paired chemosensors confer a stereo olfaction advantage on the animal’s ability to orient in space. Among vertebrates, however, this function faced a new challenge with the invasion of land. Locomotion on land created a new conflict between respiration and spatial olfaction in vertebrates. The need to resolve this conflict could explain the current diversity of vertebrate nose geometries, which could have arisen due to species differences in the demand for stereo olfaction. I will examine this idea in more detail in the order Primates, focusing on Old World primates, in particular, the evolution of an external nose in the genus Homo.

      12:30 – 1:30pmLunch
      1:30 – 2:15pmTalia KonkleTitle: The shape of things and the organization of object-selective cortex

      Abstract: When we look at the world, we effortlessly recognize the objects around us and can bring to mind a wealth of knowledge about their properties. In part 1, I’ll present evidence that neural responses to objects are organized by high-level dimensions of animacy and size, but with underlying neural tuning to mid-level shape features. In part 2, I’ll present evidence that representational structure across much of the visual system has the requisite structure to predict visual behavior. Together, these projects suggest that there is a ubiquitous “shape space” mapped across all of occipitotemporal cortex that underlies our visual object processing capacities. Based on these findings, I’ll speculate that the large-scale spatial topography of these neural responses is critical for pulling explicit content out of a representational geometry.

      2:15 – 3:00pmVijay BalasubramanianTitle: Becoming what you smell: adaptive sensing in the olfactory system

      Abstract: I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors.  In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors.  The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules.  I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors.  The resulting algorithm for “estimation by elimination” can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain.  The theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans.   It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb.

      3:00 – 3:45pmIla FeiteTitle: Invariance, stability, geometry, and flexibility in spatial navigation circuits

      Abstract: I will describe how the geometric invariances or symmetries of the external world are reflected in the symmetries of neural circuits that represent it, using the example of the brain’s networks for spatial navigation. I will discuss how these symmetries enable spatial memory, evidence integration, and robust representation. At the same time, I will discuss how these seemingly rigid circuits with their inscribed symmetries can be harnessed to represent a range of spatial and non-spatial cognitive variables with high flexibility.

      3:45 – 4:00pmL Mahadevan – summary
    • CMSA EVENT: The 2017 Charles River Lectures
      9:15 am-5:30 pm
      11/01/2019

      The 2017 Charles River Lectures

      Charles River with Bench at Sunset

      Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community.

      The 2017 lectures will take place 9:15am – 5:30pm on Monday, October 2 at Harvard University  in the Harvard Science Center.


      ***************************************************

      UPDATED LOCATION

      Harvard University

      Harvard Science Center (Halls C & E)

      1 Oxford Street, Cambridge, MA 02138 (Map)

      Monday, October 2, 2017

      9:15 AM – 5:30 PM

      **************************************************

      Please note that registration has closed.

      Speakers:

      Agenda:

      In Harvard Science Center Hall C:

      8:45 am – 9:15 amCoffee/light breakfast

      9:15 am – 10:15 am: Ofer Zeitouni

      Title: Noise stability of the spectrum of large matrices

      Abstract: The spectrum of large non-normal matrices is notoriously sensitive to perturbations, as the example of nilpotent matrices shows. Remarkably, the spectrum of these matrices perturbed by polynomially (in the dimension) vanishing additive noise is remarkably stable. I will describe some results and the beginning of a theory.

      The talk is based on joint work with Anirban Basak and Elliot Paquette, and earlier works with Feldheim, Guionnet, Paquette and Wood.

      10:20 am – 11:20 am: Andrea Montanari

      Title: Algorithms for estimating low-rank matrices 

      Abstract: Many interesting problems in statistics can be formulated as follows. The signal of interest is a large low-rank matrix with additional structure, and we are given a single noisy view of this matrix. We would like to estimate the low rank signal by taking into account optimally the signal structure. I will discuss two types of efficient estimation procedures based on message-passing algorithms and semidefinite programming relaxations, with an emphasis on asymptotically exact results.

      11:20 am – 11:45 amBreak

      11:45 am – 12:45 pm: Paul Bourgade

      Title: Random matrices, the Riemann zeta function and trees

      Abstract: Fyodorov, Hiary & Keating have conjectured that the maximum of the characteristic polynomial of random unitary matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the typical size of local maxima of the Riemann zeta function along the critical axis. I will first explain the origins of this conjecture, and then outline the proof for the leading order of the maximum, for unitary matrices and the zeta function. This talk is based on joint works with Arguin, Belius, Radziwill and Soundararajan.

      1:00 pm – 2:30 pm: Lunch

      In Harvard Science Center Hall E:

      2:45 pm – 3:45 pm: Roman Vershynin

      Title: Deviations of random matrices and applications

      Abstract: Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This lecture will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science.

      3:45 pm – 4:15 pm: Break

      4:15 pm – 5:15 pm: Massimiliano Gubinelli

      Title: Weak universality and Singular SPDEs

      Abstract: Mesoscopic fluctuations of microscopic (discrete or continuous) dynamics can be described in terms of nonlinear stochastic partial differential equations which are universal: they depend on very few details of the microscopic model. This universality comes at a price: due to the extreme irregular nature of the random field sample paths, these equations turn out to not be well-posed in any classical analytic sense. I will review recent progress in the mathematical understanding of such singular equations and of their (weak) universality and their relation with the Wilsonian renormalisation group framework of theoretical physics.

      Poster:

      2017 Charles River Lectures Poster

      Organizers:

       Alexei BorodinHenry CohnVadim GorinElchanan MosselPhilippe RigolletScott Sheffield, and H.T. Yau

    • CMSA EVENT: Kickoff Workshop on Topology and Quantum Phases of Matter
      9:20 am-3:15 pm
      11/01/2019-08/28/2018
      Topological-1

      Screen-Shot-2018-08-13-at-2.28.22-PM

      On August 27-28, 2018, the CMSA will be hosting a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines.

      This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter,  and will be the first of two workshops, in addition to a visitor program and seminars.

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

      Please register here

      Speakers: 

    • Special Seminar
      Special Seminar
      3/30/2018 Special Seminar
      9:30 am-11:00 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/18/2019 General Relativity Seminar
      9:30 am-10:30 am
      11/01/2019
    • CMSA EVENT: Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
      9:30 am-5:00 pm
      11/01/2019-03/01/2019

      From February 25 to March 1, the CMSA will be hosting a workshop on Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations. 

      Key participants of this workshop include David Jerison (MIT), Alexander Logunov (IAS), and Eugenia Malinnikova (IAS).  This workshop will have morning sessions on Monday-Friday of this week from 9:30-11:30am, and afternoon sessions on Monday, Tuesday, and Thursday from 3:00-5:00pm.
      The sessions will be held in  \(G02\) (downstairs) at 20 Garden, except for Tuesday afternoon, when the talk will be in \(G10\).

    • Special Seminar
      9:30 am
      11/01/2019
    • Seminars
      9:50 am-10:50 am
      11/01/2019

      The seminar for evolution equations, hyperbolic equations, and fluid dynamics will be held on Thursdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule of speakers is below. Titles for the talks will be added as they are received.

      DateNameTitle
      09-03-2015Long JinScattering Resonances for Convex Obstacles
      09-10-2015Chunjing XieWell/ill-posedness for the rotating shallow water system
      09-17-2015Xiangdi HuangGlobal classical and weak Solutions to the 3D fully compressible Navier-Stokes-Fourier system
      09-24-2015Felix FinsterCausal fermion systems and the causal action principle
      10-01-2015Pin YuConstruction of Cauchy data of vacuum Einstein field equations evolving to black holes
      10-08-2015Chunjing XieSteady Euler flows past a wall or through a nozzle
      10-15-2015Zhou Ping XinOn Global Well-Posedness of The Compressible Navier-Stokes Systems with Large Oscillations
      10-22-2015Xiangdi HuangOn Nash’s problem for compressible flows
      10-29-2015Pin YuShock formations for 3 dimensional wave equations
      11-05-2015No talk 
      11-12-2015Zhou Ping Xin (9:30am-10:30am) Nicolai Krylov (10:30am-11:30am)Nonlinear Asymptotic Stability of Lane-Emden Solutions for The Viscous Gaseous Star ProblemOn the existence of $\bf W^{2}_{p}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions
      11-19-2015Nicolai KrylovTo the theory of viscosity solutions for uniformly parabolic Isaacs equations
      11-26-2015ThanksgivingNo seminar
      12-4-2015John Loftin (@11:00am)Moduli of Equivariant Minimal Surfaces in CH^2$
      01-28-2016Xiaoli HanThe symplecitic and Lagrangian mean curvature flow 
      02-04-2016Pranav PanditCategorical Kähler Geometry
      02-11-2016Lydia BieriEinstein’s Equations, Energy and Gravitational Radiation
      02-18-2016Zuoqiang ShiLow dimensional manifold model for image processing
      02-25-2016Chun Peng WangSmooth Transonic Flows of Meyer Type in De Laval Nozzles
      03-03-2016Piotr ChruscielSingularities in general relativity
      03-10-2016Feimin HuangIsometric immersion of complete surface with slowly decaying negative Gauss curvature
      03-17-2016Spring BreakNo Talk
      03-24-2016Michael EichmairMinimal surfaces, isoperimetry, and non-negative scalar curvature in asymptotically flat manifolds
      03-31-2016Felix FinsterLorentzian spectral geometry and the fermionic signature operator
      04-07-2016(Room 232, Science Center)Stefano Bianchini, SISSAConcentration of entropy dissipation for scalar conservation laws
      04-14-2016Tai-peng TsaiStability of periodic waves of the 1D nonlinear Schr\”odinger equations
      04-21-2016Stefano Bianchini, SISSAQuadratic interaction functional for system of conservation laws
      04-28-2016Mihalis Dafermos, PrincetonThe linear stability of the Schwarzschild solution to gravitational perturbations
      05-05-2016Xu-Jia WangMonge-Ampere equations arising in geometric optics
      05-12-2016Stefano Bianchini
    • Special Seminar
      9:50 am-10:50 am
      11/01/2019-04/26/2016

      The seminar on geometric analysis will be held on Tuesdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule can be found below. Titles will be added as they are provided.

      DayNameTitle
      09-08-2015Binglong ChenOn the geometry of complete positively curved Kahler manifolds
      09-15-2015Hongwei XuMean Curvature Flow and Sphere Theorem
      09-22-2015Teng FeiSome new solutions to the Strominger system
      09-29-2015Xuqian FanThe Steklov eigenvalues on annuli
      10-06-2015Binglong ChenRicci flow and the moduli spaces of positive isotropic curvature metrics on four-manifolds
      10-13-2015Pengfei GuanIsometric embeddings of $(S^2,g)$ to general warped product space $(N^3,\bar g)$.
      10-20-2015Ovidiu SavinSmoothness of the eigenfunction for the Monge-Ampere equation
      10-27-2015Tom IlmanenFlow of curves by curvature in R^n
      11-03-2015Tom Hou (Caltech)Existence and stability of self-similar singularities for a 1D model of the 3D axisymmetric Euler equations
      11-10-2015Jerome Darbon (9:30am-10:30am) Adam Jacob (10:30am-11:30am)On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton-Jacobi Equations(1,1) forms with specified Lagrangian phase
      11-17-2015Ovidiu SavinExamples of singular minimizers in the calculus of variations
      11-24-2015Hongwei XuMean curvature flow meets Ricci flow:  Convergence and sphere theorems of sub manifolds arising from Yau rigidity theory
      12-01-2015Tom Ilmanen
      01-26-2016Mao ShengUniformization of p-adic curves
      02-02-2016Yi ZhangHodge Bundles on Smooth Compactifications of Siegel Varieties
      02-09-2016Valentino TosattiNon-Kahler Calabi-Yau manifolds
      02-16-2016Camillo De LellisApproaching Plateau’s problem with minimizing sequences of sets
      02-23-2016Junbin LiConstruction of black hole formation spacetimes
      03-01-2016Ben WeinkoveMonge-Ampere equations and metrics on complex manifolds
      03-08-2016Albert ChauSurvey on Kahler Ricci flow on non-negatively curved non-compact manifolds
      03-15-2016Spring Break 
      03-22-2016Richard Schoen (Standford)The geometry of eigenvalue extremal problems
      03-29-2016Piotr ChruscielMass of characteristic surfaces
      04-05-2016 (Room 232, Science Center)Niky Kamran, McGill UniversityNon-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets
      04-12-2016Connor Mooney, UT AustinFinite time blowup for parabolic systems in the plane
      04-19-2016 (Room 232, Science Center)Xu-Jia WangBoundary behaviour of solutions to singular elliptic equations
      04-26-2016Andre NevesA path to Yau’s conjecture
    • Seminars
      Seminars Colloquia & Seminar
      13/3/2018 Topology Seminar
      10:00 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/22/2018 Topology Seminar
      10:00 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/18/2019 General Relativity
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/24/2019 General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/10/18 Topology Seminar
      10:30 am-12:00 am
      11/01/2019-09/11/2018
    • Seminars
      10:30 am-11:42 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/26/2019 Topology
      10:30 am-12:40 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/16/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/11/2019 General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/13/2019 General Relativity
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/25/2019 General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/18/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/20/2019 General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      10:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/9/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      11/1/2019 General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/30/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/2/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/1/2020 Quantum Matter seminar
      10:30 am-12:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-02-2016 Random Matrix & Probability Theory Seminar
      10:32 am
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      10:36 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-07-16 Mathematical Physics Seminar
      10:38 am
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      Special Seminar
      11-04-16 Special Seminar
      10:42 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      10:43 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-09-2016 Random Matrix & Probability Theory Seminar
      10:44 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9-29-2016 Homological Mirror Symmetry Seminar
      10:46 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-08-2016 Social Sciences Applications Forum
      10:56 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-15-2016 Social Sciences Applications Forum
      10:57 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-14-16 Mathematical Physics Seminar
      10:58 am
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
    • General Relativity Seminar
    • Seminars
      Seminars Colloquia & Seminar
      02-09-2018 Mirror Symmetry Seminar
      11:00 am
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-16-2016 Random Matrix & Probability Theory Seminar
      11:00 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/19/2018 Mirror Symmetry Seminar
      11:00 am-11:00 pm
      11/01/2019
    • General Relativity Seminar
    • General Relativity Seminar
    • Seminars
      Seminars Colloquia & Seminar
      2-16-2018 Mirror Symmetry Seminar
      11:00 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2-23-2018 Mirror Symmetry Seminar
      11:00 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3-2-2018 Mirror Symmetry Seminar
      11:00 am-12:00 am
      11/01/2019-03/03/2018
    • General Relativity Seminar
    • Seminars
      Seminars Colloquia & Seminar
      4-13-2018 Mirror Symmetry Seminar
      11:00 am-12:00 am
      11/01/2019-04/14/2018
    • Member Seminar
      11:01 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-21-16 Mathematical Physics Seminar
      11:02 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:03 am-11:04 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      11:03 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:04 am
      11/01/2019

      The  CMSA Colloquium will take place every Wednesday from 4:30-5:30pm in CMSA Building, 20 Garden Street, G10.

      Spring 2020

      DateSpeakerTitle/Abstract
      1/29/2020David Yang (Harvard)

      Abstract: Data-intensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in data-intensive economies: first, states are key collectors and repositories of data; second, data is a non-rival input in innovation. We document the importance of state-collected data for innovation using comprehensive data on Chinese facial recognition AI firms and government contracts. Firms produce more commercial software and patents, particularly data-intensive ones, after receiving government public security contracts. Moreover, effects are largest when contracts provide more data. We then build a directed technical change model to study the state’s role in three applications: autocracies demanding AI for surveillance purposes, data-driven industrial policy, and data regulation due to privacy concerns. When the degree of non-rivalry is as strong as our empirical evidence suggests, the state’s collection and processing of data can shape the direction of innovation and growth of data-intensive economies.

      2/5/2020Scott Aaronson (UT Austin)

      Video

      Title: Gentle Measurement of Quantum States and Differential Privacy

      Abstract: I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography”
      of quantum states (that is, answering a large number of questions about a quantum state given few copies of it).

      Based on joint work with Guy Rothblum (arXiv:1904.08747)

      2/12/2020Scott Kominers (Harvard)Title: A Compact, Logical Approach to Large-Market Analysis

      Abstract: In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

      2/19/2020Peter Shor (MIT)Title: Quantum Money from Lattices

      Abstract: Quantum money is  a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.

      2/26/2020Daneil Wise (McGill)Title: The Cubical Route to Understanding Groups

      Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds and simultaneously dramatically extended our understanding of many infinite groups.
      3/4/2020

      4:45 – 5:45pm

      Salil Vadhan (Harvard)Title: Derandomizing Algorithms via Spectral Graph Theory

      Abstract: Randomization is a powerful tool for algorithms; it is often easier to design efficient algorithms if we allow the algorithms to “toss coins” and output a correct answer with high probability. However, a longstanding conjecture in theoretical computer science is that every randomized algorithm can be efficiently “derandomized” — converted into a deterministic algorithm (which always outputs the correct answer) with only a polynomial increase in running time and only a constant-factor increase in space (i.e. memory usage).

      In this talk, I will describe an approach to proving the space (as opposed to time) version of this conjecture via spectral graph theory. Specifically, I will explain how randomized space-bounded algorithms are described by random walks on directed graphs, and techniques in algorithmic spectral graph theory (e.g. solving Laplacian systems) have yielded deterministic space-efficient algorithms for approximating the behavior of such random walks on undirected graphs and Eulerian directed graphs (where every vertex has the same in-degree as out-degree). If these algorithms can be extended to general directed graphs, then the aforementioned conjecture about derandomizing space-efficient algorithms will be resolved.

      3/11/2020

      Postponed

      Jose Scheinkman

      (Columbia)

      This colloquium will be rescheduled at a later date. 

      Title: Menu Costs and the Volatility of Inflation

      Abstract: We present a state-dependent equilibrium pricing model that generates inflation rate fluctuations from idiosyncratic shocks to the cost of price changes of individual firms.  A firm’s nominal price increase lowers other firms’ relative prices, thereby inducing further nominal price increases. We first study a mean-field limit where the equilibrium is characterized by a variational inequality and exhibits a constant rate of inflation. We use the limit model to show that in the presence of a large but finite number n of firms the snowball effect of repricing causes fluctuations to the aggregate price level  and these fluctuations converge to zero slowly as n grows. The fluctuations caused by this mechanism are larger when the density of firms at the repricing threshold is high, and the density at the threshold is high when the trend inflation level is high. However a calibration to US data shows that this mechanism is quantitatively important even at modest levels of trend inflation and  can account for the positive relationship between inflation level and volatility that has been observed empirically.

      3/12/2020

      4:00 – 5:00pm

      Daniel Forger (University of Michigan)This meeting will be taking place virtually on Zoom.

      Title: Math, Music and the Mind; Mathematical analysis of the performed Trio Sonatas of J. S. Bach

      Abstract: I will describe a collaborative project with the University of Michigan Organ Department to perfectly digitize many performances of difficult organ works (the Trio Sonatas by J.S. Bach) by students and faculty at many skill levels. We use these digitizations, and direct representations of the score to ask how music should encoded in the mind. Our results challenge the modern mathematical theory of music encoding, e.g., based on orbifolds, and reveal surprising new mathematical patterns in Bach’s music. We also discover ways in which biophysical limits of neuronal computation may limit performance.

      Daniel Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan. He is also a visiting scholar at Harvard’s NSF-Simons Center and an Associate of the American Guild of Organists.

      3/25/2020Cancelled
      4/1/2020Mauricio Santillana (Harvard)This meeting will be taking place virtually on Zoom.

      Title: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring

      Abstract: I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.

      4/8/2020Juven Wang (CMSA)This meeting will be taking place virtually on Zoom.

      Title: Quantum Matter Adventure to Fundamental Physics and Mathematics (Continued)

      Abstract: In 1956, Parity violation in Weak Interactions is confirmed in particle physics. The maximal parity violation now is a Standard Model physics textbook statement, but it goes without any down-to-earth explanation for long. Why? We will see how the recent physics development in Quantum Matter may guide us to give an adventurous story and possibly a new elementary
      explanation.  We will see how the topology and cobordism in mathematics may come into play of anomalies and non-perturbative interactions in
      fundamental physics. Perhaps some of you (geometers,  string theorists, etc.) can team up with me to understand the “boundary conditions” of the Standard Model and Beyond

      4/15/2020
      Lars Andersson (Max-Planck Institute for Gravitational Physics)
      This meeting will be taking place virtually on Zoom.

      Title: Stability of spacetimes with supersymmetric compactifications

      Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and Shing-Tung Yau.

      4/22/2020William Minicozzi (MIT)This meeting will be taking place virtually on Zoom.

      Title: Mean curvature flow in high codimension

      Abstract: I will talk about joint work with Toby Colding on higher codimension mean curvature flow.  Some of the ideas come from function theory on manifolds with Ricci curvature bounds.

      4/29/2020Gerhard Huisken (Tübingen University / MFO)This meeting will be taking place virtually on Zoom.

      Title: Mean curvature flow of mean-convex embedded 2-surfaces in 3-manifolds

      Abstract: The lecture describes joint work with Simon Brendle on the deformation of embedded surfaces with positive mean curvature in Riemannian 3-manifolds in direction of their mean curvature vector. It is described how to find long-time solutions of this flow, possibly including singularities that are overcome by surgery, leading to a comprehensive description of embedded mean-convex surfaces and the regions they bound in a 3-manifold. The flow can be used to sweep out the region between space-like infinity and the outermost horizon in asymptotically flat 3-manifolds arising in General Relativity. (Joint with Simon Brendle.)

      5/6/2020Lydia Bieri (UMich)This meeting will be taking place virtually on Zoom.

      Title: Energy, Mass and Radiation in General Spacetimes

      Abstract: In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. Isolated gravitating systems such as binary stars, black holes or galaxies can be described in GR by asymptotically flat (AF) solutions of these equations. These are solutions that look like flat Minkowski space outside of spatially compact regions. There are well-defined notions for energy and mass for such systems. The energy-matter content as well as the dynamics of such a system dictate the decay rates at which the solution tends to the flat one at infinity. Interesting questions occur for very general AF systems of slow decay. We are also interested in spacetimes with pure radiation. In this talk, I will review what is known for these systems. Then we will concentrate on spacetimes with pure radiation. In particular, we will compare the situations of incoming radiation and outgoing radiation under various circumstances and what we can read off from future null infinity.

      5/13/2020Mikhail Lukin (Harvard)

      Video

      This meeting will be taking place virtually on Zoom.

      Title: Exploring New Frontiers of Quantum Science with Programmable Atom Arrays

      Abstract: We will discuss recent work at a new scientific interface between  many-body physics and quantum information science. Specifically, we will  describe the advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Within this system we performed quantum simulations of one dimensional spin models, discovered a new type of non-equilibrium quantum dynamics associated with the so-called many body scars and created large-scale entangled states. We will also describe the most recent developments that now allow the control over 200 atoms in two-dimensional arrays.   Ongoing efforts  to study exotic many-body phenomena and to realize and test quantum optimization algorithms within such systems will be discussed.

      5/20/2020This meeting will be taking place virtually on Zoom.

      Fall 2019

      DateSpeakerTitle/Abstract
      9/18/2019Bill Helton (UC San Diego)Title:  A taste of noncommutative convex algebraic geometry

      Abstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example,

      ◦ A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials.

      ◦ A convex NC semialgebraic set has a linear matrix inequality representation.

      ◦ The natural Nullstellensatz are falling into place.

      The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019.

      9/25/2019Pavel Etingof (MIT)

       

      Title: Double affine Hecke algebras

      Abstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications.

      10/2/2019Spiro Karigiannis (University of Waterloo)Title: Cohomologies on almost complex manifolds and their applications

      Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.

      10/9/2019Hans Lindblad (Johns Hopkins University)Title:  Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition

       

      Abstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition  satisfy the preserved wave coordinate condition.

       

      Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times.

      John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas  lainerman came up with the ‘null condition’, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition.

      Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition.

      Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to afraction and has now been used to prove global existence also with matter fields.

      Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equationsbackwards to obtain global solutions with given data at infinity.

      10/16/2019Aram Harrow (MIT)

      Video

      Title: Monogamy of entanglement and convex geometry

      Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems.

      10/23/2019No talk
      10/30/2019Nima Arkani-Hamed (IAS)

      Video

      Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity
      11/6/2019Kevin Costello (Perimeter Institute)

      Video

      Title: A unified perspective on integrability

       

      Abstract: Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics.   I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu.

      11/13/2019Heather  Harrington (University of Oxford)Title:  Algebra, Geometry and Topology of ERK Enzyme Kinetics

      Abstract: In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

      11/20/2019Xi Yin (Harvard)

      Video

      Title: An Introduction to the Non-Perturbative Bootstrap

      Abstract: I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap

      11/25/2019

      Monday

      Madhu Sudan (Harvard)
      Abstract: The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits.

      In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction.

      Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard).

      12/4/2019Xiao-Gang Wen (MIT)
      Video
      Title: Emergence of graviton-like excitations from a lattice model

      Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases.

      2018-2019

      DateSpeakerTitle/Abstract
      9/26/2018Xiao-Gang Wen (MIT)Title: A classification of low dimensional topological orders and fully extended TQFTs

      Abstract: In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1-dimension, there is no non-trivial topological orders. In 2-dimensions, the topological orders are classified by modular tensor category theory. In 3-dimensions, the topological orders are classified by a simple class of braided fusion 2-categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs.

      10/03/2018Richard Schoen (Stanford)Title: Perspectives on the scalar curvature

      Abstract: This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied.

      10/10/2018Justin Solomon (MIT)Title: Correspondence and Optimal Transport for Geometric Data Processing

      Abstract: Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make large-scale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometrically-structured data.

      10/17/2018Jeremy England (MIT)Title: Wisdom of the Jumble

      Abstract: There are certain, specific behaviors that are particularly distinctive of life. For example, living things self-replicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of life-like phenomena in a wide range of messy systems made of many interacting components.

      In this talk I will discuss some of the recent insights we have gleaned from studying emergent fine-tuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more life-like ways of computing that have the potential to either be cheaper or more powerful than existing means.

      10/31/2018Moon Duchin (Tufts)Title: Exploring the (massive) space of graph partitions

      Abstract: The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts).  I’ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics.

      11/14/2018Dusa McDuff (Columbia)Title: The virtual fundamental class in symplectic geometry

      Abstract: Essential to many constructions and applications of symplectic  geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well  understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so  that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there  are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a  construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim.

      11/19/2018Xiaoqin Wang (Johns Hopkins)Title: Computational Principles of Auditory Cortex

      Abstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication.

      11/28/2018Robert Haslhofer (University of Toronto)Title: Recent progress on mean curvature flow

      Abstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanen’s multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits.

      12/5/2018Robert McCann (University of Toronto)Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity

      Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of  probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics.

      Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf

      12/12/2018Zhiwei Yun (MIT)Title: Shtukas: what and why

      Abstract: This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them.

      1/30/2019Richard Freeman (Harvard)Title:  Innovation in Cell Phones in the US and China: Who Improves Technology Faster?

      Abstract:  Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps.  Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones.  Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality.  The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being.

      2/7/2019

      *Thursday*

      Ulrich Mueller (Princeton)Title: Inference for the Mean

      Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.

      2/13/2019Christian Santangelo (UMass Amherst)Title: 4D printing with folding forms

      Abstract: 4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target three-dimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our group’s efforts to understand and design structures that can fold from an initially flat sheet to target three-dimensional shapes. After reviewing the state-of-the-art in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome.

      2/20/2019Michael Woodford (Columbia)Title: Optimally Imprecise Memory and Biased Forecasts

      Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings.

      [authors: Rava Azeredo da Silveira (ENS) and Michael Woodford (Columbia)]

      2/27/2019

      2:30pm

      Ian Martin (LSE)Title: Sentiment and Speculation in a Market with Heterogeneous Beliefs

      Abstract: We present a dynamic model featuring risk-averse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so “the market” is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou]

      3/6/2019

      2:30pm

      Philippe Sosoe (Cornell)Title:  A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation

      Abstract:  In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS’s result, and discuss a sharp transition in the construction of the Gibbs-type invariant measures considered by these authors.  (Joint work with Tadahiro Oh and Leonardo Tolomeo)

      3/13/2019

      5:15pm

      Greg Galloway (University of Miami)Title:  On the geometry and topology of initial data sets in General Relativity

      Abstract:  A theme of long standing interest (to the speaker!)  concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness).  Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple.  The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces,  which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack.

      3/20/2019Sonia Jaffe (Microsoft)Title:  Quality Externalities on Platforms:  The Case of Airbnb

      Abstract:  We explore quality externalities on platforms:  when buyers have limited information, a seller’s quality affects whether her buyers return to the platform, thereby impacting other sellers’ future business.  We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller’s customers to return to the platform.  We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higher-GRP sellers, platforms may be able to increase overall seller surplus.  (Joint work with Peter Coles, Steven Levitt, and Igor Popov.)

      3/27/2019

      5:15pm

      Tatyana Sharpee (Salk Institute for Biological Studies)Title: Hyperbolic geometry of the olfactory space.

      Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their co-occurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical tree-like networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

      4/3/2019

      2:30pm

      Sarah Moshary (Chicago Booth)Title:  Deregulation through Direct Democracy:  Lessons from Liquor

      Abstract:  This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool.

      4/10/2019

      2:30pm

      Pietro Veronesi (Chicago Booth)Title: Inequality Aversion, Populism, and the Backlash Against Globalization

      Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model.

      Paper

      Online Appendix

      4/17/2019Yi-Zhuang You (UCSD)Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

      Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

      .

      [1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103

      [2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804

      [3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223

      4/24/2019Shengwu Li (Harvard)
      Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.
      Date…………SpeakerTitle
      02-09-2018 *Friday       Fan Chung

      (UCSD)

      Sequences: random, structured or something in between

      There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns;

      testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems.

      02-14-2018Zhengwei Liu

      (Harvard Physics)

      A new program on quantum subgroups

      Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing.

      02-21-2018Don Rubin

      (Harvard)

      Essential concepts of causal inference — a remarkable history

      Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis.

      02-26-2018 *MondayTom Hou

      (Caltech)

      Computer-assisted analysis of singularity formation of a regularized 3D Euler equation

      Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate self-similar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate self-similar solution, which implies the existence of the finite time blow-up of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu.

      03-07-2018Richard Kenyon

      (Brown)

      Harmonic functions and the chromatic polynomial

      Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam.

      03-14-2018
      03-21-2018
      03-28-2018Andrea Montanari (Stanford)A Mean Field View of the Landscape of Two-Layers Neural Networks

      Abstract: Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD).  Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties?

      We consider a simple case, namely two-layers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to `average-out’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well.
      [Based on joint work with Song Mei and Phan-Minh Nguyen]

      03-30-2018
      04-04-2018Ramesh Narayan 

      (Harvard)

      Black Holes and Naked Singularities

      Abstract: Black Hole solutions in General Relativity contain Event Horizons and
      Singularities. Astrophysicists have discovered two populations of
      black hole candidates in the Universe: stellar-mass objects with
      masses in the range 5 to 30 solar masses, and supermassive objects
      with masses in the range million to several billion solar
      masses. There is considerable evidence that these objects have Event
      Horizons. It thus appears that astronomical black hole candidates are
      true Black Holes. Direct evidence for Singularities is much harder to
      obtain since, at least in the case of Black Holes, the Singularities
      are hidden inside the Event Horizon. However, General Relativity also
      permits Naked Singularities which are visible to external
      observers. Toy Naked Singularity models have been constructed, and
      some observational features of accretion flows in these spacetimes
      have been worked out.

      04-11-2018Pablo Parrilo

      (MIT)

      Graph Structure in Polynomial Systems: Chordal Networks

      Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).

      04-18-2018Washington Taylor

      (MIT)

      On the fibration structure of known Calabi-Yau threefolds

      Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds.

      04-25-2018 Xi Yin

      (Harvard)

      How we can learn what we need to know about M-theory

      Abstract: M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory.

      05-02-2018
      05-09-2018

      2016-2017

      DateNameTitle/Abstract
      01-25-17Sam Gershman, Harvard Center for Brain Science, Department of Psychology

      Title: Spectral graph theory of cognitive maps

      Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory.

      02-01-17Sean Eddy, Harvard Department of Molecular and Cellular Biology

      Sean_Eddy

      Title: Biological sequence homology searches: the future of deciphering the past 

      Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK.

      02-08-17Matthew Headrick, Brandeis University

      matthew_headrick

      Title: Quantum entanglement, classical gravity, and convex programming: New connections

      Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differential-geometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way.

      02-15-17Masahito Yamazaki, IMPU

      Masahito Yamazaki

       Title: Geometry of 3-manifolds and Complex Chern-Simons Theory

      Abstract: The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras.

      Video

      02-22-17Steven Rayan, University of Saskatchewan

      Title: Higgs bundles and the Hitchin system

      Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics.  As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence.  From this point of view, the Hitchin map and spectral curves emerge.  We’ll use these to form an impression of what the moduli space “looks like”.  I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry.

      Video

      03-01-17Jun Liu, Harvard University

      Jun liu

      Title: Expansion of biological pathways by integrative Genomics

      Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays.

      Based on the joint work with Yang Li and the Vamsi Mootha lab.

      Video

      03-08-17Gabor Lippner, Northeastern University

      ---

      Title: Evolution of cooperation in structured populations

      Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics.  Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies.  It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution.

      In this talk I will present new results about the model where the population is represented by an interaction network.  We study the likelihood of a random mutation spreading through the entire population.  The main question is to understand how the network influences this likelihood.  After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks.
      03-15-17 Spring Break: No session
      03-22-17Gunther Uhlmann, University of Washington

      guntherUhlman

      Abstract We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of
      waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others.
      The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.
      We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.
      03-29-17Leslie Greengard, Courant InstituteLeslie_GreengardTitle: Inverse problems in acoustic scattering and cryo-electron microscopy

      Abstract: A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy.

      NOTE: This talk will begin at 4:00pm

      04-05-17Gongjie Li, Harvard University

      GongjieLi

      Title: Unveiling the Origin of Planetary Systems by Dynamical and Statistical Approaches

      Abstract: The unexpected diversity of observed extrasolar planetary systems has posed new challenges to our classical understanding of planetary formation. A lot of these challenges can be addressed by a deeper understanding of the dynamics in planetary systems, which will also allow us to construct more accurate planetary formation theories consistent with observations. In this talk, I will first explain the origin of counter orbiting planets using a new dynamical mechanism I discovered, which also has wide implications in other astrophysical systems, such as the enhancement of tidal disruption rates near supermassive black hole binaries. In addition, I will discuss the architectural properties of circumbinary planetary systems from selection biases using statistical methods, and infer the origin of such systems.

      Video

      04-12-17Shlomo Razamat, Israel Institute of Technology

      ShlomoRazamat

      Title: Complicated four-dimensional physics and simple mathematics

      Abstract: We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index,  of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of Ruijsenaars-Schneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven.

      Video

      04-19-17Cumrun Vafa, Harvard University

      CumrunVafa

      Title: String Swampland

      Abstract: In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a no-go theorem for non-supersymmetric AdS/CFT holography.

      04-27-17Mehran Kardar, MIT

      MehranKardar

      Title: Levitation by Casimir forces in and out of equilibrium

      Abstract: Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw’s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint.

      Note: This talk will begin at 3:00pm

      05-02-17Simona Cocco, Laboratoire de Physique Statistique de l’ENSTitle: Reverse modeling of protein sequence data: from graphical models to structural and functional predictions

      Body: A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing
      similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models
      have led to substantial progress in protein structural and functional
      predictions.

      Note:  This talk will begin at 4:00pm

      05-03-17Xue-Mei Li, University of WarwickTitle: Perturbation to conservation law and stochastic averaging

      Abstract: A deterministic or random system with a conservation law is often used to
      approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces.

      Note: This talk will be held in the Science Center, Room 507

      05-10-17
      05-17-17Kwok Wai Chan, Chinese University of Hong KongTitle: Scattering diagrams from asymptotic analysis on Maurer-Cartan equations

      Abstract:  In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on Maurer-Cartan equations. In this talk, I will explain some results which implement part of Fukaya’s program. More precisely, I will show how semi-classical limits of Maurer-Cartan solutions give rise naturally to consistent scattering diagrams, which are known to encode Gromov-Witten data on the mirror side and have played an important role in the works of Kontsevich-Soibelman and Gross-Siebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015).

      05-24-17 NO COLLOQUIUM
      05-31-17Peter Michor, University of Vienna

       Title: Geometry of shape spaces and diffeomorphism groups and some of their uses

      Abstract: This talk is devoted to shape spaces, Riemannian metrics on them, their geodesics and distance functions, and some of their uses, mainly in computational anatomy. The simplest Riemannian metrics have vanishing geodesic distance, so one has to use, for example, higher order Sobolev metrics on shape spaces. These have curvature, which complicates statistics on these spaces.

      DateNameTitle
      09-09-16

      Bong Lian, Brandeis

      portrait

      Title: Riemann-Hilbert Problem and Period Integrals

      Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems.

      09-14-16Sze-Man Ngai, Georgia Southern UniversityngaiTitle: The multifractal formalism and spectral asymptotics of self-similar measures with overlaps

      Abstract: Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum.  The asymptotic behavior of the eigenvalue counting function for the associated  Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results.

      09-21-16Prof. L. Mahadevan, Harvard SEAS

      Mahadevan_200x300

      Title: “Morphogenesis: Biology, Physics and Mathematics”

      Abstract:  A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology.  Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains.  I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology.

      09-28-16Hong Liu, MIT

      liu_hong

      Title: A new theory of fluctuating hydrodynamics

      Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate  for capturing  fluctuations.  In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure.

      We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular,  the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations.

      Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anti-commuting variables and the theory exhibits an emergent supersymmetry.

      10-05-16

      Alexander LogunovTel-Aviv University

      alex

      Title: Zeroes of harmonic functions and Laplace eigenfunctions

       Abs: Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete.

      10-12-16 Conan Nai Chung Leung, CUHK

      conan_profile

      Title:  Coisotropic A-branes and their SYZ transform

      Abstract: “Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit.”

      10-19-16Vaughan Jones, UC Berkeley

      vj6

      Title: Are the Thompson groups any good as a model for Diff(S^1)?

      Abstract. The Thompson groups are by definition groups of piecewise linear
      diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can
      be conjugated to a group of smooth diffeomorphisms. That’s the good news.
      The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any
      procedure analogous to the constructions of the central extension of Diff(S^1)?
      I will define all the players in this game, explain this question in detail,and present some failed attempts to answer it.

       10-26-16

      Henry Cohn, Microsoft

      ????????????????????????????????????

      Sums of squares, correlation functions, and exceptional geometric structures

      Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding.  How can we understand and prove their optimality?  In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems.

      11-02-16

      Christian Borgs, Microsoft

      Borgs

      Title:  Graphon processes and limits of   sparse graph sequences

      Abstract:  The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for so-called exchangeable random graphs.   Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection.  While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model.  

      In this talk I describe a new model, where the underlying probability space is replaced by a sigma-finite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits.  The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life.

      11-09-16

      TIME CHANGE: 4PM

      Norden E. HuangNational Central University, (Taiwan)

      member1_clip_image003

      Title: On Holo-Hilbert Spectral Analysis

      Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation.

      11-16-16Tristan Collins, Harvard University

      image

      TIME CHANGE: 3:30PM

      Title: Restricted volumes and finite time singularities of the Kahler-Ricci flow

      Abstract:  I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow.  This is joint work with Valentino Tosatti.

      11-22-16 TUESDAY

      TIME CHANGE: 4-5PM

      Xiangfeng Gu, Stonybrook

      Title: Differential Geometric Methods for Engineering Applications

      Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation.

      11-30-16

      TIME CHANGE: 4:20PM

      Sharad Ramanathan, Harvard MCB & SEAS

      Ramanathan.Sharad_200x300

      Title: Finding co-ordinate systems to monitor the development of mammalian embryos
       12-07-16

      Valentino Tosatti, Northwestern

      Title: Metric limits of hyperkahler manifolds

      Abstract: I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang.

       12-14-16

      2015-2016

      DateNameTitle
      09-02-2015Madhu SudanRobust low-degree testing
      09-09-2015Mithat Unsal
      What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
      09-16-2015Subir SachdevBekenstein-Hawking entropy and strange metals
      09-23-2015Felix FinsterLinear hyperbolic equations in a rotating black hole geometry
      09-30-2015Leslie ValiantHolographic Algorithms
      10-07-2015Christopher RoganExploring the Frontier of Size and Energy with the Large Hadron Collider: sub-atomic particles, the Higgs Boson and beyond
      10-14-2015Boaz Barak, Harvard SEASConvexity, Bayesianism, and the quest towards Optimal Algorithms
      10-21-2015Zhouping XinEntropy and Uniqueness of Weak Solutions to The Multi-Dimensional Compressible Euler Systems
      10-28-2015Cristopher MooreStatistical inference, statistical physics, and the community detection problem
      11-04-2015Tom HouBlowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations
      11-11-2015Stan Osher, UCLAOvercoming the curse of dimensionality for certain Hamilton-Jacobi (HJ) equations arising in control theory and elsewhere
      11-18-2015Xiaole Shirley LiuInference of transcriptional regulation in cancers
      11-25-2015ThanksgivingNo seminar
      12-02-2015Scott KominersGeneralized Matching Market Design: Theory and Practice
      12-09-2015Matthew HolmanDynamical Chaos in Kepler Planetary Systems
      01-27-2016Conan LeungSome modern aspects of Morse theory 
      02-03-2016Camillo De LellisFrom Nash to Onsager, funny coincidences across differential geometry and the theory of turbulence
      02-10-2016Chun Peng Wang
      02-17-2016Samuel Kou, Harvard StatisticsBig data, Google and disease detection: the statistical story
      02-24-2016Dan Xie, Harvard CMSASingularity theory and supersymmetric field theory
      03-02-2016Lydia BieriMathematical General Relativity
      03-09-2016Piotr ChruscielThe mathematics of gravitation
      03-16-2016Spring BreakNo Talk
      03-23-2016Richard Freeman, Harvard EconomicsPulling Apart of Wages and Productivity: why “identical” workers have increasingly different pay and productivity.
      03-30-2016David Garfinkel, Oakland UniversityGravitational Wave Memory
      04-04-2016 (Hall A, Science Center)Xianfeng David Gu, Stony Brook UniversityA Discrete Variational Approach for Solving Monge-Ampere Equation
      04-06-2016Lars Hernquist, HarvardNext Generation Cosmological Simulations: Galaxy Assembly and Evolution
      04-13-2016Jun Zhang, Univ. of Michigan-Ann ArborKahler and Para-Kahler Structure in Information Geometry
      04-20-2016Sijue Wu, Univ. of MichiganOn two dimensional gravity water waves with angled crests
      04-27-2016Paul Seidel, MITTopological quantum field theory and the Gauss-Manin connection
      05-04-2016Hirosi Ooguri, CaltechString Theory And Its Applications in Mathematics and Physics
      05-11-2016      (4pm – 5pm)Juerg Froehlich, ETH and IASImplications of the Chiral Anomaly – From the Quantum Hall Effect to Topological Insulators and Out to Space
    • Colloquium
      11:05 am-11:06 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:07 am-11:08 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:08 am-11:09 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-22-2016 Random Matrix & Probability Theory Seminar
      11:12 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-07-2016 Random Matrix & Probability Theory Seminar
      11:16 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12-05-16 Mathematical Physics Seminar
      11:17 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:21 am-11:22 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      11:21 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-14-2016 Random Matrix & Probability Theory Seminar
      11:22 am
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      11:24 am
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      11:25 am
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Learning from health data in the million genome era
      11:26 am
      11/01/2019

      On November 12019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system.

      Speakers: 

      • Heidi Rehm, Ph.D.
        Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform.
      • Saiju Pyarajan, Ph.D.
        Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS
      • Tianxi Cai, Sci.D
        John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health
      • Susan Redline, M.D., M.P.H
        Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center
      • Avinash Sahu, Ph.D.
        Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health
      • Peter J. Park, Ph.D.
        Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School
      • David Roberson
        Community Engagement Manager, Seven Bridges

      Registration & Schedule

    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 Quantum Field Theory Seminar
      11:30 am-12:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      01-30-2017 Mathematical Physics Seminar
      11:30 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-07-2017 Social Sciences Applications Forum
      11:32 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      02-06-2017 Mathematical Physics Seminar
      11:33 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      02-13-2017, Mathematical Physics Seminar
      11:34 am
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      11:35 am
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Spacetime and Quantum Mechanics Master Class Workshop
      11:36 am
      11/01/2019-10/30/2019
      Space-Time-poster-5

      As part of the program on Spacetime and Quantum Mechanics, Total Positivity and Motives, the CMSA will host a “Master Class Workshop”  on October 28-30, 2019. Each day of the workshop will feature an intensive full day of pedagogical lectures, with the aim of bringing actively interested but non-expert physicists and mathematicians up to speed on the featured topics.

      Everyone is welcome to attend the lectures.

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

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

      Photos of the event

      Organizers:

    • Member Seminar
      11:37 am
      11/01/2019

      Hansol Hong, Harvard

      Title: Homological Mirror Functors

      Abstract: I will first give a brief introduction to mirror symmetry, which intertwines symplectic geometry and complex geometry of a pair of Kahler manifolds, and explain mirror construction using formal deformation of a Lagrangian submanifold.  We will see that counting of holomorphic discs bounding Lagrangian naturally gives rise to a mirror space (Landau-Ginzburg model) and  a functor from Fukaya category to its mirror matrix factorization category. I will mainly focus on one specific example to give a concrete description of the construction.

    • Colloquium
      11:39 am-11:40 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:40 am-11:41 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-14-2017 Social Science Applications Forum
      11:42 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:43 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:45 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/24/2019 Quantum Matter Seminar
      11:50 am-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/31/2019 Condensed Matter Seminar
      11:50 am-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/10/2019 Condensed Matter Seminar
      11:50 am-1:00 pm
      11/01/2019
    • CMSA EVENT: Quantum Information Workshop
      11:52 am-11:53 am
      11/01/2019
      Asset-6-600x338

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

      The CMSA will host a workshop on Quantum Information. This workshop will be held virtually using Zoom.

      The workshop on Quantum information is organized by Mikhail LukinHorng-Tzer Yau, and Norman Yao.

      More information to follow.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-12-2017 Random Matrix & Probability Theory Seminar
      11:56 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:56 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:58 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-22-2017 Random Matrix & Probability Theory Seminar
      11:58 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-21-2017 Social Science Applications Forum
      11:59 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      5/6/2019 Math Physics
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4-17-2018 Special Algebraic Geometry Seminar
      12:00 pm-1:30 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/19/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12/3/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/8/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/29/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/26/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/25/2019 Fluid Dynamics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/3/2019 Condensed Matter Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/5/2018 Math Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/7/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/22/2019 Math Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/29/2018 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/15/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/9/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      1/28/2018 Mathematical Physics Seminar
      12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/4/2019 Math Physics Seminar
      12:00 pm-2:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/25/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • General Relativity Seminar
      12:00 pm-1:00 pm
      11/01/2019

      The Seminar on General Relativity will take place every Wednesday from 12pm – 1pm in CMSA Building, 20 Garden Street, G10.

      The list of speakers is below and will be updated as details are confirmed.

      DateNameTitle
      04-06-2016Mihalis Dafermos (Princeton)The black hole stability problem: the inside story
      04-13-2016Felix Finster, University of RegensburgLinear stability of Kerr black holes
      04-20-2016Paul Chesler, Harvard PhysicsNumerical relativity in asymptotically anti-de Sitter spacetime
      04-27-2016Andy Strominger (Harvard Physics) & Mihalis Dafermos (Princeton University)The Scattering Problem in General Relativity
      05-04-2016Robert Penna, MITBMS invariance and the membrane paradigm
      05-11-2016Piotr T. Chruściel, University of ViennaGluing things in general relativity
      05-18-2016Achilleas Porfyriadis, Harvard PhysicsGravitational waves from the Kerr/CFT correspondence
      05-25-2016Scott Hughes, MITThe gravitational-wave event GW150914: What we learned, and how we learned it
    • Seminars
      Seminars Colloquia & Seminar
      3/4/2019 Mathematical Physics Seminar
      12:00 pm-2:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      1-5-2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Quantum Matter Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/28/2019 Math Physics
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/16/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-2-2018 Mathematical Physics Seminar
      12:00 pm-1:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/25/2019 Math Physics Seminar
      12:00 pm-2:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/1/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/11/2019 Mathematical Physics Seminar
      12:00 pm-2:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3/19/2018 Mathematical Physics Seminar
      12:00 pm-1:30 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-26-2018 Math Physics Seminar
      12:00 pm-1:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Condensed Matter Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/30/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-22-2017 Random Matrix & Probability Theory Seminar
      12:01 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:03 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Cosmic Road to New Physics
      12:04 pm
      11/01/2019
      The colourful star cluster NGC 3532

      The CMSA will host a 3-day workshop on cosmological signatures of fundamental physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

      The next decade will see a wealth of new cosmological data, which can lead to new insights for fundamental physics. This upcoming data will span the entire history of the cosmos, from the era prior to big-bang nucleosynthesis to the inner Galactic structure today, including the intervening eras of recombination and cosmic dawn. Often, beyond-standard-model (BSM) physics will leave imprints in more than one of these eras. Thus, it is timely to gather experts in BSM physics across the entire cosmic history to exchange ideas and develop joint and powerful probes of new physics. For this program, it will be crucial to have an overlap of particle physicists, astrophysicists and cosmologists. There are a number of tools and techniques being actively developed across these disciplines. The workshop aims to provide a platform for efficient exchange of these new ideas.

      The first day we will discuss sub-Galactic probes, including Gaia data and gravitational waves. The second day we will cover cosmological probes, such as the cosmic microwave background and the 21-cm line. The third day we will discuss early Universe probes, such as inflation and phase transitions. Every day the meeting will begin with a pedagogical blackboard talk plus an overview talk, followed by about 4 talks on more specific topics.

      Organizers:

      Scientific Advisory:

      Speakers: 

      CosmicRoad_Poster

    • Colloquium
      12:05 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:06 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:08 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:09 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      12:10 pm-1:10 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

       

      Speaker: Man-Wai Cheung

      Title: Compactification for cluster varieties without frozen variables of finite type

      Abstract: Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev–Borisov construction.

    • CMSA EVENT: 2019 Ding Shum Lecture
      12:11 pm
      11/01/2019
      DingShum-2019

      DSC_0468-e1568985499370

      On October 22, 2019, the CMSA will be hosting our third annual Ding Shum lecture. This year’s lecture will be a talk on “Election Security” by Ronald L. Rivest (MIT). The lecture will take place from 4:30-5:30pm in Science Center, Hall A.

      Ronald L. Rivest is an Institute Professor at the Massachusetts Institute of Technology. He is a member of the Electrical Engineering and Computer Science Department and the Computer Science and Artificial Intelligence Laboratory (CSAIL) and a founder of the Cryptography and Information Security research group within CSAIL. His research has been in the areas of algorithms, machine learning, cryptography, and election security, for which he has received multiple awards, including: the ACM Turing Award (with Adleman and Shamir), the BBVA Frontiers of Knowledge Award, National Inventor’s Hall of Fame membership, and the Marconi Prize.

      Prof. Rivest is also well-known as a co-author of the textbook “Introduction to Algorithms” (with Cormen, Leiserson, and Stein), and as a co-inventor of the RSA public-key cryptosystem (with Adleman and Shamir). He is a co-founder of RSA and of Verisign.He has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), in charge of the Security subcommittee. He is a member of the CalTech/MIT Voting Technology Project, on the Board of Verified Voting, and an advisor to the Electronic Privacy Information Center. Additionally, he has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), as a member of the CalTech/MIT Voting Technology Project, and as an advisor to the Electronic Privacy Information Center.

      Last year featured Eric Maskin, who spoke on “How to Improve Presidential Elections: the Mathematics of Voting.” The first Ding Shum lecture took place on October 10, 2017, featuring Leslie Valiant on “Learning as a Theory of Everything.”

      This event is made possible by the generous funding of Ding Lei and Harry Shum.

      DingShum-2019

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-1-2017 Random Matrix & Probability Seminar
      12:11 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Special Lecture Series on Donaldson-Thomas and Gromov-Witten Theories
      12:11 pm
      11/01/2019-04/19/2017

      From March 8 to April 19, the Center of Mathematical Sciences and Applications will be hosting a special lecture series on Donaldson-Thomas and Gromov-Witten Theories. Artan Sheshmani (QGM Aarhus and CMSA Harvard) will give eight talks on the topic on Wednesdays and Fridays from 9:00-10:30 am, which will be recorded and promptly available on CMSA’s Youtube Channel.

    • Colloquium
      12:12 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:13 pm-12:14 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2-27-2017 Mathematical Physics Seminar
      12:14 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-7-2017 Social Science Applications Forum
      12:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/13/2019 Special Seminar
      12:15 pm-1:05 pm
      11/01/2019
    • Colloquium
      12:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-8-2017 CMSA Special Lecture Series
      12:16 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Noncommutative Analysis, Computational Complexity, and Quantum Information
      12:19 pm
      11/01/2019-10/18/2019
      Noncommutative-Analysis-Poster-3

      On October 16-18, 2019 the CMSA will be hosting a workshop on Noncommutative Analysis, Computational Complexity, and Quantum Information.

      This workshop will focus on  linking three different rapidly developing areas: noncommutative real algebraic geometry (RAG), theory of computation and quantum information theory. This mix of overlapping but independently developing topics should lead to a stimulating flow of tools and important problems into several disciplines.  Given the different communities there will be an emphasis on tutorials and making the lectures broadly understandable.

      The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by Boaz Barak, Bill Helton, Pablo Parrilo, Tselil Schramm.

      Please register here

      Speakers:

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

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-8-2017 Random Matrix & Probability Theory Seminar
      12:21 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-6-2017 Mathematical Physics Seminar
      12:24 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      12:25 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-10-2017 Special Lecture Series
      12:27 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
      12:28 pm
      11/01/2019-05/05/2019
      1 Oxford Street, Cambridge MA 02138
      Differential Geometry, Calabi-Yau theory and General Relativity

      Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau

      On May 2-5, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the  Science Center, Lecture Hall C. 

      Organizers:

      • Horng-Tzer Yau (Harvard)
      • Wilfried Schmid (Harvard)
      • Clifford Taubes (Harvard)
      • Cumrun Vafa (Harvard)

      Speakers:

      • Lydia Bieri, University of Michigan
      • Tristan Collins, MIT
      • Simon Donaldson, Imperial College
      • Fan Chung Graham, UC San Diego
      • Nigel Hitchin, Oxford University
      • Jun Li, Stanford University
      • Kefeng Liu, UCLA
      • Chiu-Chu Melissa Liu, Columbia University
      • Alina Marian, Northeastern University
      • Xenia de la Ossa, Oxford University
      • Duong H. Phong, Columbia University
      • Richard Schoen, UC Irvine
      • Andrew Strominger, Harvard University
      • Nike Sun, MIT
      • Clifford Taubes, Harvard University
      • Chuu-Lian Terng, UC Irvine
      • Valentino Tosatti, Northwestern University
      • Karen Uhlenbeck, University of Texas
      • Cumrun Vafa, Harvard University
      • Mu Tao Wang, Columbia University
      • Edward Witten, IAS
      • Stephen Yau, Tsinghua University, P.R. China
    • Seminars
      Seminars Colloquia & Seminar
      3-21-2017 Social Science Applications Forum
      12:28 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:30 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-20-2017 Mathematical Physics Seminar
      12:30 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-5-2017 Random Matrix & Probability Theory Seminar
      12:31 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:32 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Conference on Algebraic Geometry, Representation theory and Mathematical Physics
      12:33 pm
      11/01/2019-05/01/2019

      From April 29 to May 1, 2019 the CMSA will be hosting a Conference on Algebraic Geometry, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.  

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

      List of registrants

      Videos

      Speakers: 

       

      Monday, April 29

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amWei Zhang, MITTitle: The arithmetic fundamental lemma for diagonal cycles

      Abstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization, the arithmetic Gan-Gross-Prasad conjecture, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions.  The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.

      10:00 – 10:30amBreak
      10:30 – 11:30amYuri Tschinkel, NYUTitle: Equivariant birational geometry and modular symbols

      Abstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).

      11:30 – 1:30pmLunch
      1:30 – 2:30pmAlexander Efimov, MoscowTitle: Torsionness for regulators of canonical extensions

      Abstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.

      2:30 – 3:00pmBreak
      3:00 – 4:00pmAmin Gholampour, MarylandTitle: Euler Characteristics of punctual quot schemes on threefolds

      Abstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F, n) and Quot(G,n), where Quot(-,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.

      4:00 – 4:30pmBreak
      4:30 – 5:30pmMaksym Fedorchuck, BCTitle:  Stability of one-parameter families of weighted hypersurfaces

      Abstract:  We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space.  The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions, and, if time permits, examples where this machinery can be used to produce birational models with good properties.  Joint work with Hamid Ahmadinezhad and Igor Krylov.

       

      Tuesday, April 30

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amBrendan Hassett, BrownTitle: Rationality for geometrically rational threefolds

      Abstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure, like smooth complete intersections of two quadrics.  (joint with Tschinkel)

      10:00 – 10:30amBreak
      10:30 – 11:30amDennis Gaitsgory, HarvardTitle: The Fundamental Local Equivalence in quantum geometric Langlands

      Abstract: The Fundamental Local Equivalence is statement that relates the q-twisted  Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its  dual is combinatorial, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra, which in itself is a geometric device that concisely encodes the root data.

      11:30 – 1:00pmLunch
      1:00- 2:00pmAndrei Negut, MITTitle: AGT relations in geometric representation theory

      Abstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces, and the goal is to connect them with the W-algebra of type gl_n.

      2:00 – 2:15pmBreak
      2:15 – 3:15pmDan Abramovich, BrownTitle: Resolution in characteristic 0 using weighted blowing up

      Abstract: Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved.

      Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop.

      We show that there is a functorial way to resolve varieties using \emph{weighted} blowings up, in the stack-theoretic sense. To an embedded variety $X \subset Y$ one functorially assigns an invariant $(a_1,\ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , \ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.

      This is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.

      3:15 – 3:30pmBreak
      3:30 – 4:30pmFedor Bogomolov, NYUTitle: On the base of a Lagrangian fibration for a compact hyperkahler manifold.

      Abstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of  Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.

      4:30 – 4:45pmBreak
      4:45 – 5:45pmDawei Chen, BCTitle: Volumes and intersection theory on moduli spaces of Abelian differentials

      Abstract: Computing volumes of moduli spaces has significance in many fields. For instance, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

       

      Wednesday, May 1

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amPavel Etingof, MITTitle: Short star-products for filtered quantizations

      Abstract: PDF

      This is joint work with Eric Rains and Douglas Stryker.

      10:00 – 10:30amBreak
      10:30 – 11:30amRoman Bezrukavnikov, MITTitle: Stability conditions and representation theory

      Abstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)
      and its relation to modular Lie algebra representations. I will also address a potential generalization of that picture
      to modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.

      11:30 – 11:45amBreak
      11:45 – 12:45pmQile Chen, BCTitle: Counting curves in critical locus via logarithmic compactification

      Abstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles, the non-compactness of the R-maps moduli makes such powerful torus action useless.

      In this talk, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action.

      This is a joint work with Felix Janda and Yongbin Ruan.

      12:45 – 2:30pmLunch
      2:30 – 3:30pmSi Li, TsinghuaTitle: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry

      Abstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.

      3:30 – 4:00pmBreak
      4:00 – 5:00pmLudmil Katzarkov, MoscowTitle: PDE’s non commutative  motives and HMS.

      Abstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir.  Geometry will be discussed.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-29-2017 Random Matrix & Probability Theory Seminar
      12:35 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-24-2017 Random Matrix & Probability Theory Seminar
      12:37 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-30-2017 CMSA Special Seminar
      12:38 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      03-27-2017 Mathematical Physics Seminar
      12:40 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:41 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-5-2017 Special Lecture Series
      12:42 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-7-2017 Special Lecture Series
      12:43 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:43 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-12-2017 Special Lecture Series
      12:44 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:45 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-14-2017 Special Lecture Series
      12:46 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-3-2017 Mathematical Physics Seminar
      12:50 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      12:51 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-12-2017 Social Science Applications Forum
      12:53 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Workshop on Mirror Symmetry and Stability
      12:55 pm
      11/01/2019-03/20/2019
      HMS-2019-1

      This three-day workshop will take place at Harvard University on March 18-20, 2019 in Science Center room 507. The main topic will be stability conditions in homological mirror symmetry. This workshop is funded by the Simons Collaboration in Homological Mirror Symmetry.

      Organizers: Denis Auroux, Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau, Bong Lian, Shing-Tung Yau, Jingyu Zhao

      Speakers:

      Dylan Allegretti (Sheffield)
      Tristan Collins (MIT)
      Naoki Koseki (Tokyo)
      Chunyi Li (Warwick)
      Jason Lo (CSU Northridge)
      Emanuele Macrì (NEU & IHES)
      Genki Ouchi (Riken iTHEMS)
      Pranav Pandit (ICTS)
      Laura Pertusi (Edinburgh)
      Jacopo Stoppa (SISSA)
      Alex Takeda (UC Berkeley)
      Xiaolei Zhao (UC Santa Barbara)

      More details will be added later.

      Visit the event page for more information. 

       

      HMS-2019-1

    • Colloquium
      12:55 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:57 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Simons Collaboration Workshop, April 5-7, 2018
      1:00 pm-6:00 pm
      11/01/2019-04/07/2018
      banner-image-1

      The CMSA will be hosting a three-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 5-7, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

      We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

      Confirmed Speakers:

    • Seminars
      Seminars Colloquia & Seminar
      4-11-2017 Social Science Applications Forum
      1:00 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      Combinatorics & Complexity Seminar, Fridays
      1:00 pm-4:00 pm
      11/01/2019

      The seminar on Combinatorics and Complexity will be held every Friday from 1:00-4:00pm in CMSA Building, 20 Garden Street, Room G10.

      The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

      Additional information on CMSA’s Combinatorics and Complexity program can be found here.

       

      DateNameTitle/Abstract
      09-08-17TBA
      09-15-2017TBA
      09-22-17TBA
      09-29-17TBA
      10-06-17 TBA
      10-13-2017TBA
      10-20-2017TBA
      10-27-2017TBA
      11-03-2017TBA
      11-10-2017TBA
      11-17-2017TBA
      11-24-2017TBA
      12-01-2017TBA
      12-08-2017 TBA
    • CMSA EVENT: Second Annual STAR Lab Conference
      1:01 pm-1:02 pm
      11/01/2019

      The second annual STAR Lab conference is running 10/29/-10/30/2015 at the Harvard Business School.  This event is co-sponsored by the Center of Mathematical Sciences and Applications.

      For more information, please consult the event’s website.

    • Colloquium
      1:02 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:07 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-10-2017 Mathematical Physics Seminar
      1:07 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-21-2015 Mathematical Physics Seminar
      1:09 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      1:10 pm-3:00 pm
      11/01/2019
    • Colloquium
      1:10 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      08-31-2015 Mathematical Physics Seminar
      1:10 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:11 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-01-2015 Differential Geometry Seminar
      1:12 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-12-2017 Random Matrix & Probability Theory Seminar
      1:12 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:13 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-01-2015 Evolution Equation Seminar
      1:13 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-14-2015 Mathematical Physics Seminar
      1:14 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-17-2017 Mathematical Physics Seminar
      1:14 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-18-2017 Social Science Applications Forum
      1:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-08-2015 Geometric Analysis Seminar
      1:16 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-06-2015 Geometric Analysis Seminar
      1:17 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:18 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-08-2015 Evolution Equations Seminar
      1:18 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:20 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:21 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      1:21 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-13-2015 Geometric Analysis Seminar
      1:22 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-19-2017 Random Matrix & Probability Theory Seminar
      1:22 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-10-2015 Evolution Equations Seminar
      1:23 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: 2016 Big Data Conference & Workshop
      1:24 pm
      11/01/2019-08/23/2016
      1 Oxford Street, Cambridge MA 02138

      ! LOCATION CHANGE: The conference will be in Science Center Hall C on Tuesday, Aug.23, 2016.

      The Center of Mathematical Sciences and Applications will be hosting a workshop on Big Data from August 12 – 21, 2016 followed by a two-day conference on Big Data from August 22 – 23, 2016.

      Big Data Conference features many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the second conference on Big Data the Center will host as part of our annual events. The 2015 conference was a huge success.

      The conference will be hosted at Harvard Science Center Hall A (Monday, Aug.22) & Hall C (Tuesday, Aug.23): 1 Oxford Street, Cambridge, MA 02138.

      The 2016 Big Data conference is sponsored by the Center of Mathematical Sciences and Applications at Harvard University and the Alfred P. Sloan Foundation.

      Conference Speakers:

      1. Jörn Boehnke, Harvard CMSA
      2. Joan Bruna, UC Berkeley [Video]
      3. Tamara Broderick, MIT [Video]
      4. Justin Chen, MIT [Video]
      5. Yiling Chen, Harvard University [Video]
      6. Amir Farbin, UT Arlington [Video]
      7. Doug Finkbeiner, Harvard University [Video]
      8. Andrew Gelman, Columbia University [Video]
      9. Nina Holden, MIT [Video]
      10. Elchanan Mossel, MIT
      11. Alex Peysakhovich, Facebook
      12. Alexander Rakhlin, University of Pennsylvania [Video]
      13. Neal Wadhwa, MIT [Video]
      14. Jun Yin, University of Wisconsin
      15. Harry Zhou, Yale University [Video]

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

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

      Please click here for registration.

      Conference Schedule:

      August 22 – Day 1
      8:30amBreakfast
      8:55amOpening remarks
      9:00am – 9:50amYiling Chen, “Machine Learning with Strategic Data Sources” [Video]
      9:50am – 10:40amAndrew Gelman, “Taking Bayesian Inference Seriously” [Video]
      10:40am – 11:10amBreak
      11:10am – 12:00pmHarrison Zhou, “A General Framework for Bayes Structured Linear Models” [Video]
      12:00pm – 1:30pmLunch
      1:30pm – 2:20pmDouglas Finkbeiner, “Mapping the Milky Way in 3D with star colors” [Video]
      2:20pm – 3:10pmNina Holden, “Sparse exchangeable graphs and their limits” [Video]
      3:10pm – 3:40pmBreak
      3:40pm – 4:30pmAlex Peysakhovich, “How social science methods inform personalization on Facebook News Feed” [Video]
      4:30pm – 5:20pmAmir Farbin, “Deep Learning in High Energy Physics” [Video]
      August 23 – Day 2
      8:45amBreakfast
      9:00am – 9:50amJoan Bruna Estrach, “Addressing Computational and Statistical Gaps with Deep Networks” [Video]
      9:50am – 10:40amJustin Chen & Neal Wadhwa, “Smaller Than the Eye Can See: Big Engineering from Tiny Motions in Video” [Video]
      10:40am – 11:10amBreak
      11:10am – 12:00pmAlexander Rakhlin, “How to Predict When Estimation is Hard: Algorithms for Learning on Graphs” [Video]
      12:00pm – 1:30pmLunch
      1:30pm – 2:20pmTamara Broderick, “Fast Quantification of Uncertainty and Robustness with Variational Bayes” [Video]
      2:20pm – 3:10pmElchanan Mossel, “Phylogenetic Reconstruction – a Rigorous Model of Deep Learning”
      3:10pm – 3:40pmBreak
      3:40pm – 4:30pmJörn Boehnke, “Amazon’s Price and Sales-rank Data: What can one billion prices on 150 thousand products tell us about the economy?”

      Workshop Participants:

      Richard Freeman’s Group:

      1. Sen Chai, ESSEC
      2. Brock Mendel, Harvard University
      3. Raviv Muriciano-Goroff, Stanford University
      4. Sifan Zhou, CMSA

      Scott Kominer’s Group:

      1. Bradly Stadie, UC Berkeley
      2. Neal Wadhwa, MIT [Video]
      3. Justin Chen

      Christopher Rogan’s Group:

      1. Amir Farbin, UT Arlington [Video]
      2. Paul Jackson, University of Adelaide

      For more information about the workshops, please reach out directly to the individual group leaders.

      This event is sponsored by CMSA Harvard University and the Alfred P. Sloan Foundation.

    • Seminars
      Seminars Colloquia & Seminar
      10-01-2015 Evolution Equations Seminar
      1:25 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-15-2015 Geometric Analysis Seminar
      1:26 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-16-2015 Random Matrix & Probability Theory Seminar
      1:27 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-23-2015 Random Matrix & Probability Theory Seminar
      1:29 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      5-3-2017 Random Matrix & Probability Theory Seminar
      1:29 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      1:30 pm-3:00 pm
      11/01/2019
    • Special Seminar
      1:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      5-2-2017 Social Sciences Application Forum
      1:30 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11/28/2018 Hodge Lecture
      1:30 pm
      11/01/2019
    • Seminars
      1:30 pm-3:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      1/23/2019 Hodge Seminar
      1:30 pm-3:00 pm
      11/01/2019
    • Special Seminar
      Special Seminar
      4/30/2018 Special Seminar
      1:30 pm-2:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      12/5/2018 Hodge Seminar
      1:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      11/14/2018 Hodge Seminar
      1:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      11/21/2018 Hodge Seminar
      1:30 pm
      11/01/2019
    • Colloquium
      1:31 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-28-2015 Mathematical Physics Seminar
      1:31 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-24-2017 Mathematical Physics Seminar
      1:31 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      1:32 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:33 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Concluding Conference of the Special Program on Nonlinear Equations, April 8 – 10, 2016
      1:34 pm
      11/01/2019-04/10/2016

      The Center of Mathematical Sciences and Applications will be hosting a concluding conference on April 8-10, 2016 to accompany the year-long program on nonlinear equations. The conference will have 15 speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

      Speakers:

      1. Lydia Bieri (University of Michigan)
      2. Luis Caffarelli (University of Texas at Austin)
      3. Mihalis Dafermos (Princeton University)
      4. Camillo De Lellis (Universität Zürich)
      5. Pengfei Guan (McGill University)
      6. Slawomir Kolodziej (Jagiellonian University)
      7. Melissa Liu (Columbia University)
      8. Duong H. Phong (Columbia University)
      9. Richard Schoen (UC Irvine)
      10. Cliff Taubes (Harvard University)
      11. Blake Temple (UC Davis)
      12. Valentino Tosatti (Northwestern University)
      13. Tai-Peng Tsai (University of British Columbia)
      14. Mu-Tao Wang (Columbia University)
      15. Xu-jia Wang (Australian National University)

      Please click NLE Conference Schedule with Abstracts for a downloadable schedule with talk abstracts.

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

      Schedule:

      April 8 – Day 1
      8:30amBreakfast
      8:45amOpening remarks
      9:00am – 10:00amCamillo De Lellis, “A Nash Kuiper theorem for $C^{1,1:5}$ isometric immersions of disks
      10:00am – 10:15amBreak
      10:15am – 11:15amXu-Jia Wang, “Monge’s mass transport problem
      11:15am – 11:30amBreak
      11:30am – 12:30pmPeng-Fei Guan, “The Weyl isometric embedding problem in general $3$ d Riemannian manifolds
      12:30pm – 2:00pmLunch
      2:00pm – 3:00pmBlake Temple, “An instability in the Standard Model of Cosmology
      3:00pm – 3:15pmBreak
      3:15pm – 4:15pmLydia Bieri, “The Einstein Equations and Gravitational Radiation
      4:15pm – 4:30pmBreak
      4:30pm – 5:30pmValentino Tosatti, “Adiabatic limits of Ricci flat Kahler metrics
      April 9 – Day 2
      8:45amBreakfast
      9:00am – 10:00amD.H. Phong, “On Strominger systems and Fu-Yau equations”
      10:00am – 10:15amBreak
      10:15am – 11:15amSlawomir Kolodziej, “Stability of weak solutions of the complex Monge-Ampère equation on compact Hermitian manifolds”
      11:15am – 11:30amBreak
      11:30am – 12:30pmLuis Caffarelli, “Non local minimal surfaces and their interactions”
      12:30pm – 2:00pmLunch
      2:00pm – 3:00pmMihalis Dafermos, “The interior of dynamical vacuum black holes and the strong cosmic censorship conjecture in general relativity”
      3:00pm – 3:15pmBreak
      3:15pm – 4:15pmMu-Tao Wang, “The stability of Lagrangian curvature flows”
      4:15pm – 4:30pmBreak
      4:30pm – 5:30pmMelissa Liu, “Counting curves in a quintic threefold”
      April 10 – Day 3
      8:45amBreakfast
      9:00am – 10:00amRick Schoen, “Metrics of fixed area on high genus surfaces with largest first eigenvalue”
      10:00am – 10:15amBreak
      10:15am – 11:15amCliff Taubes, “The zero loci of Z/2 harmonic spinors in dimensions 2, 3 and 4”
      11:15am – 11:30amBreak
      11:30am – 12:30pmTai-Peng Tsai, “Forward Self-Similar and Discretely Self-Similar Solutions of the 3D incompressible Navier-Stokes Equations”

      * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      10-22-2015 Evolution Equations Seminar
      1:37 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/11/2017 Mathematical Physics Seminar
      1:38 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9-18-17 Mathematical Physics Seminar
      1:39 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-17-2015 Evolution Equations Seminar
      1:39 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      9-27-17 RM&PT Seminar
      1:41 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9-27-17 Mathematical Physics Seminar
      1:42 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-23-17 Mathematical Physics Seminar
      1:43 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9/11/2019 Random Matrix
      1:45 pm-2:45 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-25-17 RMPT Seminars
      1:45 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:47 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-10-2017 RM & PT Seminar
      1:48 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:51 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-22-2015 Geometric Analysis Seminar
      1:52 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:52 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-30-2015 Random Matrix & Probability Theory Seminar
      1:53 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-13-2017 Mathematical Physics Seminar
      1:53 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:54 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-21-2015 Mathematical Physics Seminar
      1:54 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-15-17 RM & PT Seminar
      1:55 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-6-2017 RM & PT Seminar
      1:56 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:58 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      2/22/2019 Social Science Applications Forum
      2:00 pm
      11/01/2019
    • Math Science Lectures in Honor of Raoul Bott
      Math Science Lectures in Honor of Raoul Bott Event
      Math Science Lectures in Honor of Raoul Bott: Freddy Cachazo
      2:00 pm-5:00 pm
      11/01/2019-04/03/2018
      1 Oxford Street, Cambridge MA 02138
      Math Science Lectures in Honor of Raoul Bott

      DSC_0170-e1525711590120

      On April 2-3, the CMSA will be hosting two lectures by Freddy Cachazo (Perimeter Institute) on “Geometry and Combinatorics in Particle Interactions.”  This will be the first of the new annual Bott Math Science Lecture Series hosted by the CMSA.

      The lectures will take place from 4:30-5:30pm in Science Center, Hall D.

       

      Cachazo-e1519325938458

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-20-2017 RM & PT Seminar
      2:00 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02/26/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      Homological Mirror Symmetry Seminar
      2:00 pm-4:00 pm
      11/01/2019-09/15/2017

      The seminar series, Homological Mirror Symmetry, will be held on selected Thursdays from 2PM – 4pm in CMSA Building, 20 Garden Street, Room G10.

      The list of speakers is below and will be updated as details are confirmed.

      DateNameTitle
      09-15-16
      09-22-16Netanel Blaier, Brandeis  “Intro to HMS.”

      Abstract: This is the first talk of the seminar series. We survey the statement of Homological Mirror Symmetry (introduced by Kontsevich in 1994) and some known results, as well as briefly discussing its importance, and the connection to other formulations of Mirror Symmetry and the SYZ conjecture. Following that, we will begin to review the definition of the A-side (namely, the Fukaya category) in some depth. No background is assumed! Also, in the last half hour, we will divide papers and topics among participants.

      Lecture Slides

      09-29-16Netanel Blaier, Brandeisblaier4“Intro to HMS 2.”

      Abstract: In the second talk, we review (some) of the nitty-gritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of J-holomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya’s differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$-structures. We will try to demonstrate all concepts in the Morse theory ‘toy model’.

      Lecture Slides

      10-06-16

      Hansol Hong, CMSAhong

      Title: Homological mirror symmetry for elliptic curves

      Abstract:
      We survey the proof of homological mirror symmetry by Polishchuk and Zaslow. Some of more recent methods to prove HMS for elliptic curves will be discussed also,
      which use homological algebra techniques and formal deformation theory of Lagrangians etc.

      Notes

      Notes (Baris)

      10-13-16

      Yu-Wei Fan, Harvard

      s_yuwei_fan

      Title: Semi-flat mirror symmetry and Fourier-Mukai transform

      Abstract: We will review the semi-flat mirror symmetry setting in Strominger-Yau-Zaslow, and discuss the correspondence between special Lagrangian sections on the A-side and deformed Hermitian-Yang-Mills connections on the B-side using real Fourier-Mukai transform, following Leung-Yau-Zaslow.

       10-20-16

      Tim Large, MIT

      Title: “Symplectic cohomology and wrapped Fukaya categories”

      Abstract: While mirror symmetry was originally conjectured for compact manifolds, the phenomenon applies to non-compact manifolds as well. In the setting of Liouville domains, a class of open symplectic manifolds including affine varieties, cotangent bundles and Stein manifolds, there is an A-infinity category called the wrapped Fukaya category, which is easier to define and often more amenable to computation than the original Fukaya category. In this talk I will construct it, along with symplectic cohomology (its closed-string counterpart), and compute some examples. We will then discuss how compactifying a symplectic manifold corresponds, on the B-side of mirror symmetry, to turning on a Landau-Ginzburg potential.

      Notes

       10-27-16

      Philip Engel, Columbia

      picture

      Title: Mirror symmetry in the complement of an anticanonical divisor”

      According to the SYZ conjecture, the mirror of a Calabi-Yau variety can be constructed by dualizing the fibers of a special Lagrangian fibration. Following Auroux, we consider this rubric for an open Calabi-Yau variety X-D given as the complement of a normal crossings anticanonical divisor D in X. In this talk, we first define the moduli space of special Lagrangian submanfiolds L with a flat U(1) connection in X-D, and note that it locally has the structure of a Calabi-Yau variety. The Fukaya category of such Lagrangians is obstructed, and the degree 0 part of the obstruction on L defines a holomorphic function on the mirror. This “superpotential” depends on counts of holomorphic discs of Maslov index 2 bounded by L. We then restrict to the surface case, where there are codimension 1 “walls” consisting of Lagrangians which bound a disc of Maslov index 0. We examine how the superpotential changes when crossing a wall and discuss how one ought to “quantum correct” the complex structure on the moduli space to undo the discontinuity introduced by these discs.

      Notes

      11-03-16

      Yusuf Baris Kartal, MIT

      HMS for Del Pezzo surfaces

      I will present Auroux-Katzarkov-Orlov’s proof of one side of the homological mirror symmetry for Del Pezzo surfaces. Namely I will prove their derived categories are equivalent to the categories of vanishing cycles for certain LG-models together with B-fields. I plan to show how the general B-field corresponds to non-commutative Del Pezzo surfaces and time allowing may mention HMS for simple degenerations of Del Pezzo surfaces. The tools include exceptional collections( and mutations for degenerate case), explicit description of NC deformations, etc.

      11-10-16No seminar this week
       12-08-16

      Lino Amorim, Boston University

      Title: The Fukaya category of a compact toric manifold

      Abstract: In this talk I will discuss the Fukaya category of a toric manifold following the work of Fukaya-Oh-Ohta-Ono. I will start with an overview of the general structure of the Fukaya category of a compact symplectic manifold. Then I will consider toric manifolds in particular the Fano case and construct its mirror.

      Video

    • CMSA EVENT: Topological Insulators and Mathematical Science – Conference and Program
      2:00 pm-7:00 pm
      11/01/2019-09/17/2014

      The CMSA will be hosting a conference on the subject of topological insulators and mathematical science on September 15-17.  Seminars will take place each day from 2:00-7:00pm in Science Center Hall D, 1 Oxford Street, Cambridge, MA.

    • Seminars
      2:00 pm-4:00 pm
      11/01/2019

      References: 

      • D. Auroux, A beginner’s introduction to Fukaya categories. arXiv:1301.7056
      • I. Smith, A symplectic prolegomenon. arXiv:1401.0269
      • D. Auroux, “Topics in geometry: mirror symmetry”, Fall 2009 (MIT Math 18.969)
      • Nick Sheridan’s IAS and Jussieu lectures. 
      • Sheel Gantara “Topics in symplectic topology”, Spring 2016 (Stanford Math 257B)
    • Seminars
      Seminars Colloquia & Seminar
      1/8/2019 Topology Seminar
      2:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-29-17 RM & PT Seminar
      2:03 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Seminars
      Seminars Colloquia & Seminar
      09-24-2015 Evolution Equations Seminar
      2:03 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-28-2015 Special Random Matrix & Probability Theory Seminar
      2:05 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-18-2015 Random Matrix & Probability Theory Seminar
      2:07 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 RM&PT Seminar
      2:08 pm
      11/01/2019
    • Colloquium
      2:08 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:10 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-29-2017 Mathematical Physics Seminar
      2:11 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Colloquium
      2:11 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-29-2015 Geometric Analysis Seminar
      2:14 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:14 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-28-2015 CMSA Special Seminar
      2:15 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-05-2015 Mathematical Physics Seminar
      2:16 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-6-2017 RM & PT Seminar
      2:16 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-15-2015 Evolution Equations Seminar
      2:17 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12-6-2017 Mathematical Physics Seminar
      2:17 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-07-2015 Random Matrix & Probability Theory Seminar
      2:19 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:20 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-29-2015 Evolution Equations Seminar
      2:20 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-14-2015 Random Matrix & Probability Theory Seminar
      2:21 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      2:21 pm
      11/01/2019-03/06/2018

      During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th, from 1:00 to 3:00pm in room G10, CMSA Building.

      You can watch Prof. Sheshmani describe the series here.

      The Syllabus is as follows:

      Date………..TopicVideo/Audio
      1-25-2018Gromov-Witten invariants 

      Definition, examples via algebraic geometry I

      Video / Audio / Combined 


      *due to technical difficulties the audio and video are split for this lecture.

       2-01-2018Gromov-Witten invariants 

      Virtual Fundamental Class I (definition)

      Video Audio / Combined 


      *due to technical difficulties the audio and video are split for this lecture

      2-13-2018Gromov-Witten invariants 

      Virtual Fundamental Class II (computation in some cases)

       2-15-2018Computing GW invariants 

      Three level GW classes

      Genus zero invariants of the projective plane

       2-20-2018Quantum Cohomology 

      Small Quantum Cohomology (Definition and Properties) I

      2-22-2018Quantum Cohomology 

      Small Quantum Cohomology (Definition and Properties) II

      2-27-2018Quantum Cohomology 

      Big Quantum Cohomology I

       3-1-2018Quantum Cohomology 

      Big Quantum Cohomology II

      GW potential

      WDVV equation

      3-6-2018GW invariants via Quantum Cohomology 

      The Quintic threefold case

      The P^2 case

      GW invariants via Quantum Cohomology 

      Dubrovin (quantum) connection

      Nakajima varieties 

      -Algebraic and symplectic reduction

      Nakajima varieties 

      Quasi maps to Nakajima varieties

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) I

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) II

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) III

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) I

       
      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) II

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) III

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) IV

       
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-21-2015 Random Matrix & Probability Theory Seminar
      2:22 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:23 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:24 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:29 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/3/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-28-2015 Random Matrix & Probability Theory Seminar
      2:30 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11/31/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/18/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/3/2019 Colloquium
      2:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Social Science Applications Forum
      2:30 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/19/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/7/2019 Social Science Applications Forum
      2:30 pm-3:00 pm
      11/01/2019
    • Colloquium
      Colloquium Colloquia & Seminar
      4/10/2019 Colloquium
      2:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/12/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      11/01/2019
    • Colloquium
      Colloquium Colloquia & Seminar
      2/27/2019 Colloquium
      2:30 pm-4:00 pm
      11/01/2019
    • General Relativity Seminar
      2:30 pm-3:30 pm
      11/01/2019-04/26/2020
    • Colloquium
      2:30 pm-3:00 pm
      11/01/2019
    • Colloquium
      2:32 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-19-2015 Mathematical Physics Seminar
      2:33 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-20-2015 Geometric Analysis Seminar
      2:35 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-26-2015 Mathematical Physics Seminar
      2:36 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      01-26-2018 Mirror Symmetry Seminar
      2:37 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-02-2015 Mathematical Physics Seminar
      2:37 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-03-2015 Geometric Analysis Seminar
      2:39 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-04-2015 Random Matrix & Probability Theory Seminar
      2:40 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      1-29-2018 Mathematical Physics Seminar
      2:42 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      Special Seminar
      1-30-2018 Special Seminar
      2:43 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      2:44 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      2-2-2018 Mirror Symmetry Seminar
      2:44 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      2:45 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:47 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      2:48 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-19-2015 Evolution Equations Seminar
      2:50 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-09-2015 CMSA Special Lecture
      2:51 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:54 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-09-2015 Mathematical Physics Seminar
      2:54 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      2:55 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:56 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-19-2015 Random Matrix and Probability Theory Seminar
      2:57 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:59 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-16-2015 Mathematical Physics Seminar
      2:59 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      2-27-2018 HMS Lecture
      3:00 pm-4:00 pm
      11/01/2019-03/01/2018
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12/5/2018 Random Matrix and Probability Theory Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/17/2019 Fluid Dynamics Seminar
      3:00 pm
      11/01/2019
    • CMSA EVENT: 2018 Ding Shum Lecture
      3:00 pm-4:00 pm
      11/01/2019
      ding-shum-2018

       

      Screen-Shot-2018-06-14-at-1.41.25-PM

      On October 24, 2018, the CMSA will be hosting our second annual Ding Shum lecture. This event was made possible by the generous funding of Ding Lei and Harry Shum. Last year featured Leslie Valiant, who spoke on “learning as a Theory of Everything.”

      This year will feature Eric Maskin, who will speak on “How to Improve Presidential Elections: the Mathematics of Voting.” This lecture will take place from 5:00-6:00pm in Science Center, Hall D. 

      Pictures of the event can be found here.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/24/2018 RM & PT Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/7/2018 Random Matrix and Probability Theory Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/14/2018 RM & PT Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/28/2018 Random Matrix and Probability Theory Seminar
      3:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      1/31/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Special Seminar
      3:00 pm-4:30 pm
      11/01/2019-05/09/2019

      In the Spring 2019 Semester, the CMSA will be hosting a special lecture series on Derived algebraic/differential geometry run by Artan Sheshmani, with lectures given by Prof. Sheshmani and Dr. Dennis Borisov. The seminar will be held on Tuesdays and Thursdays from 3:00-4:30pm in CMSA, room G10.

      Click here for reference material

      Click here for a syllabus

      Schedule:

      Section 1: Basic setting of derived geometry

      The goal: To collect the minimum set of tools needed to do algebraic geometry in the derived context.

      2/05/2019Lecture 1: Model and с-categoriesVideo
      2/07/2019Lecture 2: Grothendieck topologies and homotopy descentVideo
      2/12/2019Lecture 3: Derived Artin stacksVideo 
      2/14/2019Lecture 4: Cotangent complexes

      Section 2: Loop spaces and differential forms

      The goal: This is the algebraic heart of the course – here we learn the homological techniques that are needed for shifted symplectic forms.

      2/19/2019Lecture 5: De Rham complexes and S1-equivariant schemes (loop spaces)Video
      2/21/2019Lecture 6: Chern characterVideo
      2/26/2019

      Room G02

      Lecture 7: Local structure of closed differential forms in the derived sense Part IVideo
      2/28/2019Lecture 8: Local structure of closed differential forms in the derived sense Part IIVideo
      3/05/2019Lecture 9: Cyclic homologyVideo

      Section 3: Shifted symplectic structures
      Goal: To see applications of the algebraic techniques from above in the geometric context of the actual moduli spaces.

      3/07/2019Lecture 10: Definition and existence resultsVideo
      3/12/2019Lecture 11: Lagrangians and Lagrangian fibrationsVideo
      3/14/2019

      Room G02

      Lecture 12: Lagrangians and Lagrangian fibrationsVideo
      3/26/2019Lecture 13: Intersections of LagrangiansVideo
      3/28/2019

      Room G02

      Lecture 14: Examples and applications 2 (Part I)Video
      4/02/2019Lecture 15: Examples and applications 2 (Part II)Video

      Section 4: Uhlenbeck–Yau construction and correspondence

      4/04/2019Lecture 16: Examples and applications 2 (Part III)Video
      4/09/2019

      Room G02

      Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)Video
    • Seminars
      Seminars Colloquia & Seminar
      2/7/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/13/2019 Special Algebraic Geometry Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/14/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/20/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/6/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/8/2019 Special Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/20/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      Algebraic Geometry Seminar, Thursdays
      3:00 pm-4:00 pm
      11/01/2019

      This seminar will not be held in the Spring 2018 Semester.

      The Algebraic Geometry Seminar will be every Thursday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

      The schedule will be updated as details are confirmed.

       

       

      DateNameTitle/Abstract
      09-14-17 Yu-Wei Fan (Harvard Math)

      Entropy of an autoequivalence on Calami-Yau manifolds

      Abstract:  We will recall the notion of entropy of an autoequivalence on triangulated categories, and provide counterexamples of a conjecture by Kikuta-Takahashi.

      11-1-17

      *5:00pm, G10*

       Shamil Shakirov, Harvard Math

      Undulation invariants of plane curves

      Abstract: “One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem, described by Cayley and Salmon in 1852, is to determine whether or not a given plane curve of degree r > 3 has undulation points — the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r – 3)(3 r – 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries, and we conjecture a generalization for r = 5

      11-2-17

       

      Alexander Moll, IHES

      Hilbert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves

      ABSTRACT: By Grojnowski and Nakajima, Fock spaces are cohomology rings of Hilbert scheme of points in the plane.  On the other hand, by Pressley-Segal, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the Kähler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J.  First, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this Kähler structure.  Second, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = – e_1 e_2 that is invariant under e_2 <-> e_1.  As a corollary of Lehn’s theorem, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element.  Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin.  As time permits, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov’s BPS/CFT Correspondence.

      11-9-17  TBD  TBD
      11-16-17 TBD TBD
      11-23-17  TBD  TBD
      11-30-17  TBD  TBD
      12-7-17  TBD  TBD
      12-15-17  TBD  TBD
    • Seminars
      Seminars Colloquia & Seminar
      4/24/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Fluid Dynamics Seminar
      Fluid Dynamics Seminar
      10/9/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/03/2018 RMPT Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      5/22/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      5/15/2019 Fluid Dynamics
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      5/1/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Special Seminar
      Special Seminar
      3-28-2018 Special Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      Dmytro Shklyrov HMS Focused Lecture Series
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/4/2019 Special Seminar
      3:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      11-17-2015 Geometric Analysis Seminar
      3:00 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9/18/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      11-23-2015 Mathematical Physics Seminar
      3:01 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar (2016-2017)
      3:01 pm
      11/01/2019-12/14/2017
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      DSC_0025-768x512

      The random matrix and probability theory will be every Wednesday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

    • CMSA EVENT: Working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017
      3:02 pm-3:03 pm
      11/01/2019-01/13/2017

      The Center of Mathematical Sciences and Applications will be hosting a working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Participants:

      Gerard Ben Arous, Courant Institute of Mathematical Sciences

      Alex Bloemendal, Broad Institute

      Arup Chakraburty, MIT

      Zhou Fan, Stanford University

      Alpha Lee, Harvard University

      Matthew R. McKay, Hong Kong University of Science and Technology (HKUST)

      David R. Nelson, Harvard University

      Nick Patterson, Broad Institute

      Marc Potters, Capital Fund management

      Yasser Roudi, IAS

      Tom Trogdon, UC Irvine

      Organizers:

      Michael Brenner, Lucy Colwell, Govind Menon, Horng-Tzer Yau

      Please click Program for a downloadable schedule with talk abstracts.

      Please note that breakfast & lunch will be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants should you need recommendations for dinner.

      Schedule:

      January 9 – Day 1
      9:30am – 10:00amBreakfast & Opening remarks
      10:00am – 11:00amMarc Potters, “Eigenvector overlaps and the estimation of large noisy matrices”
      11:00am – 12:00pmYasser Roudi
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 10 – Day 2
      8:30am – 9:00amBreakfast
      9:00am – 10:00amArup Chakraburty, “The mathematical analyses and biophysical reasons underlying why the prevalence of HIV strains and their relative fitness are simply correlated, and pose the challenge of building a general theory that encompasses other viruses where this is not true.”
      10:00am – 11:00amTom Trogdon, “On the average behavior of numerical algorithms”
      11:00am – 12:00pmDavid R. Nelson, “Non-Hermitian Localization in Neural Networks”
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 11 – Day 3
      8:30am – 9:00amBreakfast
      9:00am – 10:00amNick Patterson
      10:00am – 11:00amLucy Colwell
      11:00am – 12:00pmAlpha Lee
      12:00pm – 2:00pmLunch
      2:00pm-4:00pmAfternoon Discussion
      4:00pmGerard Ben Arous (Public Talk), “Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms
      January 12 – Day 4
      8:30am – 9:00amBreakfast
      9:00am – 10:00amGovind Menon
      10:00am – 11:00amAlex Bloemendal
      11:00am – 12:00pmZhou Fan, “Free probability, random matrices, and statistics”
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 13 – Day 5
      8:30am – 9:00amBreakfast
      9:00am – 12:00pmFree for Working
      12:00pm – 2:00pmLunch
      2:00pmFree for Working

      * This event is sponsored by CMSA Harvard University.

    • Colloquium
      3:03 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-24-2015 Geometric Analysis Seminar
      3:03 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-04-2016 Evolution Equations Seminar
      3:04 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      Hodge and Noether-Lefschetz Loci Seminar
      3:06 pm
      11/01/2019

      In the Fall 2018 Semester the CMSA will be hosting a seminar on Hodge and Noether-Lefschetz loci, with lectures given by Hossein Movasati (IMPA). The seminar will occur weekly on Wednesday at 1:30 in room G10 of the CMSA.

      The schedule below will be updated as talks are confirmed.

      DateTitle/Abstract
      11/7/2018

      Video

      Title: Hodge and Noether-Lefschetz loci

      Abstract: Hodge cycles are topological cycles which are conjecturally (the millennium Hodge conjecture) supported in algebraic cycles of a given smooth projective complex manifold. Their study in families leads to the notion of Hodge locus, which is also known as Noether-Lefschetz locus in the case of surfaces. The main aim of this mini course is to introduce a computational approach to the study of Hodge loci for hypersurfaces and near the Fermat hypersurface. This will ultimately lead to the verification of the variational Hodge conjecture for explicit examples of algebraic cycles inside hypersurfaces and also the verification of integral Hodge conjecture for examples of Fermat hypersurfaces. Both applications highly depend on computer calculations of rank of huge matrices. We also aim to review some classical results on this topic, such as Cattani-Deligne-Kaplan theorem on the algebraicity of the components of the hodge loci, Deligne’s absolute Hodge cycle theorem for abelian varieties etc.

      In the theoretical side another aim is to use the available tools in algebraic geometry and construct the moduli space of projective varieties enhanced with elements in their algebraic de Rham cohomology ring. These kind of moduli spaces have been useful in mathematical physics in order to describe the generating function of higher genus Gromov-Witten invariants, and it turns out that the Hodge loci in such moduli spaces are well-behaved, for instance, they are algebraic leaves of certain holomorphic foliations. Such foliations are constructed from the underlying Gauss-Manin connection. This lectures series involves many reading activities on related topics, and contributions by participants are most welcome.

      11/14/2018

      Video

      Title:  Integral Hodge conjecture for Fermat varieties

      Abstract: We describe an algorithm which verifies whether  linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this  confirms the integral Hodge conjecture for quartic and quintic Fermat fourfolds. Our algorithm is based on computation of the list of elementary divisors of both the lattice of linear algebraic cycles, and the lattice of Hodge cycles written in terms of  vanishing cycles, and observing that these two lists are the same. This is a joint work with E. Aljovin and R. Villaflor.

      11/21/2018

      Video

      Title:  Periods of algebraic cycles

      Abstract: The tangent space of the Hodge locus at a point can be described by the so called infinitesimal variation of Hodge structures and the cohomology class of Hodge cycles. For hypersurfaces of dimension $n$ and degree $d$ it turns out that one can describe it without any knowledge of cohomology theories and in a fashion which E. Picard in 1900’s wanted to study integrals/periods. The data of cohomology class is replaced with periods of Hodge cycles, and explicit computations of these periods, will give us a computer implementable description of the tangent space.  As an application of this we show that for examples of $n$ and $d$, the locus of hypersurfaces containing two linear cycles whose intersection is of low dimension, is a reduced component of the Hodge locus in the underlying parameter space.

      11/28/2018

      Video

      Title: Periods of Complete Intersection Algebraic Cycles

      Speaker: Roberto Villaflor

      Abstract: In order to compute periods of algebraic cycles inside even dimensional smooth degree d hypersurfaces of the projective space, we restrict ourselves to cycles supported in a complete intersection subvariety. When the description of the complete intersection is explicit, we can compute its periods, and furthermore its cohomological class. As an application, we can use this data to describe the Zariski tangent space of the corresponding Hodge locus, as the degree d part of some Artinian Gorenstein ideal of the homogeneous coordinate ring of the projective space. Using this description, we can show that for d>5, the locus of hypersurfaces containing two linear cycles, is a reduced component of the Hodge locus in the underlying parameter space.

      12/05/2018

      Room G02

      Title: Some explicit Hodge cycles

      Abstract: Explicit examples of Hodge cycles are due to D. Mumford and A. Weil in the case of CM abelian varieties. In this talk, I will describe few other examples for the Fermat variety. Effective verification of the Hodge conjecture for these cycles is not known.

      12/12/2018

      Video

      Title: A conjectural Hodge locus for cubic tenfold

      Abstract: In this talk we will consider the difference  of two linear algebraic cycles of dimension 5 inside a smooth cubic tenfold and such that the dimension of their intersection is 3. We will show some computer assisted evidences to the fact that the corresponding Hodge locus is bigger than the expected locus of algebraic deformations of the cubic tenfold together with its linear cycles. A similar discussion will be also presented for cubic six and eightfold,  for which we will prove that the corresponding second and third order infinitesimal Hodge loci are smooth. The main ingredient is a computer implementation of power series of periods of hypersurfaces.

      1/16/2019Title: Algebraic BCOV anomaly equation

      Abstract: We introduce the moduli space T of  non-rigid compact Calabi-Yau threefolds enhanced with differential forms and a Lie algebra of vector fields in T. This will be used in order to give a purely algebraic interpretation of topological string partition functions and the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation (joint work with M. Alim, E. Scheidegger, S.-T. Yau).  We will also define similar moduli spaces for even dimensional Calabi-Yau varieties, where we have the notion of Hodge locus.

      1/23/2019

      Video

      Title: A new model for modular curves

      Abstract: One of the non-trivial examples of a Hodge locus is the modular curve X_0(N), which is due to isogeny of elliptic curves (a Hodge/algebraic cycle in the product of two elliptic curves). After introducing the notion of enhanced moduli of elliptic curves, I will describe a new model for X_0(N) in the weighted projective space of dimension 4 and with weights (2,3,2,3,1). I will also introduce some elements in the defining ideal of such a model.

      The talk is based on the article arXiv:1808.01689.

      1/30/2019

      Video

      Title: Constant Yukawa couplings

      Abstract: In this talk I will first introduce algebraic Yukawa couplings for any moduli of enhanced Calabi-Yau n-folds. Then I will list many examples in support of the following conjecture. A moduli of Calabi-Yau n-folds is a quotient of a Hermitian symmetric domain (constructed from periods) by an arithmetic group if and only if the corresponding Yukawa couplings are constants.

      2/6/2019

      Video

      Title: Integrality properties of CY modular forms

      Abstract: The integrality of the coefficients of the mirror map is a central problem in the arithmetic of Calabi-Yau varieties and it has been investigated  by Lian-Yau (1996, 1998), Hosono-Lian-Yau (1996), Zudilin (2002), Kontsevich-Schwarz-Vologodsky (2006) Krattenthaler-Rivoal (2010). The central tool in most of these works has been the so called Dwork method.  In this talk we use this method and classify all hypergeometric differential equations with a maximal unipotent monodromy whose mirror map has integral coefficients.

      We also  give a computable condition on the parameters of a hypergeometric function which conjecturally computes all the primes which appear in the denominators of the coefficients of the mirror map. This is a joint work with Kh. Shokri.

      2/13/2019Title: Foliations and Hodge loci

      Abstract: In this talk I will introduce a holomorphic foliation in a larger parameter space attached to families of enhanced projective varieties. Irreducible components of the Hodge locus with constant periods are algebraic leaves of such a foliation. Under the hypothesis that these are all the algebraic leaves,  we get the fact that such algebraic leaves are defined over the algebraic closure of the base field and that Hodge classes are weak absolute in the sense of C. Voisin.

       

      References:

    • Seminars
      Seminars Colloquia & Seminar
      02-02-2016 Geometric Analysis Seminar
      3:06 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      3:06 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Data Analysis Workshop, April 4 – 8, 2016
      3:09 pm-3:10 pm
      11/01/2019-04/08/2016

      The Center of Mathematical Sciences and Applications will be hosting a 5-day workshop on Data Analysis and related areas on April 4 – 8, 2016.

      Workshop Locations:

      April 4 – 7 (Monday ~ Thursday)

      Room G10,
      20 Garden Street, Cambridge, MA 02138 

      April 8 (Friday)

      EPS Faculty Lounge, Room 409, 4th floor, Hoffman Lab
      20 Oxford Street, Cambridge, MA 02138

       Participants:

      • Peter Hubyers (Harvard University)
      • Eli Tziperman (Harvard University)
      • Andrew Rhines (University of Washington)
      • Karen McKinnon (UCAR)
      • Douglas MacMartin (Caltech)
      • Thomas Laepple (Alfred Wegener Institute)
      • Yossi Ashkenazy (Ben-Gurion University)
      • Marlene Kretschamer (Potsdam Institute for Climate Impact Research)
      • Natesh Pillai (Harvard University)
      • Judah Cohen (Atmospheric and Environmental Research)
      • Cristian Proistosescu (Harvard University)

      Please click Workshop Agenda for a downloadable agenda.

      * This event is sponsored by CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      02-11-2016 Evolution Equations Seminar
      3:09 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      3:09 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2-16-2018 RM & PT Seminar
      3:09 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Colloquium
      3:11 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-03-2016 Random Matrix & Probability Theory Seminar
      3:11 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      3:13 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 RMPT Seminar
      3:15 pm-4:15 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/9/2019 RM & PT Seminar
      3:15 pm-4:15 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/30/2019 Random Matrix and Probability Theory Seminar
      3:15 pm-4:15 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/16/2019 RM & PT Seminar
      3:15 pm
      11/01/2019
    • Colloquium
      3:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-16-2016 Geometric Analysis Seminar
      3:16 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-15-2016 Mathematical Physics Seminar
      3:17 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-18-2016 Evolution Equations Seminar
      3:19 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-22-2016 Mathematical Physics Seminar
      3:20 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-23-2016 Geometric Analysis Seminar
      3:22 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-24-2016 Random Matrix & Probability Theory
      3:23 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Mini-workshop on SYZ and Homological Mirror Symmetry
      3:23 pm
      11/01/2019-12/02/2016

      The Center of Mathematical Sciences and Applications will be hosting a 4-day workshop on SYZ and Homological Mirror Symmetry and related areas on November 28 – December 2, 2016 at Harvard CMSA Building: Room G10, 20 Garden Street, Cambridge, MA 02138.

      Organizers:

      Bong Lian (Brandeis University), Siu-Cheong Lau (Boston University), Shing-Tung Yau (Harvard University)

      Speakers:

      1. Conan Leung, Chinese University of Hong Kong
      2. Junwu Tu, University of Missouri
      3. Jingyu Zhao, Columbia University
      4. David Treumann, Boston College
      5. Hiro Lee Tanaka, Harvard University
      6. Fabian Haiden, Harvard University
      7. Hansol Hong, Harvard CMSA/Brandeis University
      8. Netanel Blaier, Harvard CMSA/Brandeis University
      9. Garret Alston, The University of Oklahoma

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

      Conference Schedule:

      Monday, November 28 – Day 1
      10:30am –11:30amHiro Lee Tanaka“Floer theory through spectra”
      Lunch
      1:00pm – 2:30pmFabian Haiden“Categorical Kahler Geometry”
       2:30pm-2:45pm Break
      2:45pm – 4:15pmFabian Haiden“Categorical Kahler Geometry”
      4:30pm – 5:15pmGarret Alston“Potential Functions of Non-exact fillings”
      Tuesday, November 29 – Day 2
      10:30am –11:30amConan Leung, “Remarks on SYZ”
      Lunch
      1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
       2:30pm-2:45pm Break
      2:45pm – 4:15pmHiro Lee Tanaka“Floer theory through spectra”
      4:30pm – 5:15pmHansol Hong, “Mirror Symmetry for punctured Riemann surfaces and gluing construction”
      Wednesday, November 30 – Day 3
      10:30am –11:30amJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
      Lunch
      1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
       2:30-2:45pm Break
      2:45pm – 4:15pmDavid Treumann, “Invariants of Lagrangians via microlocal sheaf theory”
      Thursday, December 1 – Day 4
      10:30am –11:30amDavid Treumann“Some examples in three dimensions”
      Lunch
      1:00pm – 2:30pmJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
       2:30-2:45pm Break
      2:45pm – 3:30pmNetanel Blaier, “The quantum Johnson homomorphism, and the symplectic mapping class group of 3-folds”

      * This event is sponsored by the Simons Foundation and CMSA Harvard University.

    • Colloquium
      3:25 pm
      11/01/2019

      During the Spring 2021 semester, and until further notice, all seminars will take place virtually.

      The 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually, using zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed.

      To learn how to attend, please fill out this form.

      Information on previous colloquia can be found here.

      Spring 2021:

      DateSpeakerTitle/Abstract
      1/27/2021Evelyn Tang (Max Planck Institute for Dynamics and Self-Organization)

      Slides

      Video

      Title: Topology protects chiral edge currents in stochastic systems

      Abstract: Living systems can exhibit time-scales much longer than those of the underlying components, as well as collective dynamical behavior. How such global behavior is subserved by stochastic constituents remains unclear. I will present two-dimensional stochastic networks that consist of out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. I will discuss the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, stochastic growth and shrinkage, and synchronization.

      2/3/2021André Luiz de Gouvêa (Northwestern)

      Video

      Title: The Brave Nu World

      Abstract: Neutrinos are the least understood of the fundamental particles that make up the so-called Standard Model of Particle Physics. Measuring neutrino properties and identifying how they inform our understanding of nature at the smallest distant scales is among the highest priorities of particle physics research today. I will discuss our current understanding of neutrinos, concentrating on the observation of neutrino oscillations and neutrino masses, along with all the open questions that came of these discoveries from the end of the 20th century.

      2/10/2021Mykhaylo Shkolnikov (Princeton)

      Video

      Title: Probabilistic approach to free boundary problems and applications

      Abstract: We will discuss a recently developed probabilistic approach to (singular) free boundary problems, such as the supercooled Stefan problem. The approach is based on a new notion of solution, referred to as probabilistic, which arises naturally in the context of large system limits of interacting particle systems. In the talk, I will give an example of how such interacting particle systems arise in applications (e.g., finance), then obtain a solution of a free boundary problem in the large system limit, and discuss how this solution can be analyzed mathematically (thereby answering natural questions about the systemic risk in financial systems and neural synchronization in the brain). The talk is based on recent and ongoing joint works with Sergey Nadtochiy, Francois Delarue, Jiacheng Zhang and Xiling Zhang

      2/17/2021
      9:00 – 10:00PM ET
      C. Seshadhri (UC Santa Cruz)

      Video

      Title: Studying the (in)effectiveness of low dimensional graph embeddings

      Abstract: Low dimensional graph embeddings are a fundamental and popular tool used for machine learning on graphs. Given a graph, the basic idea is to produce a low-dimensional vector for each vertex, such that “similarity” in geometric space corresponds to “proximity” in the graph. These vectors can then be used as features in a plethora of machine learning tasks, such as link prediction, community labeling, recommendations, etc. Despite many results emerging in this area over the past few years, there is less study on the core premise of these embeddings. Can such low-dimensional embeddings effectively capture the structure of real-world (such as social) networks? Contrary to common wisdom, we mathematically prove and empirically demonstrate that popular low-dimensional graph embeddings do not capture salient properties of real-world networks. We mathematically prove that common low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, which have been widely established to be empirically true for real-world networks. Empirically, we observe that the embeddings generated by popular methods fail to recreate the triangle structure of real-world networks, and do not perform well on certain community labeling tasks. (Joint work with Ashish Goel, Caleb Levy, Aneesh Sharma, and Andrew Stolman.)

      2/24/2021David Ben-Zvi (U Texas)

      Video

      Title: Electric-Magnetic Duality for Periods and L-functions

      Abstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory.
      A fundamental aspect of the Langlands correspondence — the relative Langlands program — studies the representation of L-functions of Galois representations as integrals of automorphic forms. However, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don’t seem to line up.
      We present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely, we rewrite the relative Langlands program as duality in the presence of supersymmetric boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.

      3/3/2021

      9:00pm ET

      Omer Tamuz (Caltech)Title: Monotone Additive Statistics

      Abstract: How should a random quantity be summarized by a single number? We study mappings from random variables to real numbers, focussing on those with the following two properties: (1) monotonicity with respect to first-order stochastic dominance, and (2) additivity for sums of independent random variables. This problem turns out to be connected to the following question: Under what conditions on the random variables X and Y does there exist an independent Z so that X + Z first-order stochastically dominates Y + Z?

      (Joint work with Tobias Fritz, Xiaosheng Mu, Luciano Pomatto and Philipp Strack.)

      3/10/2021

      9:00pm ET

      Piotr Indyk (MIT)Title: Learning-Based Sampling and Streaming

      Abstract: Classical algorithms typically provide “one size fits all” performance, and do not leverage properties or patterns in their inputs. A recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. In this talk I will present two examples of this type, in the context of streaming and sampling algorithms. In particular, I will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (ICLR’19), and (b) sampling algorithms for estimating the support size of a distribution (ICLR’21). Both algorithms use an ML-based predictor that, given a data item, estimates the number of times the item occurs in the input data set. (The talk will cover material from papers co-authored with T Eden, CY Hsu, D Katabi, S Narayanan, R Rubinfeld, S Silwal, T Wagner and A Vakilian.

      3/17/2021
      9:00pm ET
      Chiu-Chu Melissa Liu (Columbia)Title: Topological Recursion and Crepant Transformation Conjecture

      Abstract: The Crepant Transformation Conjecture (CTC), first proposed by Yongbin Ruan and later refined/generalized by others, relates Gromov-Witten (GW) invariants of K-equivalent smooth varieties or smooth Deligne-Mumford stacks. We will outline a proof of all-genus open and closed CTC for symplectic toric Calabi-Yau 3-orbifolds based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong. Our proof relies on the Remodeling Conjecture (proposed by Bouchard-Klemm-Marino-Pasquetti and proved in full generality by Fang, Zong and the speaker) relating open and closed GW invariants of a symplectic toric Calabi-Yau 3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin Topological Recursion.

      3/24/2021Weinan E (Princeton)

      Video

      Title: Machine Learning and PDEs

      Abstract: I will discuss two topics:
      (1) Machine learning-based algorithms and “regularity” theory for very high dimensional PDEs;
      (2) Formulating machine learning as PDE (more precisely, integral-differental equation) problems.

      3/31/2021Thore Graepel (DeepMind/UCL)

      Video

      Title: From AlphaGo to MuZero – Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model

      Abstract: Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a perfect simulator is available. However, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. MuZero learns a model that, when applied iteratively, predicts the quantities most directly relevant to planning: the reward, the action-selection policy, and the value function. When evaluated on 57 different Atari games – the canonical video game environment for testing AI techniques, in which model-based planning approaches have historically struggled – our new algorithm achieved a new state of the art. When evaluated on Go, chess and shogi, without any knowledge of the game rules, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.

      4/7/2021Kui Ren (Columbia)Title: Inversion via Optimization: Revisiting the Classical Least-Squares Formulation of Inverse Problems

      Abstract: The classical least-squares formulation of inverse problems has provided a successful framework for the computational solutions of those problems. In recent years, modifications and alternatives have been proposed to overcome some of the disadvantages of this classical formulation in dealing with new applications. This talk intends to provide an (likely biased) overview of the recent development in constructing new least-squares formulations for model and data-driven solutions of inverse problems.

      4/14/2021Siu-Cheong Lau (Boston U)Title: An algebro-geometric formulation of computing machines

      Abstract: Neural network in machine learning has obvious similarity with quiver representation theory.  The main gap between the two subjects is that network functions produced from two isomorphic quiver representations are not equal, due to the presence of non-linear activation functions which are not equivariant under the automorphism group.  This violates the important math/physics principle that isomorphic objects should produce the same results.  In this talk, I will introduce a general formulation using moduli spaces of framed modules of (noncommutative) algebra and fix this gap.  Metrics over the moduli space are crucial.  I will also explain uniformization between spherical, Euclidean and hyperbolic moduli.

      4/21/2021Vasco Carvalho (Cambridge)Title: The Economy as a Complex Production Network
      Abstract: A modern economy is an intricately linked web of specialized production units, each relying on the flow of inputs from their suppliers to produce their own output, which in turn is routed towards other downstream units. From this production network vantage point we: (i) present the theoretical foundations for the role of such input linkages as a shock propagation channel and as a mechanism for transforming micro-level shocks into macroeconomic, economy-wide fluctuations (ii) selectively survey both empirical and simulation-based studies that attempt to ascertain the relevance and quantitative bite of this argument and (time permitting) (iii) discuss a range of domains where this networked production view is currently being extended to.
      4/28/2021

      9:00 – 10:00pm ET

      Shamit Kachru (Stanford)

      Slides

      Title: K3 Metrics from String Theory

      Abstract: Calabi-Yau manifolds have played a central role in important developments in string theory and mathematical physics.  Famously, they admit Ricci flat metrics — but the proof of that fact is not constructive, and the metrics remain mysterious.  K3 is perhaps the simplest non-trivial compact Calabi-Yau space.  In this talk, I describe two different methods of constructing (smooth, Ricci flat) K3 metrics, and a string theory duality which relates them.  The duality re-sums infinite towers of disc instanton corrections via a purely classical infinite-dimensional hyperkahler quotient construction, which can be practically implemented.


      Fall 2020:

      DateSpeakerTitle/Abstract
      9/23/2020David Kazhdan (Hebrew University)Title: On Applications of Algebraic Combinatorics to Algebraic Geometry

      Abstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.

      10/7/2020

      10:00am

      Mariangela Lisanti (Princeton University)

      Video

      Title: Mapping the Milky Way’s Dark Matter Halo with Gaia

      Abstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium, as typically assumed, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments, which search for the interactions of these particles in terrestrial targets.

      10/14/2020Gil Kalai (Hebrew University and IDC Herzliya)

      Video

      Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers

      Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to
      a) My general argument “against” quantum computers,
      b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
      Relevant papers:
      Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.
      wordpress.com/2019/11/stat-quantum2.pdf

      Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.
      wordpress.com/2020/08/laws-blog2.pdf

      Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.
      wordpress.com/2019/09/main-pr.pdf

      10/21/2020Marta Lewicka (University of Pittsburgh)

      Video

      Title: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models

      Abstract: We propose results that relate the following two contexts:
      (i) Given a Riemann metric G on a thin plate, we study the question of what is its closest isometric immersion, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.
      (ii) We perform the full scaling analysis of E^h, in the context of dimension reduction as the plate’s thickness h goes to 0, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).
      For each n, we identify conditions for the validity of the corresponding scaling, in terms of the vanishing of Riemann curvatures of G up to appropriate orders, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth, swelling, shrinkage, plasticity, etc. Our results display the interaction of calculus of variations,
      geometry and mechanics of materials in the prediction of patterns and shape formation.

      10/28/2020Jonathan Heckman (University of Pennsylvania)

      Video

      Title: Top Down Approach to Quantum Fields

      Abstract: Quantum Field theory (QFT) is the common language of particle physicists, cosmologists, and condensed matter physicists. Even so, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory, highlighting in particular the special role of seemingly “exotic”  higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs, and are now using this to extra observables from strongly correlated systems in theories with more than four spacetime dimensions, as well as in spacetimes with four or fewer spacetime dimensions. Along the way, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems

      11/4/2020
      9:00pm ET
      Surya Ganguli (Stanford)

      Video

      Title: Weaving together machine learning, theoretical physics, and neuroscience through mathematics

      Abstract: An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning, theoretical physics, and neuroscience.  The unification of these fields will likely enable us to exploit the power of complex systems analysis, developed in theoretical physics and applied mathematics, to elucidate the design principles governing neural systems, both biological and artificial, and deploy these principles to develop better algorithms in machine learning.  We will give several vignettes in this direction, including:  (1) determining the best optimization problem to solve in order to perform regression in high dimensions;  (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) developing interpretable machine learning to derive and understand state of the art models of the retina; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) delineating fundamental theoretical limits on the energy, speed and accuracy with which non-equilibrium sensors can detect signals
      Selected References:
      M. Advani and S. Ganguli, Statistical mechanics of optimal convex inference in high dimensions, Physical Review X, 6, 031034, 2016.
      M. Advani and S. Ganguli, An equivalence between high dimensional Bayes optimal inference and M-estimation, NeurIPS, 2016.
      A.K. Lampinen and S. Ganguli, An analytic theory of generalization dynamics and transfer learning in deep linear networks, International Conference on Learning Representations (ICLR), 2019.
      H. Tanaka, A. Nayebi, N. Maheswaranathan, L.M. McIntosh, S. Baccus, S. Ganguli, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction, NeurIPS 2019.
      S. Deny, J. Lindsey, S. Ganguli, S. Ocko, The emergence of multiple retinal cell types through efficient coding of natural movies, Neural Information Processing Systems (NeurIPS) 2018.
      B. Sorscher, G. Mel, S. Ganguli, S. Ocko, A unified theory for the origin of grid cells through the lens of pattern formation, NeurIPS 2019.
      Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
      S.E. Harvey, S. Lahiri, and S. Ganguli, A universal energy accuracy tradeoff in nonequilibrium cellular sensing, https://arxiv.org/abs/2002.10567

      11/11/2020Kevin Buzzard (Imperial College London)

      Video

      Title: Teaching proofs to computers

      Abstract: A mathematical proof is a sequence of logical statements in a precise language, obeying some well-defined rules. In that sense it is very much like a computer program. Various computer tools have appeared over the last 50 years which take advantage of this analogy by turning the mathematical puzzle of constructing a proof of a theorem into a computer game. The newest tools are now capable of understanding some parts of modern research mathematics. In spite of this, these tools are not used in mathematics departments, perhaps because they are not yet capable of telling mathematicians *something new*.
      I will give an overview of the Lean theorem prover, showing what it can currently do. I will also talk about one of our goals: using Lean to make practical tools which will be helpful for future researchers in pure mathematics.

      11/18/2020Jose A. Scheinkman (Columbia)

      Video

      Title: Re-pricing avalanches

      Abstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive.  Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper, we show that a state-dependent  pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment.  These fluctuations, in turn, cause fluctuations  in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)

      11/25/2020

      10:45am

      Eric J. Heller (Harvard)

      Video

      Title: Branched Flow

      Abstract: In classical and quantum  phase space flow, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In  evolution under smooth, random, weakly deflecting  but persistent perturbations, a remarkable regime develops, called branched flow. Lying between the first cusp catastrophes at the outset, leading to fully chaotic  statistical flow much later, lies the visually beautiful regime of branched flow.  It applies to tsunami wave propagation, freak wave formation, light propagation, cosmic microwaves arriving from pulsars, electron flow in metals and devices, sound propagation in the atmosphere and oceans, the large scale structure of the universe, and much more. The mathematical structure of this flow is only partially understood, involving exponential instability coexisting with “accidental” stability. The flow is qualitatively universal, but this has not been quantified.  Many questions arise, including the scale(s) of the random medium,  and the time evolution of manifolds and “fuzzy” manifolds in phase space.  The classical-quantum (ray-wave)  correspondence in this flow is only partially understood.  This talk will be an introduction to the phenomenon, both visual and mathematical, emphasizing unanswered questions

      12/2/2020Douglas Arnold (U of Minnesota)

      Video

      Title: Preserving geometry in numerical discretization

      Abstract: An important design principle for numerical methods for differential equations is that the discretizations preserve key geometric, topological, and algebraic structures of the original differential system.  For ordinary differential equations, such geometric integrators were developed at the end of the last century, enabling stunning computations in celestial mechanics and other applications that would have been impossible without them.  Since then, structure-preserving discretizations have been developed for partial differential equations.  One of the prime examples has been the finite element exterior calculus or FEEC, in which the structures to preserve are related to Hilbert complexes underlying the PDEs, the de Rham complex being a canonical example.  FEEC has led to highly successful new numerical methods for problems in fluid mechanics, electromagnetism, and other applications which relate to the de Rham complex.  More recently, new tools have been developed which extend the applications of FEEC far beyond the de Rham complex, leading to progress in discretizations of problems from solid mechanics, materials science, and general relativity.

      12/9/2020Manuel Blum and Lenore Blum (Carnegie Mellon)

      Video

      Title: What can Theoretical Computer Science Contribute to the Discussion of Consciousness?

      Abstract: The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We study consciousness from the perspective of theoretical computer science. This is done by formalizing the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. We give a precise formal definition of a Conscious Turing Machine (CTM), also called Conscious AI, in the spirit of Alan Turing’s simple yet powerful definition of a computer. We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness.
      After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness, the range of related concepts that the model explains easily and naturally, and the extent of the theory’s agreement with scientific evidence

    • Seminars
      Seminars Colloquia & Seminar
      02-25-2016 Evolution Equations Seminar
      3:25 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-03-2016 Evolution Equations Seminar
      3:26 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-29-2016 Geometric Analysis Seminar
      3:27 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-5-2018 Mathematical Physics Seminar
      3:27 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Seminars
      Seminars Colloquia & Seminar
      04-07-2016 Evolution Equations Seminar
      3:28 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: JDG 2017 Conference, April 28 – May 2, 2017
      3:29 pm
      11/01/2019-05/02/2017

      In celebration of the Journal of Differential Geometry’s 50th anniversary, the Harvard Math Department will be hosting the Tenth Conference on Geometry and Topology (JDG 2017) from April 28 – May 2, 2017.

      Registration and additional information on the conference can be found at http://abel.harvard.edu/jdg/index.html.

      Confirmed Speakers

      * This event is co-sponsored by Lehigh University and partially supported by the National Science Foundation.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2-23-2018 RM & PT Seminar
      3:30 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Seminars
      Seminars Colloquia & Seminar
      4/4/2019 General Relativity Seminar
      3:30 pm-4:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      02-29-2016 Social Science Application Forum
      3:30 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/14/2019 General Relativity Seminar
      3:30 pm-4:30 pm
      11/01/2019
    • Colloquium
      3:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/15/2019 Spacetime Seminar
      3:30 pm-5:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/10/2019 Spacetime Seminar
      3:30 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/17/2018 RM & PT Seminar
      3:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      02-29-2016 Mathematical Physics Seminar
      3:31 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-01-2016 Geometric Analysis Seminar
      3:32 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-10-2016 Evolution Equations Seminar
      3:34 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Working Conference on Materials and Data Analysis, March 27-30, 2017
      3:34 pm
      11/01/2019-03/30/2017

      The Center of Mathematical Sciences and Applications will be hosting a 5-day working Conference on Materials and Data Analysis and related areas, March 27-30, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Photos of the event can be found on CMSA’s Blog.

       Participants:

      Organizers:

      * This event is sponsored by CMSA Harvard University.

      Schedule:

      Monday, March 27

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amKieron Burke, University of California, IrvineBackground in DFT and electronic structure calculations
      10:00am – 11:00amKieron Burke, University of California, Irvine

      The density functionals machines can learn

      11:00am – 12:00pmSadasivan Shankar, Harvard UniversityA few key principles for applying Machine Learning to Materials (or Complex Systems) — Scientific and Engineering Perspectives

      Tuesday, March 28

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amRyan Adams, HarvardTBA
      10:00am – 11:00amGábor Csányi, University of Cambridge

      Interatomic potentials using machine learning: accuracy, transferability and chemical diversity

      11:00am – 1:00pmLunch Break
      1:00pm – 2:00pmEvan Reed, Stanford UniversityTBA

       Wednesday, March 29 

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amPatrick Riley, GoogleThe Message Passing Neural Network framework and its application to molecular property prediction
      10:00am – 11:00amJörg Behler, University of GöttingenTBA
      11:00am – 12:00pmEkin Doğuş Çubuk, Stanford UniversTBA
      4:00pmLeslie Greengard, Courant InstituteInverse problems in acoustic scattering and cryo-electron microscopy

      CMSA Colloquium

      Thursday, March 30

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amMatthias Rupp, Fitz Haber Institute of the Max Planck SocietyTBA
      10:00am – 11:00amPetros Koumoutsakos, Radcliffe Institute for Advanced Study, HarvardTBA
      11:00am – 1:00pmLunch Break
      1:00pm – 2:00pmDennis Sheberla, Harvard UniversityRapid discovery of functional molecules by a high-throughput virtual screening
    • CMSA EVENT: Workshop on Discrete and Topological Models for Effective Field Theories, January 9-13, 2017
      3:35 pm-3:36 pm
      11/01/2019-01/13/2017

      The Center of Mathematical Sciences and Applications will be hosting a Workshop on “Discrete and Topological Models for Effective Field Theories,” January 9-13, 2017.  The workshop will be hosted in G02 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Titles, abstracts and schedule will be provided nearer to the event.

      Participants:

      Dan Freed, UT Austin

      Anton Kapustin, California Institute of Technology

      Alexei Y. Kitaev, California Institute of Technology

      Greg Moore, Rutgers University

      Constantin Teleman, University of Oxford

      Organizers:

      Mike Hopkins, Shing-Tung Yau

      * This event is sponsored by CMSA Harvard University.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-09-2016 Random Matrix & Probability Theory
      3:35 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-23-2016 Random Matrix & Probability Theory
      3:37 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-04-2016 Social Science Applications Forum
      3:38 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Working Conference on Covariance Analysis in Biology, May 1-4, 2017
      3:40 pm-3:41 pm
      11/01/2019-05/02/2017

      The Center of Mathematical Sciences and Applications will be hosting a working Conference on Covariance Analysis in Biology, May 1-4, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      This event is open and free.  If you would like to attend, please register here to help us keep a headcount. A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Speakers:

      Orr Ashenberg, Fred Hutchinson Cancer Research Center

      John Barton, Massachusetts Institute of Technology

      Simona Cocco, Laboratoire de Physique Statistique de l’ENS

      Sean Eddy, Harvard University

      Efthimios Kaxiras, Harvard University

      Michael Laub, Massachusetts Institute of Technology

      Debora S. Marks, Harvard University

      Govind Menon, Brown University

      Rémi Monasson, Laboratoire de Physique Théorique de l’ENS

      Andrew Murray, Harvard University

      Ilya Nemenman, Emory College

      Chris Sander, Dana-Farber Cancer Institute, Harvard Medical School

      Dave Thirumalai, University of Texas at Austin

      Martin Weigt, IBPS, Université Pierre et Marie Curie

      Matthieu Wyart, EPFL

      More speakers will be confirmed soon.

       

      Schedule:

      (Please click here for a downloadable version of the schedule.)

      Please note that the schedule for both days is currently tentative and is subject to change.

      May 1, Monday

      TimeSpeakerTopic
      9:00-10:00amSean EddyTBA
      10:00-11:00amMike LaubTBA
      11:00am-12:00pmIlya NemenmanTBA
      May 2, Tuesday
      TimeSpeakerTopic
      9:00-10:00amOrr AshenbergTBA
      10:00-11:00amDebora MarksTBA
      11:00am-12:00pmMartin WeigtTBA
      4:30pm-5:30pmSimona CoccoCMSA Colloquia

       

      May 3, Wednesday
      TimeSpeakerTopic
      9:00-10:00amAndrew MurrayTBA
      10:00-11:00amMatthieu WyartTBA
      11:00am-12:00pmRémi MonassonTBA

       

      May 4, Thursday
      TimeSpeakerTopic
      9:00-10:00amDavid ThirumalaiTBA
      10:00-11:00amChris SanderTBA
      11:00am-12:00pmJohn BartonTBA

       

      Organizers:

      Michael Brenner, Lucy Colwell, Elena Rivas, Eugene Shakhnovich

      * This event is sponsored by CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      03-07-2016 Mathematical Physics Seminar
      3:41 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2-26-2018 Mathematical Physics Seminar
      3:42 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-11-2016 Random Matrix & Probability Theory
      3:42 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: A Celebration of Symplectic Geometry: 15 Years of JSG, June 5-6, 2017
      3:44 pm
      11/01/2019-05/04/2017

      In celebration of the Journal of Symplectic Geometry’s 15th anniversary, the Center of Mathematical Sciences and Applications will be hosting A Celebration of Symplectic Geometry: 15 Years of JSG on June 5-6, 2017.

      To register for this event, please click here.

      Confirmed speakers:

      The conference is co-organized by Denis Auroux and Victor Guillemin. Additional information on the conference will be announced closer to the event.

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

      Schedule:

      The schedule for both days is currently tentative and is subject to change. A pdf version of the schedule can also be downloaded here.

      June 5, Monday (Full day)

      TimeSpeakerTopic
      8:30am – 9:0amBreakfast
      9:00am – 10:00amJonathan WeitsmanTitle: On the geometric quantization of (some) Poisson manifolds
      10:30am – 11:30amEckhard MeinrenkenTitle: On Hamiltonian loop group spaces

      Abstract: Let G be a compact Lie group. We explain a construction of an LG-equivariant spinor module over any Hamiltonian loop group space with proper moment map. It may be regarded as its `canonical spin-c structure’. We show how to reduce to finite dimensions, resulting in actual spin-s structure on transversals, as well as twisted spin-c structures for the associated quasi-hamiltonian space. This is based on joint work with Yiannis Loizides and Yanli Song.

      11:30am – 1:30pmBreak
      1:30pm – 2:30pmAna Rita PiresTitle: Infinite staircases in symplectic embedding problems

      Abstract: McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with Cristofaro-Gardiner, Holm and Mandini.

      Video

      3:00pm – 4:00pmSobhan SeyfaddiniTitle: Rigidity of conjugacy classes in groups of area-preserving homeomorphisms

      Abstract: Motivated by understanding the algebraic structure of groups of area-preserving homeomorphims F. Beguin, S. Crvoisier, and F. Le Roux were lead to the following question: Can the conjugacy class of a Hamiltonian homeomorphism be dense? We will show that one can rule out existence of dense conjugacy classes by simply counting fixed points. This is joint work with Le Roux and Viterbo.

      4:30pm – 5:30pmRoger CasalsTitle: Differential Algebra of Cubic Graphs
      Abstract: In this talk we will associate a combinatorial dg-algebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations and examples. From there we study the Legendrian surfaces behind these constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.Video

      June 6, Tuesday (Full day)

      TimeSpeakerTopic
      8:30am – 9:00amBreakfast
      9:00am – 10:00amAlejandro UribeTitle: Semi-classical wave functions associated with isotropic submanifolds of phase space

      Abstract: After reviewing fundamental ideas on the quantum-classical correspondence, I will describe how to associate spaces of semi-classical wave functions to isotropic submanifolds of phase space satisfying a Bohr-Sommerfeld condition. Such functions have symbols that are symplectic spinors, and they satisfy a symbol calculus under the action of quantum observables. This is the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin, and it is joint work with Victor Guillemin and Zuoqin Wang. I will inlcude applications and open questions.

      Video

      10:30am – 11:30amAlisa KeatingTitle: Symplectomorphisms of exotic discs

      Abstract: It is a theorem of Gromov that the group of compactly supported symplectomorphisms of R^4, equipped with the standard symplectic form, is contractible. While nothing is known in higher dimensions for the standard symplectic form, we show that for some exotic symplectic forms on R^{4n}, for all but finitely n, there exist compactly supported symplectomorphisms that are smoothly non-trivial. The principal ingredients are constructions of Milnor and Munkres, a symplectic and contact version of the Gromoll filtration, and Borman, Eliashberg and Murphy’s work on existence of over-twisted contact structures. Joint work with Roger Casals and Ivan Smith.

      Video

      11:30am – 1:30pmBreak
      1:30pm – 2:30pmChen HeTitle: Morse theory on b-symplectic manifolds

      Abstract: b-symplectic (or log-symplectic) manifolds are Poisson manifolds equipped with symplectic forms of logarithmic singularity. Following Guillemin, Miranda, Pires and Scott’s introduction of Hamiltonian group actions on b-symplectic manifolds, we will survey those classical results of Hamiltonian geometry to the b-symplectic case.

      Video

      3:00pm – 4:00pmYael KarshonTitle: Geometric quantization with metaplectic-c structures

      Abstract: I will present a variant of the Kostant-Souriau geometric quantization procedure that uses metaplectic-c structures to incorporate the “half form correction” into the prequantization stage. This goes back to the late 1970s but it is not widely known and it has the potential to generalize and improve upon recent works on geometric quantization.

      Video


    • Seminars
      Seminars Colloquia & Seminar
      03-08-2016 Geometric Analysis Seminar
      3:44 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-21-2016 Mathematical Physics Seminar
      3:46 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-24-2016 Evolution Equations Seminar
      3:47 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: 2017 Big Data Conference
      3:47 pm
      11/01/2019-08/19/2017
      1 Oxford Street, Cambridge MA 02138

      The Center of Mathematical Sciences and Applications will be hosting a conference on Big Data from August 18 – 19, 2017, in Hall D of the Science Center at Harvard University.

      The Big Data Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the third conference on Big Data the Center will host as part of our annual events, and is co-organized by Richard Freeman, Scott Kominers, Jun Liu, Horng-Tzer Yau and Shing-Tung Yau.

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

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

      Confirmed Speakers:

       

      Following the conference, there will be a two-day workshop from August 20-21. The workshop is organized by Scott Kominers, and will feature:

      • Jörn Boehnke, Harvard University
      • Nikhil Naik, Harvard University
      • Bradly Stadie, Open AI, University of California, Berkeley

       

      Conference Schedule

      A PDF version of the schedule below can also be downloaded here.

      August 18, Friday (Full day)

      TimeSpeakerTopic
      8:30 am – 9:00 amBreakfast
      9:00 am – 9:40 amMohammad Akbarpour

      Video

      Title: Information aggregation in overlapping generations and the emergence of experts

      Abstract: We study a model of social learning with “overlapping generations”, where agents meet others and share data about an underlying state over time. We examine under what conditions the society will produce individuals with precise knowledge about the state of the world. There are two information sharing regimes in our model: Under the full information sharing technology, individuals exchange the information about their point estimates of an underlying state, as well as their sources (or the precision of their signals) and update their beliefs by taking a weighted average. Under the limited information sharing technology, agents only observe the information about the point estimates of those they meet, and update their beliefs by taking a weighted average, where weights can depend on the sequence of meetings, as well as the labels. Our main result shows that, unlike most social learning settings, using such linear learning rules do not guide the society (or even a fraction of its members) to learn the truth, and having access to, and exploiting knowledge of the precision of a source signal are essential for efficient social learning (joint with Amin Saberi & Ali Shameli).

      9:40 am – 10:20 amLucas Janson

      Video

      Title: Model-Free Knockoffs For High-Dimensional Controlled Variable Selection

      Abstract: Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new framework of model-free knockoffs, which reads from a different perspective the knockoff procedure (Barber and Candès, 2015) originally designed for controlling the false discovery rate in linear models. The key innovation of our method is to construct knockoff variables probabilistically instead of geometrically. This enables model-free knockoffs to deal with arbitrary (and unknown) conditional models and any dimensions, including when the dimensionality p exceeds the sample size n, while the original knockoffs procedure is constrained to homoscedastic linear models with n greater than or equal to p. Our approach requires the design matrix be random (independent and identically distributed rows) with a covariate distribution that is known, although we show our procedure to be robust to unknown/estimated distributions. As we require no knowledge/assumptions about the conditional distribution of the response, we effectively shift the burden of knowledge from the response to the covariates, in contrast to the canonical model-based approach which assumes a parametric model for the response but very little about the covariates. To our knowledge, no other procedure solves the controlled variable selection problem in such generality, but in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case-control study of Crohn’s disease in the United Kingdom, making twice as many discoveries as the original analysis of the same data.

      Slides

      10:20 am – 10:50 amBreak
      10:50 pm – 11:30 pmNoureddine El Karoui

      Video

      Title: Random matrices and high-dimensional statistics: beyond covariance matrices

      Abstract: Random matrices have played a central role in understanding very important statistical methods linked to covariance matrices (such as Principal Components Analysis, Canonical Correlation Analysis etc…) for several decades. In this talk, I’ll show that one can adopt a random-matrix-inspired point of view to understand the performance of other widely used tools in statistics, such as M-estimators, and very common methods such as the bootstrap. I will focus on the high-dimensional case, which captures well the situation of “moderately” difficult statistical problems, arguably one of the most relevant in practice. In this setting, I will show that random matrix ideas help upend conventional theoretical thinking (for instance about maximum likelihood methods) and highlight very serious practical problems with resampling methods.

      11:30 am – 12:10 pmNikhil Naik

      Video

      Title: Understanding Urban Change with Computer Vision and Street-level Imagery

      Abstract: Which neighborhoods experience physical improvements? In this work, we introduce a computer vision method to measure changes in the physical appearances of neighborhoods from time-series street-level imagery. We connect changes in the physical appearance of five US cities with economic and demographic data and find three factors that predict neighborhood improvement. First, neighborhoods that are densely populated by college-educated adults are more likely to experience physical improvements. Second, neighborhoods with better initial appearances experience, on average, larger positive improvements. Third, neighborhood improvement correlates positively with physical proximity to the central business district and to other physically attractive neighborhoods. Together, our results illustrate the value of using computer vision methods and street-level imagery to understand the physical dynamics of cities.

      (Joint work with Edward L. Glaeser, Cesar A. Hidalgo, Scott Duke Kominers, and Ramesh Raskar.)

      12:10 pm – 12:25 pmVideo #1

      Video #2

      Data Science Lightning Talks
      12:25 pm – 1:30 pmLunch
      1:30 pm – 2:10 pmTracy Ke

      Video

      Title: A new SVD approach to optimal topic estimation

      Abstract: In the probabilistic topic models, the quantity of interest—a low-rank matrix consisting of topic vectors—is hidden in the text corpus matrix, masked by noise, and Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank matrix and the singular vectors of the text corpus matrix are usually complicated and hard to spell out, so how to use SVD for learning topic models faces challenges.

      We overcome the challenge by revealing a surprising insight: there is a low-dimensional simplex structure which can be viewed as a bridge between the low-rank matrix of interest and the SVD of the text corpus matrix, and which allows us to conveniently reconstruct the former using the latter. Such an insight motivates a new SVD-based approach to learning topic models.

      For asymptotic analysis, we show that under a popular topic model (Hofmann, 1999), the convergence rate of the l1-error of our method matches that of the minimax lower bound, up to a multi-logarithmic term. In showing these results, we have derived new element-wise bounds on the singular vectors and several large deviation bounds for weakly dependent multinomial data. Our results on the convergence rate and asymptotical minimaxity are new. We have applied our method to two data sets, Associated Process (AP) and Statistics Literature Abstract (SLA), with encouraging results. In particular, there is a clear simplex structure associated with the SVD of the data matrices, which largely validates our discovery.

      2:10 pm – 2:50 pmAlbert-László Barabási

      Video

      Title: Taming Complexity: From Network Science to Controlling Networks

      Abstract: The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here we explore the controllability of an arbitrary complex network, identifying the set of driver nodes whose time-dependent control can guide the system’s entire dynamics. We apply these tools to several real networks, unveiling how the network topology determines its controllability. Virtually all technological and biological networks must be able to control their internal processes. Given that, issues related to control deeply shape the topology and the vulnerability of real systems. Consequently unveiling the control principles of real networks, the goal of our research, forces us to address series of fundamental questions pertaining to our understanding of complex systems.

       

      2:50 pm – 3:20 pmBreak
      3:20 pm – 4:00 pmMarena Lin

      Video

      Title: Optimizing climate variables for human impact studies

      Abstract: Estimates of the relationship between climate variability and socio-economic outcomes are often limited by the spatial resolution of the data. As studies aim to generalize the connection between climate and socio-economic outcomes across countries, the best available socio-economic data is at the national level (e.g. food production quantities, the incidence of warfare, averages of crime incidence, gender birth ratios). While these statistics may be trusted from government censuses, the appropriate metric for the corresponding climate or weather for a given year in a country is less obvious. For example, how do we estimate the temperatures in a country relevant to national food production and therefore food security? We demonstrate that high-resolution spatiotemporal satellite data for vegetation can be used to estimate the weather variables that may be most relevant to food security and related socio-economic outcomes. In particular, satellite proxies for vegetation over the African continent reflect the seasonal movement of the Intertropical Convergence Zone, a band of intense convection and rainfall. We also show that agricultural sensitivity to climate variability differs significantly between countries. This work is an example of the ways in which in-situ and satellite-based observations are invaluable to both estimates of future climate variability and to continued monitoring of the earth-human system. We discuss the current state of these records and potential challenges to their continuity.

      4:00 pm – 4:40 pmAlex Peysakhovich Title: Building a cooperator

      Abstract: A major goal of modern AI is to construct agents that can perform complex tasks. Much of this work deals with single agent decision problems. However, agents are rarely alone in the world. In this talk I will discuss how to combine ideas from deep reinforcement learning and game theory to construct artificial agents that can communicate, collaborate and cooperate in productive positive sum interactions.

      4:40 pm – 5:20 pmTze Leung Lai

      Video

      Title: Gradient boosting: Its role in big data analytics, underlying mathematical theory, and recent refinements

      Abstract: We begin with a review of the history of gradient boosting, dating back to the LMS algorithm of Widrow and Hoff in 1960 and culminating in Freund and Schapire’s AdaBoost and Friedman’s gradient boosting and stochastic gradient boosting algorithms in the period 1999-2002 that heralded the big data era. The role played by gradient boosting in big data analytics, particularly with respect to deep learning, is then discussed. We also present some recent work on the mathematical theory of gradient boosting, which has led to some refinements that greatly improves the convergence properties and prediction performance of the methodology.

      August 19, Saturday (Full day)

      TimeSpeakerTopic
      8:30 am – 9:00 amBreakfast
      9:00 am – 9:40 amNatesh Pillai

      Video

      Title: Accelerating MCMC algorithms for Computationally Intensive Models via Local Approximations

      Abstract: We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler’s exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this article: when the likelihood has some local regularity, the number of model evaluations per Markov chain Monte Carlo (MCMC) step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ordinary differential equation (ODE) and partial differential equation (PDE) inference problems, with both synthetic and real data.

      9:40 am – 10:20 amRavi Jagadeesan

      Video

      Title: Designs for estimating the treatment effect in networks with interference

      Abstract: In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring” on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide range of interference functions encountered in applications, we show both by theory and simulations that the classical Neymanian estimator for the direct effect has desirable properties for our designs. This further extends to settings where homophily is present in addition to interference.

      10:20 am – 10:50 amBreak
      10:50 am – 11:30 amAnnie Liang

      Video

      Title: The Theory is Predictive, but is it Complete? An Application to Human Generation of Randomness

      Abstract: When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? This question is difficult to answer, because in general we do not know how much “predictable variation” there is in the problem. In this paper, we consider approaches motivated by machine learning algorithms as a means of constructing a benchmark for the best attainable level of prediction.  We illustrate our methods on the task of predicting human-generated random sequences. Relative to a theoretical machine learning algorithm benchmark, we find that existing behavioral models explain roughly 15 percent of the predictable variation in this problem. This fraction is robust across several variations on the problem. We also consider a version of this approach for analyzing field data from domains in which human perception and generation of randomness has been used as a conceptual framework; these include sequential decision-making and repeated zero-sum games. In these domains, our framework for testing the completeness of theories provides a way of assessing their effectiveness over different contexts; we find that despite some differences, the existing theories are fairly stable across our field domains in their performance relative to the benchmark. Overall, our results indicate that (i) there is a significant amount of structure in this problem that existing models have yet to capture and (ii) there are rich domains in which machine learning may provide a viable approach to testing completeness (joint with Jon Kleinberg and Sendhil Mullainathan).

      11:30 am – 12:10 pmZak Stone

      Video

      Title: TensorFlow: Machine Learning for Everyone

      Abstract: We’ve witnessed extraordinary breakthroughs in machine learning over the past several years. What kinds of things are possible now that weren’t possible before? How are open-source platforms like TensorFlow and hardware platforms like GPUs and Cloud TPUs accelerating machine learning progress? If these tools are new to you, how should you get started? In this session, you’ll hear about all of this and more from Zak Stone, the Product Manager for TensorFlow on the Google Brain team.

      12:10 pm – 1:30 pmLunch
      1:30 pm – 2:10 pmJann Spiess

      Video

      Title: (Machine) Learning to Control in Experiments

      Abstract: Machine learning focuses on high-quality prediction rather than on (unbiased) parameter estimation, limiting its direct use in typical program evaluation applications. Still, many estimation tasks have implicit prediction components. In this talk, I discuss accounting for controls in treatment effect estimation as a prediction problem. In a canonical linear regression framework with high-dimensional controls, I argue that OLS is dominated by a natural shrinkage estimator even for unbiased estimation when treatment is random; suggest a generalization that relaxes some parametric assumptions; and contrast my results with that for another implicit prediction problem, namely the first stage of an instrumental variables regression.

      2:10 pm – 2:50 pmBradly StadieTitle: Learning to Learn Quickly: One-Shot Imitation and Meta Learning

      Abstract: Many reinforcement learning algorithms are bottlenecked by data collection costs and the brittleness of their solutions when faced with novel scenarios.
      We will discuss two techniques for overcoming these shortcomings. In one-shot imitation, we train a module that encodes a single demonstration of a desired behavior into a vector containing the essence of the demo. This vector can subsequently be utilized to recover the demonstrated behavior. In meta-learning, we optimize a policy under the objective of learning to learn new tasks quickly. We show meta-learning methods can be accelerated with the use of auxiliary objectives. Results are presented on grid worlds, robotics tasks, and video game playing tasks.

      2:50 pm – 3:20 pmBreak
      3:20 pm – 4:00 pmHau-Tieng Wu

      Video

      Title: When Medical Challenges Meet Modern Data Science

      Abstract: Adaptive acquisition of correct features from massive datasets is at the core of modern data analysis. One particular interest in medicine is the extraction of hidden dynamics from a single observed time series composed of multiple oscillatory signals, which could be viewed as a single-channel blind source separation problem. The mathematical and statistical problems are made challenging by the structure of the signal which consists of non-sinusoidal oscillations with time varying amplitude/frequency, and by the heteroscedastic nature of the noise. In this talk, I will discuss recent progress in solving this kind of problem by combining the cepstrum-based nonlinear time-frequency analysis and manifold learning technique. A particular solution will be given along with its theoretical properties. I will also discuss the application of this method to two medical problems – (1) the extraction of a fetal ECG signal from a single lead maternal abdominal ECG signal; (2) the simultaneous extraction of the instantaneous heart/respiratory rate from a PPG signal during exercise; (3) (optional depending on time) an application to atrial fibrillation signals. If time permits, the clinical trial results will be discussed.

      4:00 pm – 4:40 pmSifan Zhou

      Video

      Title: Citing People Like Me: Homophily, Knowledge Spillovers, and Continuing a Career in Science

      Abstract: Forward citation is widely used to measure the scientific merits of articles. This research studies millions of journal article citation records in life sciences from MEDLINE and finds that authors of the same gender, the same ethnicity, sharing common collaborators, working in the same institution, or being geographically close are more likely (and quickly) to cite each other than predicted by their proportion among authors working on the same research topics. This phenomenon reveals how social and geographic distances influence the quantity and speed of knowledge spillovers. Given the importance of forward citations in academic evaluation system, citation homophily potentially put authors from minority group at a disadvantage. I then show how it influences scientists’ chances to survive in the academia and continue publishing. Based on joint work with Richard Freeman.

       

      To view photos and video interviews from the conference, please visit the CMSA blog.

       

    • Seminars
      Seminars Colloquia & Seminar
      12-07-2015 Mathematical Physics Seminar
      3:49 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-22-2016 Geometric Analysis Seminar
      3:51 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/16/2019 Colloquium
      4:00 pm
      11/01/2019
    • Yip Lecture Series
      Yip Lecture Series Event
      Yip Annual Lecture
      4:00 pm-5:00 pm
      11/01/2019
      1 Oxford Street, Cambridge MA 02138

      On April 18, 2019 Harvard CMSA hosted the inaugural Yip lecture. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Peter Galison (Harvard Physics).

      The lecture was held from 4:00-5:00pm in Science Center, Hall A.

      Credit:Bronzwaer/Davelaar/Moscibrodzka/Falcke/Radboud University
    • Seminars
      4:00 pm-5:00 pm
      11/01/2019

    • Math Science Lectures in Honor of Raoul Bott
      Math Science Lectures in Honor of Raoul Bott Event
      Math Science Lectures in Honor of Raoul Bott: Mina Aganagic
      4:00 pm
      11/01/2019-04/10/2019
      1 Oxford Street, Cambridge MA 02138

      On April 9 and 10, 2019 the CMSA hosted two lectures by Mina Aganagic (UC Berkeley).  This was the second annual Math Science Lecture Series held in honor of Raoul Bott.

      The lectures took place in Science Center, Hall C

      “Two math lessons from string theory”

      Lecture 1:

       

       

       

       

       

      April 9, 2019

      Title: “Lesson on Integrability”

       

      Abstract: The quantum Knizhnik-Zamolodchikov (qKZ) equation is a difference generalization of the famous Knizhnik-Zamolodchikov (KZ) equation. The problem to explicitly capture the monodromy of the qKZ equation has been open for over 25 years. I will describe the solution to this problem, discovered jointly with Andrei Okounkov. The solution comes from the geometry of Nakajima quiver varieties and has a string theory origin.

      Part of the interest in the qKZ monodromy problem is that its solution leads to integrable lattice models, in parallel to how monodromy matrices of the KZ equation lead to knot invariants. Thus, our solution of the problem leads to a new, geometric approach, to integrable lattice models. There are two other approaches to integrable lattice models, due to Nekrasov and Shatashvili and to Costello, Witten and Yamazaki. I’ll describe joint work with Nikita Nekrasov which explains how string theory unifies the three approaches to integrable lattice models.

      Lecture 2:

       

       

       

       

       

      April 10, 2019

      Title: “Lesson on Knot Categorification”

       

      Abstract: An old problem is to find a unified approach to the knot categorification problem. The new string theory perspective on the qKZ equation I described in the first talk can be used to derive two geometric approaches to the problem.

      The first approach is based on a category of B-type branes on resolutions of slices in affine Grassmannians. The second is based on a category of A-branes in a Landau-Ginzburg theory. The relation between them is two dimensional (equivariant) mirror symmetry. String theory also predicts that a third approach to categorification, based on counting solutions to five dimensional Haydys-Witten equations, is equivalent to the first two.

      This talk is mostly based on joint work with Andrei Okounkov.

       

      Information about last year’s Math Science Bott lecture can be found here. 

      Aganagic

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      03-28-2016 Mathematical Physics Seminar
      4:08 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-06-2016 Random Matrix & Probability Theory
      4:10 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-30-2016 Random Matrix & Probability Theory Seminar
      4:11 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-14-2016 Evolution Equations Seminar
      4:13 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-12-2016 Geometric Analysis Seminar
      4:14 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Special Seminar
      4:15 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      03-31-2016 Evolution Equations Seminar
      4:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      4:15 pm-5:15 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      Duality String Seminar, Thursdays
      4:15 pm-6:00 pm
      11/01/2019-10/12/2016

      The Duality String  Seminar is held every Thursday at 4:15pm in Jefferson Lab, 453.

      For details, please visit the website.

      * The Duality String Seminar is sponsored by the Center of Mathematical Sciences and Applications’ Cheng Yu-Tong Fund, for Research at the Interface of Mathematics and Physics.

    • Seminars
      Seminars Colloquia & Seminar
      04-04-2016 Mathematical Physics Seminar
      4:20 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-05-2016 Geometric Analysis Seminar
      4:21 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-11-2016 Mathematical Physics Seminar
      4:22 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-07-2016 Evolution Equations Seminar
      4:24 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-06-2016 Seminar on General Relativity
      4:25 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-11-2016 Random Matrix & Probability Theory Seminar
      4:28 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-13-2016 General Relativity Seminar
      4:29 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:30 pm
      11/01/2019
    • Seminars
      4:30 pm-5:30 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2/14/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      Colloquium Colloquia & Seminar
      2/20/2019 Colloquium
      4:30 pm-5:00 pm
      11/01/2019
    • Colloquium
      Colloquium Colloquia & Seminar
      2/13/2019 Colloquium
      4:30 pm-5:00 pm
      11/01/2019
    • Seminars
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
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      Seminars Colloquia & Seminar
      1/30/2019 Colloquium
      4:30 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/4/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      11/01/2019
    • Seminars
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      10/3/2019 RM & PT Seminar
      4:30 pm-5:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/24/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/9/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Seminars
      4:30 pm-5:30 pm
      11/01/2019
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      Seminars Colloquia & Seminar
      4/17/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/2/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/18/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
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      Seminars Colloquia & Seminar
      04-20-2016 General Relativity Seminar
      4:30 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/20/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3/28/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      11/01/2019
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      Seminars Colloquia & Seminar
      04-18-2016 Social Science Application Forum
      4:31 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:33 pm
      11/01/2019

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    • Seminars
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      04-19-2016 Geometric Analysis Seminar
      4:33 pm
      11/01/2019

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      04-18-2016 Mathematical Physics Seminar
      4:34 pm
      11/01/2019

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    • Colloquium
      4:34 pm
      11/01/2019

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      04-21-2016 Evolution Equations Seminar
      4:35 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:36 pm
      11/01/2019

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    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-20-2016 Random Matrix & Probability Theory Seminar
      4:37 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      04-26-2016 Geometric Analysis Seminar
      4:38 pm
      11/01/2019

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    • Colloquium
      4:39 pm
      11/01/2019

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      04-25-2016 Mathematical Physics Seminar
      4:39 pm
      11/01/2019

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    • Colloquium
      4:41 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-27-2016 Random Matrix & Probability Theory Seminar
      4:42 pm
      11/01/2019

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    • Seminars
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      04-27-2016 General Relativity Seminar
      4:44 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      04-28-2016 CMSA Special Seminar
      4:45 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      04-28-2016 Evolution Equations Seminar
      4:46 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      05-04-2016 General Relativity Seminar
      4:48 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-29-2016 CMSA Special Seminar
      4:49 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      05-02-2016 Mathematical Physics Seminar
      4:50 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-05-2016 Evolution Equations Seminar
      4:51 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-25-2016 General Relativity Seminar
      4:52 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      4:54 pm
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
      4:58 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      5:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2018 HMS Focused Lecture Series
      5:00 pm
      11/01/2019

      As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester. The lectures will take place  on Tuesdays and Thursdays in the CMSA Building, 20 Garden Street, Room G10.

      The schedule will be updated below.

      DateSpeakerTitle/Abstract
      January 23, 25, 30 and February 1 

      3-5pm

      *Room G10*

      Ivan Losev 

      (Northeastern)

      Title: BGG category O: towards symplectic duality 

      Abstract: We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson, Ginzburg and Soergel on the Koszul duality for such categories, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting.

      Approximate (optimistic) plan of the lectures:

      1) Preliminaries and BGG category O.

      2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem.

      3) Localization theorem continued. Soergel modules.

      4) Koszul algebras and Koszul duality for categories O.

      Time permitting: other instances of Symplectic duality.

      Prerequisites:

      Semi-simple Lie algebras and their finite dimensional representation theory.

      Some  Algebraic geometry. No prior knowledge of category O/ Geometric

      Representation theory is assumed.

      Scanned from a Xerox Multifunction Device

      February 27, 

      and March 1

      3-5pm

      Colin Diemer 

      (IHES)

      Title: Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS. 

      Abstract: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau’s the role of the mirror map is well-appreciated. In these talks I’ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov, Kontsevich, Pantev), the interplay of the topology  of LG models with autoequivalence relations in the Calabi-Yau setting, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we’ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster).

      March 6 and 8 

      4-5pm

      Adam Jacob 

      (UC Davis)

      Title: The deformed Hermitian-Yang-Mills equation 

      Abstract: In this series I will discuss the deformed Hermitian-Yang-Mills equation, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible, and cover joint work with T.C. Collins and S.-T. Yau.

      March 6, 8, 13, 15 

      3-4pm

      Dmytro Shklyarov 

      (TU Chemnitz)

      Title: On categories of matrix factorizations and their homological invariants 

      Abstract: The talks will cover the following topics:

      1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements.

      2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the “classical” mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models.

      3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data, namely, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type, open varieties, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which, just as their non-equivariant cousins, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds.

      April 10 & 12 

      3-4pm

      Mauricio Romo 

      (IAS)

      Title: Gauged Linear Sigma Models, Supersymmetric Localization and Applications 

      Abstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with  CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs).

      Lecture notes

      April 17, 19, 26 

      3-5pm

      Andrew  Harder 

      (University of Miami)

      Title: Perverse sheaves of categories on surfaces 

      Abstract: Perverse sheaves of categories on a Riemann surface S are systems of categories and functors which are encoded by a graphs on S, and which satisfy conditions that resemble the classical characterization of perverse sheaves on a disc.

      I’ll review the basic ideas behind Kapranov and Schechtman’s notion of a perverse schober and generalize this to perverse sheaves of categories on a punctured Riemann surface. Then I will give several examples of perverse sheaves of categories in both algebraic geometry, symplectic geometry, and category theory. Finally, I will describe how one should be able to use related ideas to prove homological mirror symmetry for certain noncommutative deformations of projective 3-space.

       

      May 15, 17 

      1-3pm

      Charles Doran 

      (University of Alberta)

      Lecture One:
      Title: Picard-Fuchs uniformization and Calabi-Yau geometry
      Abstract:
      Part 1:  We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties, with emphasis on Calabi-Yau manifolds.  Specializing to the case of K3 surfaces, we explore general results on “Picard-Fuchs uniformization” of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces.  As an application, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces.
      Part 2:  We next consider families with one natural complex structure modulus, (e.g., elliptic curves, rank 19 K3 surfaces, b_1=4 Calabi-Yau threefolds, …), where the Picard-Fuchs equations are ODEs.  What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces?  Using Hodge theory and parabolic cohomology, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space.  In particular, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau.

       

      Lecture Two:
      Title: Calabi-Yau fibrations: construction and classification
      Abstract:

      Part 1:  Codimension one Calabi-Yau submanifolds induce fibrations, with the periods of the total space relating to those of the fibers and the structure of the fibration.  We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals.

      Part 2:  We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces.  The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces.  When the total space of the fibration is a Calabi-Yau threefold, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations.  The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1.

    • CMSA EVENT: Noga Alon Public Talk, 9-7-17
      5:00 pm-6:00 pm
      11/01/2019

      Noga Alon (Tel Aviv University) will be giving a public talk on September 7, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

      Title: Graph Coloring: Local and Global

      Abstract: Graph Coloring is arguably the most popular subject in Discrete Mathematics, and its combinatorial, algorithmic and computational aspects have been studied intensively. The most basic notion in the area, the chromatic number of a graph, is an inherently global property. This is demonstrated by the hardness of computation or approximation of this invariant as well as by the existence of graphs with arbitrarily high chromatic number and no short cycles. The investigation of these graphs had a profound impact on Graph Theory and Combinatorics. It combines combinatorial, probabilistic, algebraic and topological techniques with number theoretic tools. I will describe the rich history of the subject focusing on some recent results.

    • CMSA EVENT: 2017 Ding Shum Lecture
      5:00 pm-6:00 pm
      11/01/2019
      1 Oxford Street, Cambridge MA 02138

      Leslie Valiant will be giving the inaugural talk of the Ding Shum Lectures on Tuesday, October 10 at 5:00 pm in Science Center Hall D, Cambridge, MA.

      Learning as a Theory of Everything

      Abstract: We start from the hypothesis that all the information that resides in living organisms was initially acquired either through learning by an individual or through evolution. Then any unified theory of evolution and learning should be able to characterize the capabilities that humans and other living organisms can possess or acquire. Characterizing these capabilities would tell us about the nature of humans, and would also inform us about feasible targets for automation. With this purpose we review some background in the mathematical theory of learning. We go on to explain how Darwinian evolution can be formulated as a form of learning. We observe that our current mathematical understanding of learning is incomplete in certain important directions, and conclude by indicating one direction in which further progress would likely enable broader phenomena of intelligence and cognition to be realized than is possible at present.

       

    • CMSA EVENT: Jennifer Chayes Public Talk, 11-02-17
      5:00 pm-6:00 pm
      11/01/2019

      Jennifer Chayes (Microsoft Research) will be giving a public talk on November 02, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

      Title: Network Science: From the Online World to Cancer Genomics

      Abstract: Everywhere we turn these days, we find that networks can be used to describe relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage many human diseases. In this talk, I look quite generally at some of the models we are using to describe these networks, processes we are studying on the networks, algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. I’ll discuss in some detail particular applications to cancer genomics, applying network algorithms to suggest possible drug targets for certain kinds of cancer.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      05-11-2016 Random Matrix & Probability Theory Seminar
      5:00 pm
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
      5:02 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      06-01-2016 Random Matrix & Probability Theory Seminar
      5:03 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      06-08-2016 Random Matrix & Probability Theory Seminar
      5:04 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      07-12-2016 Chinese Economy Seminar
      5:06 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      07-19-2016 Chinese Economy Seminar
      5:07 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      08-02-2016 China Gazetteer Seminar
      5:08 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-12-2016 Mathematical Physics Seminar
      5:10 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-19-2016 Mathematical Physics Seminar
      5:11 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-21-2016 Random Matrix & Probability Theory Seminar
      5:13 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      Colloquium Colloquia & Seminar
      3/27/2019 Colloquium
      5:15 pm-6:15 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-23-2018 Math Physics
      5:15 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      Colloquium Colloquia & Seminar
      2/13/2019 Colloquium
      5:15 pm-6:15 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4-16-2018 Social Science Applications Forum
      5:16 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-20-2018 Social Science Applications Forum
      5:18 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-26-16 Mathematical Physics Seminar
      5:32 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-28-2016 Random Matrix & Probability Theory Seminar
      5:35 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      5:36 pm
      11/01/2019

      As part of the Program on Topological Aspects of Condensed Mattera weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

      DateSpeakerTitle/Abstract
      8/29/2018Zeng-Cheng GuTitle: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory

      Abstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.

      9/10/2018Dominic Else, MIT

      Video

      Title: Phases and topology in periodically driven (Floquet) systems

      Abstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.

      9/17/2018Adrian Po, MIT

      Video

      Title: A modern solution to the old problem of symmetries in band theory

      Abstract: There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants.

      9/24/2018Maxim MetlitskiTitle: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs

      Abstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.

      10/1/2018Cancelled
      10/9/2018

      Tuesday

      3:00-4:30pm

      Sagar VijayTitle: Fracton Phases of Matter

      Abstract:  Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped, point-like excitations (“fractons”) that are strictly immobile at zero temperature, and by degenerate ground-states that are locally indistinguishable.  Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions, and these states of matter are a gateway for exploring mechanisms for quantum information storage, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases, constructions of these states using well-studied two-dimensional topological phases, and a model in which the fracton excitations carry a protected internal degeneracy, which provides a natural generalization of non-Abelian anyons to three spatial dimensions.  I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.

      10/15/2018Ethan LakeTitle: A primer on higher symmetries

      Abstract: The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.

      10/22/2018

      Room G02

      Yin-Chen He, PerimeterTitle: Emergent QED3 and QCD3 in condensed matter system

      Abstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.

      10/29/2018Dominic Williamson, Yale

      Video

      Title: Symmetry and topological order in tensor networks

      Abstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.

      11/13/2018

      Tuesday

      3:00-4:30pm

      Jason Alicea, CaltechTitle: Time-crystalline topological superconductors
      11/19/2018X. G. Wen, MIT

      Video

      Title: A classification of 3+1D topological orders

      Abstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.

      12/3/2018

      *Room G02*

      Claudio Chamon, Boston UniversityTitle: Many-body scar states with topological properties in 1D, 2D, and 3D.

      Abstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies.

      12/10/2018

      Room G02

      Anders Sandvik, Boston University and Institute of Physics, CAS, BeijingTitle: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets

      Abstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.

      1/8/2019Lukasz Fidkowski, Univ. of Washington

      Video

      Title: Non-trivial quantum cellular automata in 3 dimensions

      Abstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom.  This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.

      3/18/2019Ari Turner, Technion

      Video

      Title:  Trapping Excitations at Phantasmagoric Wave Vectors

      Abstract:  This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this, and also introduce “finite fields”, which are the number systems one needs to define exponentials mod. 2.

      4/1/2019Yi-Zhuang You (UCSD)Title: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points

      Abstract: Noether’s theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s  theorem at the deconfined quantum critical point (DQCP), which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.

      4/8/2019Adam Nahum (Oxford)Title: Emergent statistical mechanics of entanglement in random unitary circuits

      Abstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.

      4/16/2019

      Lyman 425

      1:30pm

      Xie Chen (Calthech)Title: Foliated Fracton Order

      Abstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk, I will present a new framework, which we call the “foliated fracton order”, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models, but also points to the direction of search for interesting new features.

      4/24/2019

      10:30am

      Michael Freedman (Microsoft Station Q)

      Video

      Title: Quantum cellular automata in higher dimensions

      Abstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.

      4/26/2019

      10:30am

      Maissam Barkeshli (University of Maryland)

      Video

      Title: Relative anomalies in (2+1)D symmetry enriched topological states

      Abstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.

      5/3/2019Yuan-Ming Lu (Ohio State)Title: Spontaneous symmetry breaking from anyon condensation

      Abstract: In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

      5/9/2019

      10:30am

      Michael Zaletel (UC Berkeley)Title: Three-partite entanglement in CFTs and chiral topological orders

      Abstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement, multi-partite entanglement is far richer, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure, the “entanglement of purification,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders, and solicit the audience’s help in proving or disproving it.

      5/28/2019

      10:30am

      Masaki Oshikawa (U Tokyo)Title: Gauge invariance, polarization, and conductivity

       

      Abstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors, and also to general constraints on the electric conductivity.

      7/18/2019Eslam Khalaf (Harvard)

      Title: Dynamical correlations in anomalous disordered wires

      Abstract: In a (multichannel) disordered wire, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case, the classical dynamics are described by diffusion + drift, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.
      The problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.
      The mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.
    • Seminars
      Seminars Colloquia & Seminar
      Spacetime and Quantum Mechanics Seminar
      5:38 pm
      11/01/2019

      As part of the program on Spacetime and Quantum Mechanics, the CMSA will be hosting a weekly seminar on Thursdays at 2:30pm in room G10.

      DateSpeakerTitle/Abstract
      9/12/2019Pasha Pylyavskyy (University of Minnesota)Title: Vector-relation configurations and plabic graphs
      19/18/2019

      2:00pm

      G02

      Francis Brown (University of Oxford)Title: Amplitudes, Polylogs and Moduli Spaces
      9/19/2019Chuck Doran (University of Alberta)Title: Calabi-Yau geometry of the N-loop sunset Feynman integrals

      Abstract: I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals.

      Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli.

      These include: (1) an iterated fibration structure which allows one to “bootstrap” both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (“jump loci”) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via “creative telescoping”; and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties.

      Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev.

      9/26/2019Tomasz Taylor (Northeastern)Title: Celestial Amplitudes
      10/3/2019Simon Caron-Huot (McGill)Title: Poincare Duals of Feynman Integrals
      10/10/2019

      3:30pm

      Yutin Huang (National Taiwan University)Title: Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian
      10/15/2019

      Tuesday

      3:30pm

       

      Sergey Fomin (Univ. of Michigan)

       

      Title: “Morsifications and mutations” (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston). 
      10/18/2019

      Friday 

      G02

      Sebastian Franco (The City College of New York)Title: Graded quivers, generalized dimer models, and topic geometry
      10/31/2019Junjie Rao (Albert Einstein Institute)Title: All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
      11/1/2019

      SC 232

      1:30pm

      George Lusztig (MIT)Title: Total positivity in Springer fibres
      11/12/2019

      Tuesday

      G02

      3:30pm

       

      Pierpaolo Mastrolia (University of Padova)

      Title: Feynman Integrals and Intersection Theory
      11/14/2019

      G02

      Pierpaolo Mastrolia (University of Padova)Title: Feynman Integrals and Intersection Theory Pt. II
      11/21/2019Cristian Vergu (Niels Bohr Institute)Title: The Octagonal Alphabet
      11/26/2019Stephan Stieberger (IAS)Title: Strings on the Celestial Sphere
      12/4/2019Hadleigh Frost (Oxford)Title: BCJ numerators, $\mathcal{M}_{0,n}$, and ABHY

      Abstract: We relate the BCJ numerator Jacobi property to the classical fact that the top homology group of $\mathcal{M}_{0,n}$ is isomorphic to a component of the free Lie algebra. We describe ways to get BCJ numerators, and caution that the BCJ Jacobi property doesn’t imply the existence of what has been called a ‘kinematic algebra.’

       12/5/2019David Kosower (IAS)Title: From scattering amplitudes to classical observables
      12/10/2019Ramis Movassagh (MIT)Title: Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law

      Abstract: In recent years, there has been a surge of activities in proposing “exactly solvable” quantum spin chains with surprising high amount of ground state entanglement–exponentially more than the critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $\sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and ‘generic’ aspects of local spin chains.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-05-2016 Random Matrix & Probability Theory Seminar
      5:41 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/10/2018 Math-Physics Seminar
      5:41 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      5:42 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3/14/2019 Random Matrix and Probability Theory Seminar
      5:45 pm
      11/01/2019
    • Seminars
      5:48 pm
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
      5:52 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/17/2018 Math-Physics Seminar
      5:53 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/24/2018 Math-Physics Seminar
      5:55 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      5:56 pm
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
      5:59 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Workshop on Additive Combinatorics, Oct. 2-6, 2017
      6:00 pm-6:01 pm
      11/01/2019-10/06/2017

      The workshop on additive combinatorics will take place October 2-6, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      Additive combinatorics is a mathematical area bordering on number theory, discrete mathematics, harmonic analysis and ergodic theory. It has achieved a number of successes in pure mathematics in the last two decades in quite diverse directions, such as:

      • The first sensible bounds for Szemerédi’s theorem on progressions (Gowers);
      • Linear patterns in the primes (Green, Tao, Ziegler);
      • Construction of expanding sets in groups and expander graphs (Bourgain, Gamburd);
      • The Kakeya Problem in Euclidean harmonic analysis (Bourgain, Katz, Tao).

      Ideas and techniques from additive combinatorics have also had an impact in theoretical computer science, for example

      • Constructions of pseudorandom objects (eg. extractors and expanders);
      • Constructions of extremal objects (eg. BCH codes);
      • Property testing (eg. testing linearity);
      • Algebraic algorithms (eg. matrix multiplication).

      The main focus of this workshop will be to bring together researchers involved in additive combinatorics, with a particular inclination towards the links with theoretical computer science. Thus it is expected that a major focus will be additive combinatorics on the boolean cube (Z/2Z)^n , which is the object where the exchange of ideas between pure additive combinatorics and theoretical computer science is most fruitful. Another major focus will be the study of pseudorandom phenomena in additive combinatorics, which has been an important contributor to modern methods of generating provably good randomness through deterministic methods. Other likely topics of discussion include the status of major open problems (the polynomial Freiman-Ruzsa conjecture, inverse theorems for the Gowers norms with bounds, explicit correlation bounds against low degree polynomials) as well as the impact of new methods such as the introduction of algebraic techniques by Croot–Pach–Lev and Ellenberg–Gijswijt.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Ben GreenSwastik KoppartyRyan O’DonnellTamar Ziegler.

      Monday, October 2

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast 
      9:30-10:20amJacob FoxTower-type bounds for Roth’s theorem with popular differences

      Abstract: A famous theorem of Roth states that for any $\alpha > 0$ and $n$ sufficiently large in terms of $\alpha$, any subset of $\{1, \dots, n\}$ with density $\alpha$ contains a 3-term arithmetic progression. Green developed an arithmetic regularity lemma and used it to prove that not only is there one arithmetic progression, but in fact there is some integer $d > 0$ for which the density of 3-term arithmetic progressions with common difference $d$ is at least roughly what is expected in a random set with density $\alpha$. That is, for every $\epsilon > 0$, there is some $n(\epsilon)$ such that for all $n > n(\epsilon)$ and any subset $A$ of $\{1, \dots, n\}$ with density $\alpha$, there is some integer $d > 0$ for which the number of 3-term arithmetic progressions in $A$ with common difference $d$ is at least $(\alpha^3-\epsilon)n$. We prove that $n(\epsilon)$ grows as an exponential tower of 2’s of height on the order of $\log(1/\epsilon)$. We show that the same is true in any abelian group of odd order $n$. These results are the first applications of regularity lemmas for which the tower-type bounds are shown to be necessary.

      The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

      10:20-11:00amCoffee Break 
      11:00-11:50amYufei ZhaoTower-type bounds for Roth’s theorem with popular differences

      Abstract:  Continuation of first talk by Jacob Fox. The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

      12:00-1:30pmLunch 
      1:30-2:20pmJop BriëtLocally decodable codes and arithmetic progressions in random settings

      Abstract: This talk is about a common feature of special types of error correcting codes, so-called locally decodable codes (LDCs), and two problems on arithmetic progressions in random settings, random differences in Szemerédi’s theorem and upper tails for arithmetic progressions in a random set in particular. It turns out that all three can be studied in terms of the Gaussian width of a set of vectors given by a collection of certain polynomials. Using a matrix version of the Khintchine inequality and a lemma that turns such polynomials into matrices, we give an alternative proof for the best-known lower bounds on LDCs and improved versions of prior results due to Frantzikinakis et al. and Bhattacharya et al. on arithmetic progressions in the aforementioned random settings.

      Joint work with Sivakanth Gopi

      2:20-3:00pmCoffee Break 
      3:00-3:50pmFernando Shao

      Large deviations for arithmetic progressions

      Abstract: We determine the asymptotics of the log-probability that the number of k-term arithmetic progressions in a random subset of integers exceeds its expectation by a constant factor. This is the arithmetic analog of subgraph counts in a random graph. I will highlight some open problems in additive combinatorics that we encountered in our work, namely concerning the “complexity” of the dual functions of AP-counts.

      4:00-6:00pmWelcome Reception

      Tuesday, October 3

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amEmanuele ViolaInterleaved group products

      Authors: Timothy Gowers and Emanuele Viola

      Abstract: Let G be the special linear group SL(2,q). We show that if (a1,a2) and (b1,b2) are sampled uniformly from large subsets A and B of G^2 then their interleaved product a1 b1 a2 b2 is nearly uniform over G. This extends a result of Gowers (2008) which corresponds to the independent case where A and B are product sets. We obtain a number of other results. For example, we show that if X is a probability distribution on G^m such that any two coordinates are uniform in G^2, then a pointwise product of s independent copies of X is nearly uniform in G^m, where s depends on m only. Similar statements can be made for other groups as well.

      These results have applications in computer science, which is the area where they were first sought by Miles and Viola (2013).

      10:20-11:00amCoffee Break
      11:00-11:50amVsevolod LevOn Isoperimetric Stability

      Abstract: We show that a non-empty subset of an abelian group with a small edge boundary must be large; in particular, if $A$ and $S$ are finite, non-empty subsets of an abelian group such that $S$ is independent, and the edge boundary of $A$ with respect to $S$ does not exceed $(1-c)|S||A|$ with a real $c\in(0,1]$, then $|A|\ge4^{(1-1/d)c|S|}$, where $d$ is the smallest order of an element of $S$. Here the constant $4$ is best possible.

      As a corollary, we derive an upper bound for the size of the largest independent subset of the set of popular differences of a finite subset of an abelian group. For groups of exponent $2$ and $3$, our bound translates into a sharp estimate for the additive  dimension of the popular difference set.

      We also prove, as an auxiliary result, the following estimate of possible independent interest: if $A\subseteq{\mathbb Z}^n$ is a finite, non-empty downset, then, denoting by $w(z)$ the number of non-zero components of the vector $z\in\mathbb{Z}^n$, we have   $$ \frac1{|A|} \sum_{a\in A} w(a) \le \frac12\, \log_2 |A|. $$

      12:00-1:30pmLunch
      1:30-2:20pmElena GrigorescuNP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem

      Abstract: I will discuss the complexity of decoding Reed-Solomon codes, and some results establishing NP-hardness for asymptotically smaller decoding radii than the maximum likelihood decoding radius. These results follow from the study of a generalization of the classical Subset Sum problem to higher moments, which may be of independent interest. I will further discuss a connection with the Prouhet-Tarry-Escott problem studied in Number Theory, which turns out to capture a main barrier in extending our techniques to smaller radii.

      Joint work with Venkata Gandikota and Badih Ghazi.

      2:20-3:00pmCoffee Break
      3:00-3:50pmSean PrendivillePartition regularity of certain non-linear Diophantine equations.

      Abstract:  We survey some results in additive Ramsey theory which remain valid when variables are restricted to sparse sets of arithmetic interest, in particular the partition regularity of a class of non-linear Diophantine equations in many variables.

      Wednesday, October 4

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast 
      9:30-10:20amOlof SisaskBounds on capsets via properties of spectra

      Abstract: A capset in F_3^n is a subset A containing no three distinct elements x, y, z satisfying x+z=2y. Determining how large capsets can be has been a longstanding problem in additive combinatorics, particularly motivated by the corresponding question for subsets of {1,2,…,N}. While the problem in the former setting has seen spectacular progress recently through the polynomial method of Croot–Lev–Pach and Ellenberg–Gijswijt, such progress has not been forthcoming in the setting of the integers. Motivated by an attempt to make progress in this setting, we shall revisit the approach to bounding the sizes of capsets using Fourier analysis, and in particular the properties of large spectra. This will be a two part talk, in which many of the ideas will be outlined in the first talk, modulo the proof of a structural result for sets with large additive energy. This structural result will be discussed in the second talk, by Thomas Bloom, together with ideas on how one might hope to achieve Behrend-style bounds using this method.

      Joint work with Thomas Bloom.

      10:20-11:00amCoffee Break 
      11:00-11:50amThomas BloomBounds on capsets via properties of spectra

      This is a continuation of the previous talk by Olof Sisask.

      12:00-1:30pmLunch 
      1:30-2:20pmHamed HatamiPolynomial method and graph bootstrap percolation

      Abstract: We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori and multidimensional grids (in particular hypercubes). The former answers a question of Morrison and Noel, and the latter provides an alternative and simpler proof for one of their main results. This is based on a joint work with Lianna Hambardzumyan and Yingjie Qian.

      2:20-3:00pmCoffee Break
      3:00-3:50pmArnab BhattacharyyaAlgorithmic Polynomial Decomposition

      Abstract: Fix a prime p. Given a positive integer k, a vector of positive integers D = (D_1, …, D_k) and a function G: F_p^k → F_p, we say a function P: F_p^n → F_p admits a (k, D, G)-decomposition if there exist polynomials P_1, …, P_k: F_p^n -> F_p with each deg(P_i) <= D_i such that for all x in F_p^n, P(x) = G(P_1(x), …, P_k(x)). For instance, an n-variate polynomial of total degree d factors nontrivially exactly when it has a (2, (d-1, d-1), prod)-decomposition where prod(a,b) = ab.

      When show that for any fixed k, D, G, and fixed bound d, we can decide whether a given polynomial P(x_1, …, x_n) of degree d admits a (k,D,G)-decomposition and if so, find a witnessing decomposition, in poly(n) time. Our approach is based on higher-order Fourier analysis. We will also discuss improved analyses and algorithms for special classes of decompositions.

      Joint work with Pooya Hatami, Chetan Gupta and Madhur Tulsiani.

      Thursday, October 5

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amMadhur TulsianiHigher-order Fourier analysis and approximate decoding of Reed-Muller codes

       Abstract: Decomposition theorems proved by Gowers and Wolf provide an appropriate notion of “Fourier transform” for higher-order Fourier analysis. I will discuss some questions and techniques that arise from trying to develop polynomial time algorithms for computing these decompositions.

      I will discuss constructive proofs of these decompositions based on boosting, which reduce the problem of computing these decompositions to a certain kind of approximate decoding problem for codes. I will also discuss some earlier and recent works on this decoding problem.

      Based on joint works with Arnab Bhattacharyya, Eli Ben-Sasson, Pooya Hatami, Noga Ron-Zewi and Julia Wolf.

      10:20-11:00amCoffee Break
      11:00-11:50amJulia WolfStable arithmetic regularity

      The arithmetic regularity lemma in the finite-field model, proved by Green in 2005, states that given a subset A of a finite-dimensional vector space over a prime field, there exists a subspace H of bounded codimension such that A is Fourier-uniform with respect to almost all cosets of H. It is known that in general, the growth of the codimension of H is required to be of tower type depending on the degree of uniformity, and that one must allow for a small number of non-uniform cosets.

      Our main result is that, under a natural model-theoretic assumption of stability, the tower-type bound and non-uniform cosets in the arithmetic regularity lemma are not necessary.  Specifically, we prove an arithmetic regularity lemma for k-stable subsets in which the bound on the codimension of the subspace is a polynomial (depending on k) in the degree of uniformity, and in which there are no non-uniform cosets.

      This is joint work with Caroline Terry.

      12:00-1:30pmLunch 
      1:30-2:20pmWill Sawin

      Constructions of Additive Matchings

      Abstract: I will explain my work, with Robert Kleinberg and David Speyer, constructing large tri-colored sum-free sets in vector spaces over finite fields, and how it shows that some additive combinatorics problems over finite fields are harder than corresponding problems over the integers. 

      2:20-3:00pmCoffee Break
      3:00-3:50pmMei-Chu ChangArithmetic progressions in multiplicative groups of finite fields

      Abstract:   Let G be a multiplicative subgroup of the prime field F_p of size |G|> p^{1-\kappa} and r an arbitrarily fixed positive integer. Assuming \kappa=\kappa(r)>0 and p large enough, it is shown that any proportional subset A of G contains non-trivial arithmetic progressions of length r.

      Friday, October 6

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amAsaf FerberOn a resilience version of the Littlewood-Offord problem

      Abstract:  In this talk we consider a resilience version of the classical Littlewood-Offord problem. That is, consider the sum X=a_1x_1+…a_nx_n, where the a_i-s are non-zero reals and x_i-s are i.i.d. random variables with     (x_1=1)= P(x_1=-1)=1/2. Motivated by some problems from random matrices, we consider the question: how many of the x_i-s  can we typically allow an adversary to change without making X=0? We solve this problem up to a constant factor and present a few interesting open problems.

      Joint with: Afonso Bandeira (NYU) and Matthew Kwan (ETH, Zurich).

      10:20-11:00amCoffee Break
      11:00-11:50amKaave HosseiniProtocols for XOR functions and Entropy decrement

      Abstract: Let f:F_2^n –> {0,1} be a function and suppose the matrix M defined by M(x,y) = f(x+y) is partitioned into k monochromatic rectangles.  We show that F_2^n can be partitioned into affine subspaces of co-dimension polylog(k) such that f is constant on each subspace. In other words, up to polynomial factors, deterministic communication complexity and parity decision tree complexity are equivalent.

      This relies on a novel technique of entropy decrement combined with Sanders’ Bogolyubov-Ruzsa lemma.

      Joint work with Hamed Hatami and Shachar Lovett

      12:00-1:30pmLunch
      1:30-2:20pmGuy Kindler

      From the Grassmann graph to Two-to-Two games

      Abstract: In this work we show a relation between the structure of the so called Grassmann graph over Z_2 and the Two-to-Two conjecture in computational complexity. Specifically, we present a structural conjecture concerning the Grassmann graph (together with an observation by Barak et. al., one can view this as a conjecture about the structure of non-expanding sets in that graph) which turns out to imply the Two-to-Two conjecture.

      The latter conjecture its the lesser-known and weaker sibling of the Unique-Games conjecture [Khot02], which states that unique games (a.k.a. one-to-one games) are hard to approximate. Indeed, if the Grassmann-Graph conjecture its true, it would also rule out some attempts to refute the Unique-Games conjecture, as these attempts provide potentially efficient algorithms to solve unique games, that would actually also solve two-to-two games if they work at all.

      These new connections between the structural properties of the Grassmann graph and complexity theoretic conjectures highlight the Grassmann graph as an interesting and worthy object of study. We may indicate some initial results towards analyzing its structure.

      This is joint work with Irit Dinur, Subhash Khot, Dror Minzer, and Muli Safra.

    • CMSA EVENT: Current Developments In Mathematics 2018
      6:00 pm-5:00 pm
      11/01/2019-11/17/2018
      CDM2018

      Current Developments in Mathematics 2018 Conference.

      Friday, Nov. 16, 2018 2:15 pm – 6:00 pm

      Saturday, Nov. 17, 2018  9:00 am – 5:00 pm

      Harvard University Science Center, Hall B

      Visit the conference page here 

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/01/2018 Math-Physics Seminar
      6:01 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Fluid turbulence and Singularities of the Euler/ Navier Stokes equations
      6:02 pm
      11/01/2019-03/15/2018
      Fluid turbulence

      The Workshop on Fluid turbulence and Singularities of the Euler/ Navier Stokes equations will take place on March 13-15, 2019. This is the first of two workshop organized by Michael Brenner, Shmuel Rubinstein, and Tom Hou. The second, Machine Learning for Multiscale Model Reduction, will take place on March 27-29, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

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

      List of registrants

      Speakers: 

    • General Relativity Seminar
      6:03 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/08/2018 Math-Physics Seminar
      6:04 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      6:05 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Blockchain Conference
      6:05 pm
      11/01/2019-01/25/2018
      Blockchain

      On January 24-25, 2019 the Center of Mathematical Sciences will be hosting a conference on distributed-ledger (blockchain) technology. The conference is intended to cover a broad range of topics, from abstract mathematical aspects (cryptography, game theory, graph theory, theoretical computer science) to concrete applications (in accounting, government, economics, finance, management, medicine). The talks will take place in Science Center, Hall D.

      https://youtu.be/FyKCCutxMYo

      List of registrants

      Photos

      Speakers: 

    • Special Seminar
      6:06 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Workshop on Algebraic Methods in Combinatorics
      6:07 pm
      11/01/2019-11/17/2017

      The workshop on Algebraic Methods in Combinatorics will take place November 13-17, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      The main focus of the workshop is the application of algebraic method to study problems in combinatorics.  In recent years there has been a large number of results in which the use of algebraic technique has resulted in significant improvements to long standing open problems. Such problems include the finite field Kakeya problem, the distinct distance problem of Erdos and, more recently, the cap-set problem. The workshop will include talks on all of the above mentioned problem as well as on recent development in related areas combining combinatorics and algebra.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Zeev DvirLarry Guth, and Shubhangi Saraf.

      Click here for a list of registrants.

      Monday, Nov. 13

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Jozsef Solymosi

       

      On the unit distance problem

      Abstract: Erdos’ Unit Distances conjecture states that the maximum number of unit distances determined by n points in the plane is almost linear, it is O(n^{1+c}) where c goes to zero as n goes to infinity. In this talk I will survey the relevant results and propose some questions which would imply that the maximum number of unit distances is o(n^{4/3}). 

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

       

      Orit RazIntersection of linear subspaces in R^d and instances of the PIT problem 

      Abstract: In the talk I will tell about a new deterministic, strongly polynomial time algorithm which can be viewed in two ways. The first is as solving a derandomization problem, providing a deterministic algorithm to a new special case of the PIT (Polynomial Identity Testing) problem. The second is as computing the dimension of the span of a collection of flats in high dimensional space. The talk is based on a joint work with Avi Wigderson.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Andrew Hoon Suk

      Ramsey numbers: combinatorial and geometric

      Abstract:  In this talk, I will discuss several results on determining the tower growth rate of Ramsey numbers arising in combinatorics and in geometry.  These results are joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Janos Pach, and Benny Sudakov.

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Josh Zahl

      Cutting curves into segments and incidence geometry

      4:00-6:00pmWelcome Reception

      Tuesday, Nov. 14

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Péter Pál Pach

      Polynomials, rank and cap sets

      AbstractIn this talk we will look at a new variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like $\mathbb{Z}_4^n$ and $\mathbb{F}_q^n$ are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets and mention further applications of the method.

      10:30-11:00amCoffee Break
      11:00-12:00pmJordan Ellenberg

      The Degeneration Method

      Abstract:  In algebraic geometry, a very popular way to study (nice, innocent, nonsingular) varieties is to degenerate them to (weird-looking, badly singular, nonreduced) varieties (which are actually not even varieties but schemes.)  I will talk about some results in combinatorics using this approach (joint with Daniel Erman) and some ideas for future applications of the method.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Larry GuthThe polynomial method in Fourier analysis

      Abstract: This will be a survey talk about how the polynomial method helps to understand problems in Fourier analysis.  We will review some applications of the polynomial method to problems in combinatorial geometry.  Then we’ll discuss some problems in Fourier analysis, explain the analogy with combinatorial problems, and discuss how to adapt the polynomial method to the Fourier analysis setting.

       

      2:30-3:00pm

      Coffee Break
      3:00-4:00pmOpen Problem

      Wednesday, Nov. 15

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

       

      Avi Wigderson

      The “rank method” in arithmetic complexity: Lower bounds and barriers to lower bounds

      Abstract: Why is it so hard to find a hard function? No one has a clue! In despair, we turn to excuses called barriers. A barrier is a collection of lower bound techniques, encompassing as much as possible from those in use, together with a  proof that these techniques cannot prove any lower bound better than the state-of-art (which is often pathetic, and always very far from what we expect for complexity of random functions).

      In the setting of  Boolean computation of Boolean functions (where P vs. NP is the central open problem),  there are several famous barriers which provide satisfactory excuses, and point to directions in which techniques may be strengthened.

      In the setting of Arithmetic computation of polynomials and tensors (where  VP vs. VNP is the central open problem) we have no satisfactory barriers, despite some recent interesting  attempts.

      This talk will describe a new barrier for the Rank Method in arithmetic complexity, which encompass most lower bounds in this field. It also encompass most lower bounds on tensor rank in algebraic geometry (where the the rank method is called Flattening).

      I will describe the rank method, explain how it is used to prove lower bounds, and then explain its limits via the new barrier result. As an example, it shows that while the best lower bound on the tensor rank of any explicit 3-dimensional tensor of side n (which is achieved by a rank method) is 2n, no rank method can prove a lower bound which exceeds 8n

      (despite the fact that a random such tensor has rank quadratic in n).

      No special background knowledge is assumed. The audience is expected to come up with new lower bounds, or else, with new excuses for their absence.

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Venkat Guruswami

      Subspace evasion, list decoding, and dimension expanders

       Abstract: A subspace design is a collection of subspaces of F^n (F = finite field) most of which are disjoint from every low-dimensional subspace of F^n. This notion was put forth in the context of algebraic list decoding where it enabled the construction of optimal redundancy list-decodable codes over small alphabets as well as for error-correction in the rank-metric. Explicit subspace designs with near-optimal parameters have been constructed over large fields based on polynomials with structured roots. (Over small fields, a construction via cyclotomic function fields with slightly worse parameters is known.) Both the analysis of the list decoding algorithm as well as the subspace designs crucially rely on the *polynomial method*.

      Subspace designs have since enabled progress on linear-algebraic analogs of Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In particular, they yield an explicit construction of constant-degree dimension expanders over large fields. While constructions of such dimension expanders are known over any field, they are based on a reduction to a highly non-trivial form of vertex expanders called monotone expanders. In contrast, the subspace design approach is simpler and works entirely within the linear-algebraic realm. Further, in recent (ongoing) work, their combination with rank-metric codes yields dimension expanders with expansion proportional to the degree.

      This talk will survey these developments revolving around subspace designs, their motivation, construction, analysis, and connections.

      (Based on several joint works whose co-authors include Chaoping Xing, Swastik Kopparty, Michael Forbes, Nicolas Resch, and Chen Yuan.)

      12:00-1:30pmLunch
      1:30-2:30pm

       

      David Conlon

      Finite reflection groups and graph norms

      Abstract: For any given graph $H$, we may define a natural corresponding functional $\|.\|_H$. We then say that $H$ is norming if $\|.\|_H$ is a semi-norm. A similar notion $\|.\|_{r(H)}$ is defined by $\| f \|_{r(H)} := \| | f | \|_H$ and $H$ is said to be weakly norming if $\|.\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. Using results from the theory of finite reflection groups, we identify a much larger class of weakly norming graphs. This result includes all previous examples of weakly norming graphs and adds many more. We also discuss several applications of our results. In particular, we define and compare a number of generalisations of Gowers’ octahedral norms and we prove some new instances of Sidorenko’s conjecture. Joint work with Joonkyung Lee.

       

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Laszlo Miklós Lovasz

      Removal lemmas for triangles and k-cycles.

      Abstract: Let p be a fixed prime. A k-cycle in F_p^n is an ordered k-tuple of points that sum to zero; we also call a 3-cycle a triangle. Let N=p^n, (the size of F_p^n). Green proved an arithmetic removal lemma which says that for every k, epsilon>0 and prime p, there is a delta>0 such that if we have a collection of k sets in F_p^n, and the number of k-cycles in their cross product is at most a delta fraction of all possible k-cycles in F_p^n, then we can delete epsilon times N elements from the sets and remove all k-cycles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in particular, asked whether a polynomial bound holds. Despite considerable attention, prior to our work, the best known bound for any k, due to Fox, showed that 1/delta can be taken to be an exponential tower of twos of height logarithmic in 1/epsilon (for a fixed k).

      In this talk, we will discuss recent work on Green’s problem. For triangles, we prove an essentially tight bound for Green’s arithmetic triangle removal lemma in F_p^n, using the recent breakthroughs with the polynomial method. For k-cycles, we also prove a polynomial bound, however, the question of the optimal exponent is still open.

      The triangle case is joint work with Jacob Fox, and the k-cycle case with Jacob Fox and Lisa Sauermann.

      Thursday, Nov. 16

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Janos PachLet’s talk about multiple crossings

      Abstract: Let k>1 be a fixed integer. It is conjectured that any graph on n vertices that can be drawn in the plane without k pairwise crossing edges has O(n) edges. Two edges of a hypergraph cross each other if neither of them contains the other, they have a nonempty intersection, and their union is not the whole vertex set. It is conjectured that any hypergraph on n vertices that contains no k pairwise crossing edges has at most O(n) edges. We discuss the relationship between the above conjectures and explain some partial answers, including a recent result of Kupavskii, Tomon, and the speaker, improving a 40 years old bound of Lomonosov.

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Misha Rudnev

      Few products, many sums

      Abstract: This is what I like calling “weak Erd\H os-Szemer\’edi conjecture”, still wide open over the reals and in positive characteristic. The talk will focus on some recent progress, largely based on the ideas of I. D. Shkredov over the past 5-6 years of how to use linear algebra to get the best out of the Szemer\’edi-Trotter theorem for its sum-product applications. One of the new results is strengthening (modulo the log term hidden in the $\lesssim$ symbol) the textbook Elekes inequality

      $$

      |A|^{10} \ll |A-A|^4|AA|^4

      $$

      to

      $$|A|^{10}\lesssim |A-A|^3|AA|^5.$$

      The other is the bound 

      $$E(H) \lesssim |H|^{2+\frac{9}{20}}$$ for additive energy of sufficiently small multiplicative subgroups in $\mathbb F_p$.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Adam Sheffer

      Geometric Energies: Between Discrete Geometry and Additive Combinatorics

      Abstract: We will discuss the rise of geometric variants of the concept of Additive energy. In recent years such variants are becoming more common in the study of Discrete Geometry problems. We will survey this development and then focus on a recent work with Cosmin Pohoata. This work studies geometric variants of additive higher moment energies, and uses those to derive new bounds for several problems in Discrete Geometry.  

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Boris Bukh

      Ranks of matrices with few distinct entries

      Abstract: Many applications of linear algebra method to combinatorics rely on the bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these application. I will also present a classification of sets L for which no low-rank matrix with entries in L exists.

      Friday, Nov. 17

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Benny Sudakov

      Submodular minimization and set-systems with restricted intersections

      AbstractSubmodular function minimization is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint types under which it remains efficiently solvable. The arguably most relevant non-trivial constraint class for which polynomial algorithms are known are parity constraints, i.e., optimizing submodular function only over sets of odd (or even) cardinality. Parity constraints capture classical combinatorial optimization problems like the odd-cut problem, and they are a key tool in a recent technique to efficiently solve integer programs with a constraint matrix whose subdeter-minants are bounded by two in absolute value.

      We show that efficient submodular function minimization is possible even for a significantly larger class than parity constraints, i.e., over all sets (of any given lattice) of cardinality r mod m, as long as m is a constant prime power. To obtain our results, we combine tools from Combinatorial Optimization, Combinatorics, and Number Theory. In particular, we establish an interesting connection between the correctness of a natural algorithm, and the non-existence of set systems with specific intersection properties.

      Joint work with M. Nagele and R. Zenklusen

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Robert Kleinberg 

      Explicit sum-of-squares lower bounds via the polynomial method

      AbstractThe sum-of-squares (a.k.a. Positivstellensatz) proof system is a powerful method for refuting systems of multivariate polynomial inequalities, i.e. proving that they have no solutions. These refutations themselves involve sum-of-squares (sos) polynomials, and while any unsatisfiable system of inequalities has a sum-of-squares refutation, the sos polynomials involved might have arbitrarily high degree. However, if a system admits a refutation where all polynomials involved have degree at most d, then the refutation can be found by an algorithm with running time polynomial in N^d, where N is the combined number of variables and inequalities in the system.

      Low-degree sum-of-squares refutations appear throughout mathematics. For example, the above proof search algorithm captures as a special case many a priori unrelated algorithms from theoretical computer science; one example is Goemans and Williamson’s algorithm to approximate the maximum cut in a graph. Specialized to extremal graph theory, they become equivalent to flag algebras. They have also seen practical use in robotics and optimal control.

      Therefore, it is of interest to identify “hard” systems of low-degree polynomial inequalities that have no solutions but also have no low-degree sum-of-squares refutations. Until recently, the only known examples were either not explicit (i.e., known to exist by non-constructive means such as the probabilistic method) or not robust (i.e., a system is constructed which is not refutable by degree d sos polynomials, but becomes refutable when perturbed by an amount tending to zero with d). We present a new family of instances derived from the cap-set problem, and we show a super-constant lower bound on the degree of its sum-of-squares refutations. Our instances are both explicit and robust.

      This is joint work with Sam Hopkins.

      12:00-1:30pmLunch

       

    • Special Seminar
      6:10 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      6:11 pm-6:12 pm
      11/01/2019-10/25/2016

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/10/2018 RM & PT Seminar
      6:11 pm
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
      6:12 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-03-16 Mathematical Physics Seminar
      6:13 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/15/2018 Topology Seminar
      6:14 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/15/2018 Math Physics Seminar
      6:15 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-12-2016 Random Matrix & Probability Theory Seminar
      6:16 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      6:17 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-24-2016 Random Matrix & Probability Theory Seminar
      6:18 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/30/2018 RM & PT Seminar
      6:19 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      6:19 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/26/2018 Social Science Applications Forum
      6:20 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-19-2016 Random Matrix & Probability Theory Seminar
      6:22 pm
      11/01/2019

      No additional detail for this event.

    • Member Seminar
      6:24 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/22/2018 Mathematical Physics Seminar
      6:24 pm
      11/01/2019
    • Member Seminar
      6:26 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-26-2016 Random Matrix & Probability Theory Seminar
      6:27 pm
      11/01/2019

      No additional detail for this event.

    • Member Seminar
      6:29 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-24-16 Mathematical Physics Seminar
      6:30 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      6:32 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      6:34 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-01-2016 Social Sciences Applications Forum
      6:36 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-19-2016 Random Matrix & Probability Theory Seminar
      6:37 pm
      11/01/2019

      No additional detail for this event.

    • Member Seminar
      6:40 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-17-16 Mathematical Physics Seminar
      6:41 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-26-2016 Random Matrix & Probability Theory Seminar
      6:46 pm
      11/01/2019

      No additional detail for this event.

    • Member Seminar
      6:52 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-24-16 Mathematical Physics Seminar
      6:53 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      6:54 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      6:59 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-01-2016 Social Sciences Applications Forum
      7:00 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      7:03 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-31-16 Mathematical Physics Seminar
      7:05 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12/10/2018 Mathematical Physics Seminar
      8:42 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      12/10/2018 Topology Seminar
      8:43 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      12/12/2018 Hodge Seminar
      8:43 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      8:45 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      1/16/2019 Hodge Seminar
      8:46 pm
      11/01/2019

      No additional detail for this event.

    • Fluid Dynamics Seminar
      Fluid Dynamics Seminar
      4/3/2019 Fluid Dynamics Seminar
      8:54 pm
      11/01/2019

      No additional detail for this event.

    • Program
      9:39 pm
      11/01/2019-12/18/2014

      arge random matrices provide some of the simplest models for large, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a rigorous understanding of universality in the case of orthogonal, Hermitian, or symplectic matrices with independent entries, resolving a conjecture of Wigner-Dyson-Mehta dating back 50 years. These new developments have exploited techniques from a wide range of mathematical areas in addition to probability, including combinatorics, partial differential equations, and hydrodynamic limits. It is hoped that these new techniques will be useful in the analysis of universal behaviour in matrix ensembles with more complicated structure such as random regular graph models, or 2D matrix ensembles, as well as more physically relevant systems such as band matrices and random Schroedinger-type Hamiltonians. For some of these models, results in the direction of universality have already been obtained.

      Here is a partial list of the mathematicians who are participating in this program

    • Program
      9:44 pm
      11/01/2019-12/28/2013

      During Academic year 2018-19, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines.

      As part of the Program, the CMSA will be hosting two workshops:

      .

      Additionally, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

      Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program
      NameTentative Visiting Dates

      Jason Alicea

      11/12/2018-11/16/2018
      Maissam Barkeshli4/22/2019 – 4/26/2019
      Xie Chen4/15-17/2019 4/19-21/2019 4/24-30/2019

      Lukasz Fidkowski

      1/7/2019-1/11/2019

      Zhengcheng Gu

      8/15/2018-8/30/2018 & 5/9/2019-5/19/2019

      Yin Chen He

      10/14/2018-10/27/2018
      Anton Kapustin8/26/2018-8/30/2018 & 3/28/2019-4/5/2019

      Michael Levin

      3/11/2019-3/15/2019
      Yuan-Ming Lu4/29/2019-6/01/2019

      Adam Nahum

      4/2/2019- 4/19/2019

      Masaki Oshikawa

      4/22/2019-5/22/2019
      Chong Wang 10/22/2018-11/16/2018

      Juven Wang

      4/1/2019-4/16/2019
      Cenke Xu 8/26/2018-10/1/2018

      Yi-Zhuang You

      4/1/2019-4/19/2019

      Mike Zaletel

      5/1/2019-5/10/2019
    • Program
      9:45 pm-9:46 pm
      11/01/2019-12/31/2010

      During Academic year 2018-19, the CMSA will be hosting a Program on Mathematical Biology.

      Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape.

      In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. And in mathematics and computation, there has been a revolution in terms of posing and solving problems at the intersection of computational geometry, statistics and inference.  So, how far are we from realizing a descriptive, predictive and controllable theory of biological shape?

      In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems

      The CMSA will be hosting three workshops as part of this program. The Workshop on Morphometrics, Morphogenesis and Mathematics will take place on October 22-26. 

      A workshop on Morphogenesis: Geometry and Physics will take place on December 3-6, 2018.

      A workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

    • Program
      9:48 pm
      11/01/2019-12/31/2010

      Recent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during fall 2019, with between 20-30 participants. They will also invite 10-20 longer-term visitors throughout the semester. Additionally, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10.

      Organizers:

      .

      Workshops:

       

      Here is a partial list of the mathematicians and physicists who have indicated that they will attend part or all of this special program as a visitor:

    • Program
      9:49 pm
      11/01/2019-12/23/2010

      The Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry, Symplectic geometry, Arithmetic geometry, Quantum topology and mathematical aspects of high energy physics, specially string theory with the goal of proving the homological mirror symmetry conjecture (HMS) in full generality and explore its applications. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model). We are happy to announce that the Simons Foundation has agreed to renew funding for the HMS collaboration program for three additional years.

      A brief induction of the Brandeis-Harvard CMSA HMS/SYZ research agenda and team members are as follow:


      Directors:


      Shing-Tung Yau (Harvard University)

      Born in Canton, China, in 1949, S.-T. Yau grew up in Hong Kong, and studied in the Chinese University of Hong Kong from 1966 to 1969. He did his PhD at UC Berkeley from 1969 to 1971, as a student of S.S. Chern. He spent a year as a postdoc at the Institute for Advanced Study in Princeton, and a year as assistant professor at SUNY at Stony Brook. He joined the faculty at Stanford in 1973. On a Sloan Fellowship, he spent a semester at the Courant Institute in 1975. He visited UCLA the following year, and was offered a professorship at UC Berkeley in 1977. He was there for a year, before returning to Stanford. He was a plenary speaker at the 1978 ICM in Helsinki. The following year, he became a faculty member at the IAS in Princeton. He moved to UCSD in 1984. Yau came to Harvard in 1987, and was appointed the Higgins Professor of Mathematics in 1997. He has been at Harvard ever since. Yau has received numerous prestigious awards and honors throughout his career. He was named a California Scientist of the Year in 1979. In 1981, he received a Oswald Veblen Prize in Geometry and a John J. Carty Award for the Advancement of Science, and was elected a member of the US National Academy of Sciences. In 1982, he received a Fields Medal for “his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex MongeAmpre equations”. He was named Science Digest, America’s 100 Brightest Scientists under 40, in 1984. In 1991, he received a Humboldt Research Award from the Alexander von Humboldt Foundation in Germany. He was awarded a Crafoord Prize in 1994, a US National Medal of Science in 1997, and a China International Scientific and Technological Cooperation Award, for “his outstanding contribution to PRC in aspects of making progress in sciences and technology, training researchers” in 2003. In 2010, he received a Wolf Prize in Mathematics, for “his work in geometric analysis and mathematical physics”. Yau has also received a number of research fellowships, which include a Sloan Fellowship in 1975-1976, a Guggenheim Fellowship in 1982, and a MacArthur Fellowship in 1984-1985. Yau’s research interests include differential and algebraic geometry, topology, and mathematical physics. As a graduate student, he started to work on geometry of manifolds with negative curvature. He later became interested in developing the subject of geometric analysis, and applying the theory of nonlinear partial differential equations to solve problems in geometry, topology, and physics. His work in this direction include constructions of minimal submanifolds, harmonic maps, and canonical metrics on manifolds. The most notable, and probably the most influential of this, was his solution of the Calabi conjecture on Ricci flat metrics, and the existence of Kahler-Einstein metrics. He has also succeeded in applying his theory to solve a number of outstanding conjectures in algebraic geometry, including Chern number inequalities, and the rigidity of complex structures of complex projective spaces. Yau’s solution to the Calabi conjecture has been remarkably influential in mathematical physics over the last 30 years, through the creation of the theory of Calabi-Yau manifolds, a theory central to mirror symmetry. He and a team of outstanding mathematicians trained by him, have developed many important tools and concepts in CY geometry and mirror symmetry, which have led to significant progress in deformation theory, and on outstanding problems in enumerative geometry. Lian, Yau and his postdocs have developed a systematic approach to study and compute period integrals of CY and general type manifolds. Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula of Candelas et al for worldsheet instantons on the quintic threefold. In the course of understanding mirror symmetry, Strominger, Yau, and Zaslow proposed a new geometric construction of mirror symmetry, now known as the SYZ construction. This has inspired a rapid development in CY geometry over the last two decades. In addition to CY geometry and mirror symmetry, Yau has done influential work on nonlinear partial differential equations, generalized geometry, Kahler geometry, and general relativity. His proof of positive mass conjecture is a widely regarded as a cornerstone in the classical theory of general relativity. In addition to publishing well over 350 research papers, Yau has trained more than 60 PhD students in a broad range of fields, and mentored dozens of postdoctoral fellows over the last 40 years.


      Professor Bong Lian (Brandeis University)

      BongBorn in Malaysia in 1962, Bong Lian completed his PhD in physics at Yale University under the direction of G. Zuckerman in 1991. He joined the permanent faculty at Brandeis University in 1995, and has remained there since. Between 1995 and 2013, he had had visiting research positions at numerous places, including the National University of Taiwan, Harvard University, and Tsinghua University. Lian received a J.S. Guggenheim Fellowship in 2003. He was awarded a Chern Prize at the ICCM in Taipei in 2013, for his “influential and fundamental contributions in mathematical physics, in particular in the theory of vertex algebras and mirror symmetry.” He has also been co-Director, since 2014, of the Tsinghua Mathcamp, a summer outreach program launched by him and Yau for mathematically talented teenagers in China. Since 2008, Lian has been the President of the International Science Foundation of Cambridge, a non-profit whose stated mission is “to provide financial and logistical support to scholars and universities, to promote basic research and education in mathematical sciences, especially in the Far East.” Over the last 20 years, he has mentored a number of postdocs and PhD students. His research has been supported by an NSF Focused Research Grant since 2009. Published in well over 60 papers over 25 years, Lian’s mathematical work lies in the interface between representation theory, Calabi-Yau geometry, and string theory. Beginning in the late 80’s, Lian, jointly with Zuckerman, developed the theory of semi-infinite cohomology and applied it to problems in string theory. In 1994, he constructed a new invariant (now known as the Lian- Zuckerman algebra) of a topological vertex algebra, and conjectured the first example of a G algebra in vertex algebra theory. The invariant has later inspired a new construction of quantum groups by I. Frenkel and A. Zeitlin, as semi-infinite cohomology of braided vertex algebras, and led to a more recent discovery of new relationships between Courant algebroids, A-algebras, operads, and deformation theory of BV algebras. In 2010, he and his students Linshaw and Song developed important applications of vertex algebras in equivariant topology. Lian’s work in CY geometry and mirror symmetry began in early 90’s. Using a characteristic p version of higher order Schwarzian equations, Lian and Yau gave an elementary proof that the instanton formula of Candelas et al implies Clemens’s divisibility conjecture for the quintic threefold, for infinitely many degrees. In 1996, Lian (jointly with Hosono and Yau) answered the so-called Large Complex Structure Limit problem in the affirmative in many important cases. Around the same year, they announced their hyperplane conjecture, which gives a general formula for period integrals for a large class of CY manifolds, extending the formula of Candelas et al. Soon after, Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula. In 2003, inspired by mirror symmetry, Lian (jointly with Hosono, Oguiso and Yau) discovered an explicit counting formula for Fourier-Mukai partners, and settled an old problem of Shioda on abelian and K3 surfaces. Between 2009 and 2014, Lian (jointly with Bloch, Chen, Huang, Song, Srinivas, Yau, and Zhu) developed an entirely new approach to study the so-called Riemann-Hilbert problem for period integrals of CY manifolds, and extended it to general type manifolds. The approach leads to an explicit description of differential systems for period integrals with many applications. In particular, he answered an old question in physics on the completeness of Picard-Fuchs systems, and constructed new differential zeros of hypergeometric functions.


      Denis Auroux (Harvard University)

      AurouxDenis Auroux’s research concerns symplectic geometry and its applications to mirror symmetry. While his early work primarily concerned the topology of symplectic 4-manifolds, over the past decade Auroux has obtained pioneering results on homological mirror symmetry outside of the Calabi-Yau setting (for Fano varieties, open Riemann surfaces, etc.), and developed an extension of the SYZ approach to non-Calabi-Yau spaces.After obtaining his PhD in 1999 from Ecole Polytechnique (France), Auroux was employed as Chargé de Recherche at CNRS and CLE Moore Instructor at MIT, before joining the faculty at MIT in 2002 (as Assistant Professor from 2002 to 2004, and as Associate Professor from 2004 to 2009, with tenure starting in 2006). He then moved to UC Berkeley as a Full Professor in 2009.
      Auroux has published over 30 peer-reviewed articles, including several in top journals, and given 260 invited presentations about his work. He received an Alfred P. Sloan Research Fellowship in 2005, was an invited speaker at the 2010 International Congress of Mathematicians, and in 2014 he was one of the two inaugural recipients of the Poincaré Chair at IHP. He has supervised 10 PhD dissertations, won teaching awards at MIT and Berkeley, and participated in the organization of over 20 workshops and conferences in symplectic geometry and mirror symmetry.




      Senior Personnel:

      Artan Sheshmani (Harvard CMSA)

      unnamedArtan Sheshmani’s research is focused on enumerative algebraic geometry and mathematical aspects of string theory. He is interested in applying techniques in algebraic geometry, such as, intersection theory, derived category theory, and derived algebraic geometry to construct and compute the deformation invariants of algebraic varieties, in particular Gromov-Witten (GW) or Donaldson-Thomas (DT) invariants. In the past Professor Sheshmani has worked on proving modularity property of certain DT invariants of K3-fibered threefolds (as well as their closely related Pandharipande-Thomas (PT) invariants), local surface threefolds, and general complete intersection Calabi-Yau threefolds. The modularity of DT/PT invariants in this context is predicted in a famous conjecture of  string theory called S-duality modularity conjecture, and his joint work has provided the proof to some cases of it, using degenerations, virtual localizations, as well as wallcrossing techniques. Recently, Sheshmani has focused on proving a series of dualities relating the various enumerative invariants over threefolds, notably the GW invariants and invariants that arise in topological gauge theory. In particular in his joint work with Gholampour, Gukov, Liu, Yau he studied DT gauge theory and its reductions to D=4 and D=2 which are equivalent to local theory of surfaces in Calabi-Yau threefolds. Moreover, in a recent joint work with Yau and Diaconescu, he has studied the construction and computation of DT invariants of Calabi-Yau fourfolds via a suitable derived categorical reduction of the theory to the DT theory of threefolds. Currently Sheshmani is interested in a wide range of problems in enumerative geometry of CY varieties in dimensions 3,4,5.

      Artan has received his PhD and Master’s degrees in pure mathematics under Sheldon Katz and Thomas Nevins from the University of Illinois at Urbana Champaign (USA) in 2011 and 2008 respectively. He holds a Master’s degree in Solid Mechanics (2004) and two Bachelor’s degrees, in Mechanical Engineering and Civil Engineering from the Sharif University of Technology, Tehran, Iran.  Artan has been a tenured Associate Professor of Mathematics with joint affiliation at Harvard CMSA and center for Quantum Geometry of Moduli Spaces (QGM), since 2016. Before that he has held visiting Associate Professor and visiting Assistant Professor positions at MIT.

      An Huang (Brandeis University)

      unnamedThe research of An Huang since 2011 has been focused on the interplay between algebraic geometry, the theory of special functions and mirror symmetry. With S. Bloch, B. Lian, V. Srinivas, S.-T. Yau, X. Zhu, he has developed the theory of tautological systems, and has applied it to settle several important problems concerning period integrals in relation to mirror symmetry. With B. Lian and X. Zhu, he has given a precise geometric interpretation of all solutions to GKZ systems associated to Calabi-Yau hypersurfaces in smooth Fano toric varieties. With B. Lian, S.-T. Yau, and C.-L. Yu, he has proved a conjecture of Vlasenko concerning an explicit formula for unit roots of the zeta functions of hypersurfaces, and has further related these roots to p-adic interpolations of complex period integrals. Beginning in 2018, with B. Stoica and S.-T. Yau, he has initiated the study of p-adic strings in curved spacetime, and showed that general relativity is a consequence of the self-consistency of quantum p-adic strings. One of the goals of this study is to understand p-adic A and B models.

      An Huang received his PhD in Mathematics from the University of California at Berkeley in 2011. He was a postdoctoral fellow at the Harvard University Mathematics Department, and joined Brandeis University as an Assistant Professor in Mathematics in 2016.



      Siu Cheong Lau (Boston University)
      unnamed

      The research interest of Siu Cheong Lau lies in SYZ mirror symmetry, symplectic and algebraic geometry.  His thesis work has successfully constructed the SYZ mirrors for all toric Calabi-Yau manifolds based on quantum corrections by open Gromov-Witten invariants and their wall-crossing phenomenon.  In collaboration with N.C. Leung, H.H. Tseng and K. Chan, he derived explicit formulas for the open Gromov-Witten invariants for semi-Fano toric manifolds which have an obstructed moduli theory.  It has a beautiful relation with mirror maps and Seidel representations.   Recently he works on a local-to-global approach to SYZ mirror symmetry.  In joint works with C.H. Cho and H. Hong, he developed a noncommutative local mirror construction for immersed Lagrangians, and a natural gluing method to construct global mirrors.  The construction has been realized in various types of geometries including orbifolds, focus-focus singularities and pair-of-pants decompositions of Riemann surfaces.

      Siu-Cheong Lau has received the Doctoral Thesis Gold Award (2012) and the Best Paper Silver Award (2017) at the International Congress of Chinese Mathematicians.  He was awarded the Simons Collaboration Grant in 2018.  He received a Certificate of Teaching Excellence from Harvard University in 2014.


      Affiliates:

      • Netanel Rubin-Blaier (Cambridge)
      • Kwokwai Chan (Chinese University of Hong Kong)
      • Mandy Cheung (Harvard University, BP)
      • Chuck Doran (University of Alberta)
      • Honsol Hong (Yonsei University)
      • Shinobu Hosono (Gakushuin University, Japan)
      • Conan Leung (Chinese University of Hong Kong)
      • Yu-shen Lin (Boston University)
      • Hossein Movassati (IMPA Brazil)
      • Arnav Tripathhy (Harvard University, BP)

       

      Postdocs:

      • Dennis Borisov
      • Tsung-Ju Lee
      • Dingxin Zhang
      • Jingyu Zhao
      • Yang Zhou

      Jobs:

      Postdoctoral Fellowship in Algebraic Geometry

      Postdoctoral Fellowship in Mathematical Sciences

       

      To learn about previous programming as part of the Simons Collaboration, click here.

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  • CMSA EVENT: Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks
    11:19 am
    11/12/2019-11/14/2019
    Dynamics-12-x-18-683x1024

    On November 12-14, 2019 the CMSA will be hosting a workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Biological cells are the fundamental units of life, and predictive modeling of cellular dynamics is essential for understanding a myriad of biological processes and functions. Rapid advances in technologies have made it possible for biologists to measure many variables and outputs from complex molecular and cellular networks with various inputs and environmental conditions. However, such advances are far ahead of the development of mathematical theory, models and methods needed to secure a deep understanding of how high-level robust behaviors emerge from the interactions in complex structures, especially in dynamic and stochastic environments. This workshop will bring together mathematicians and biological scientists involved in developing mathematical theories and methods for understanding, predicting and controlling dynamic behavior of molecular and cellular networks. Particular emphasis will be placed on efforts directed towards discovering underlying biological principles that govern function, adaptation and evolution, and on the development of associated mathematical theories.

    Organizers: Jeremy Gunawardena (Harvard) and Ruth Williams (University of California, San Diego)

    A limited amount of funding is available to help in defraying the travel costs of early career researchers, women, and underrepresented minorities, participating the workshop. Early career researchers are researchers who received their Ph.D. in 2014 or later, or who are Ph.D. students expecting to complete their Ph.D. by the end of 2020.

    To apply, please send a CV, a statement of why you wish to attend, and, if you are a grad student, a letter of support from your advisor to Sarah LaBauve at slabauve@math.harvard.edu

    All applications received by 5pm, EDT, October 28, 2019 will receive full consideration.

    Speakers: 

    Videos from the workshop can be found in the Youtube playlist.

  • Seminars

    Seminars Colloquia & Seminar
    11/12/2019 Spacetime Seminar

    3:30 pm
    11/12/2019
  • Seminars

    Seminars Colloquia & Seminar
    11/13/2019 Colloquium

    4:30 pm-5:30 pm
    11/12/2019
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  • CMSA EVENT: Current Developments in Mathematics 2019
    1:30 pm-5:00 pm
    11/22/2019-11/23/2019
    CDM-POSTER-2019.email_-662x1024

     

    cdmFriday, Nov. 22, 2019 1:30 pm – 5:20 pm

    Saturday, Nov. 23, 2019  9:00 am – 5:00 pm

    Harvard University Science Center, Hall C

    Speakers:

    ·      Svetlana Jitomirskaya (UC Irvine)

    ·      Subash Khot (NYU)

    ·      Jun Li (Stanford)

    ·      André Neves (Chicago)

    ·      Geordie Williamson (U Sidney)

    Free and open to the public – registration is required.
    Please register in advance online at www.math.harvard.edu/cdm

    CDM_2019-agenda-791x1024

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  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-16-2018 Mathematical Physics Seminar

    12:00 am
    11/01/2019
  • Seminars

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

    12:00 am-1:00 pm
    11/01/2019
  • CMSA EVENT: Quantum Matter Workshop
    All day
    11/01/2019
    Layer-2-600x338

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

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

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

     

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

    Speakers:

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-9-2018 Math Physics Seminar

    12:00 am
    11/01/2019
  • Colloquium
    5:00 am
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Workshop on Quantum Information
    8:00 am-6:07 pm
    11/01/2019-04/24/2017
    banner-image-1

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

    Register for the event here.

    The following speakers are confirmed:

  • CMSA EVENT: From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
    8:30 am-5:20 pm
    11/01/2019-08/20/2018
    Mumford-3

    David_Mumford-1

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

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

    Speakers:

    Organizers:

     

    Publication:

    Pure and Applied Mathematics Quarterly

    Special Issue: In Honor of David Mumford

    Guest Editors: Ching-Li Chai, Amnon Neeman

     

  • CMSA EVENT: Big Data Conference 2018
    8:30 am-2:50 pm
    11/01/2019-08/24/2018
    1 Oxford Street, Cambridge MA 02138
    Big-Data-2018-1

     

    shutterstock_547250785-e1527881194717

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

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

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

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

    Please register here. 

    Confirmed Speakers: 

    Organizers: 

    • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
    • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
    • Richard Freeman, Herbert Ascherman Professor of Economics, Harvard University
    • Jun Liu, Professor of Statistics, Harvard University
    • Horng-Tzer Yau, Professor of Mathematics, Harvard University
  • CMSA EVENT: F-Theory Conference
    8:30 am-3:00 pm
    11/01/2019-09/30/2018

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

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

    Click here for videos of the talks. 

    Organizers:

    Speakers:

  • CMSA EVENT: Workshop on Foundations of Computational Science
    8:30 am-2:45 pm
    11/01/2019-08/31/2019
    AI-Poster-3

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

    Please register here. 

    Speakers:

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

  • CMSA EVENT: Workshop on Aspects of General Relativity
    8:30 am-3:30 pm
    11/01/2019-05/26/2017

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

    Speakers:

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

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

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

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

    Schedule:

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

    Organizers: Piotr T. Chruściel and Shing-Tung Yau

  • CMSA EVENT: Workshop on Morphometrics, Morphogenesis and Mathematics
    8:30 am-2:00 pm
    11/01/2019-10/24/2018

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

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

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

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

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

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

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

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

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

    Videos of the talks

    Confirmed Speakers:

  • CMSA EVENT: Morphogenesis: Geometry and Physics
    8:30 am-2:30 pm
    11/01/2019-12/05/2018

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

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

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

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

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

    Videos

    Please Register Here

    PDF of the Schedule

    Speakers:

  • CMSA EVENT: Geometric Analysis Approach to AI Workshop
    8:30 am-5:30 pm
    11/01/2019-01/21/2019
    Geo-Analysis-Poster-final-e1547584167900

    Geo-Analysis-1-e1543848888343

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

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

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

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

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

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

    Please register here

    Speakers: 

  • CMSA EVENT: 2019 Big Data Conference
    8:30 am-4:40 pm
    11/01/2019-08/20/2019
    1 Oxford Street, Cambridge MA 02138
    Big-Data-2019-Poster-5-2

    shutterstock_547250785-e1527881194717

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

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

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

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

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

  • CMSA EVENT: 2015 Conference on Big Data
    8:45 am-4:00 pm
    11/01/2019-10/26/2015
    1 Oxford Street, Cambridge MA 02138

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

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

     

    Registration for the conference is now closed.

    Please click here for a downloadable version of this schedule.

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

    Monday, August 24

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

    Tuesday, August 25

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

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

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

     Wednesday, August 26 

    TimeSpeakerTitle
    8:45amMeet and Greet
    9:00amAnkur MoitraBeyond Matrix Completion
    9:45amFlorent KrzakalaOptimal compressed sensing with spatial coupling and message passing
    10:30amBreak
    10:45amPiotr IndykFast Algorithms for Structured Sparsity
    11:30amGuido ImbensExact p-values for network inference
    12:15pmBreak for lunch
    2:00pmEdo AiroldiSome fundamental ideas for causal inference on large networks
    2:45pmRonitt RubinfeldSomething for almost nothing: sublinear time approximation algorithms
    3:30pmBreak
    3:45pmLenka ZdeborovaClustering of sparse networks:  Phase transitions and optimal algorithms
    4:30pmJelani NelsonDimensionality reductions via sparse matrices
  • CMSA EVENT: Workshop on Probabilistic and Extremal Combinatorics
    9:00 am-1:30 pm
    11/01/2019-02/09/2018

    The workshop on Probabilistic and Extremal Combinatorics will take place February 5-9, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    Extremal and Probabilistic Combinatorics are two of the most central branches of modern combinatorial theory. Extremal Combinatorics deals with problems of determining or estimating the maximum or minimum possible cardinality of a collection of finite objects satisfying certain requirements. Such problems are often related to other areas including Computer Science, Information Theory, Number Theory and Geometry. This branch of Combinatorics has developed spectacularly over the last few decades. Probabilistic Combinatorics can be described informally as a (very successful) hybrid between Combinatorics and Probability, whose main object of study is probability distributions on discrete structures.

    There are many points of interaction between these fields. There are deep similarities in methodology. Both subjects are mostly asymptotic in nature. Quite a few important results from Extremal Combinatorics have been proven applying probabilistic methods, and vice versa. Such emerging subjects as Extremal Problems in Random Graphs or the theory of graph limits stand explicitly at the intersection of the two fields and indicate their natural symbiosis.

    The symposia will focus on the interactions between the above areas. These topics include Extremal Problems for Graphs and Set Systems, Ramsey Theory, Combinatorial Number Theory, Combinatorial Geometry, Random Graphs, Probabilistic Methods and Graph Limits.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Benny Sudakov and David Conlon.  More details about this event, including participants, will be updated soon.

  • CMSA EVENT: Simons Collaboration on Homological Mirror Symmetry
    9:00 am-5:00 pm
    11/01/2019-05/08/2016

    The Center of Mathematical Sciences and Applications will be hosting a 3-day workshop on Homological Mirror Symmetry and related areas on May 6 – May 8, 2016 at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

    Organizers:

    D. Auroux, S.C. Lau, N.C. Leung, Bong Lian, C.C. Liu, S.T. Yau

    Speakers:

    1. Netanel Blaier (MIT)
    2. Kwokwai Chan (CUHK)
    3. Bohan Fang (Peking University)
    4. Amanda Francis (BYU)
    5. Hansol Hong (CUHK)
    6. Heather Lee (Purdue University)
    7. Si Li (Tsinghua University)
    8. Yu-Shen Lin (Stanford University)
    9. Alex Perry (Harvard University)
    10. Hiro Tanaka (Harvard University)
    11. Sara Tukachinsky (HUJ)
    12. Michael Viscardi (MIT)
    13. Eric Zaslow (Northwestern University)
    14. Jingyu Zhao (Columbia University)

    Please click here for the conference Main Website.

    Please click Simons Workshop Schedule with Abstract for a downloadable schedule with talk abstracts.

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

    Schedule:

    May 6 – Day 1
    9:00amBreakfast
    9:35amOpening remarks
    9:45am – 10:45amSi Li, “Quantum master equation, chiral algebra, and integrability”
    10:45am – 11:15amBreak
    11:15am – 12:15pmSara Tukachinsky, “Point like bounding chains and open WDVV
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmBohan Fang, “Mirror B model for toric Calabi Yau 3 folds
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmHiro Tanaka, “Toward Fukaya categories over arbitrary coefficients
    4:00pm – 4:15pmBreak
    4:15pm – 5:15pmHansol Hong, “Noncommutative mirror functors
    May 7 – Day 2
    9:00amBreakfast
    9:45am – 10:45amEric Zaslow, “Lagrangian fillings what does the sheaf say?
    10:45am – 11:15amBreak
    11:15am – 12:15pmAlex Perry, “Derived categories of Gushel Mukai varieties
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmAmanda Francis, “A Landau Ginzburg mirror theorem inspired by Borcea Voisin symmetry
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmHeather Lee, “Homological mirror symmetry for open Riemann surfaces from pair of pants decompositions
    4:00pm – 4:15pmBreak
    4:15pm – 5:15pmYu-Shen Lin, “Counting Holomorphic Discs via Tropical Discs on K3 Surfaces
    May 8 – Day 3
    9:00amBreakfast
    9:45am – 10:45amKwokwai Chan, “HMS for local CY manifolds via SYZ
    10:45am – 11:15amBreak
    11:15am – 12:15pmNetanel Blaier, “The quantum Johnson homomorphism, formality and symplectic isotopy
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmJingyu Zhao, “Periodic symplectic cohomology and the Hodge filtration
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmMichael Viscardi, “Equivariant quantum cohomology and the geometric Satake equivalence
    * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Simons Collaboration on Homological Mirror symmetry“.

    This event is sponsored by the Simons Foundation and CMSA Harvard University.

  • CMSA EVENT: Workshop on Geometry, Imaging, and Computing
    9:00 am-6:15 pm
    11/01/2019-03/26/2018
    GIC-Poster-2-e1520002551865

    On March 24-26, The Center of Mathematical Sciences and Applications will be hosting a workshop on Geometry, Imaging, and Computing, based off  the journal of the same name. The workshop will take place in CMSA building, G10.

    The organizing committee consists of Yang Wang (HKUST), Ronald Lui (CUHK), David Gu (Stony Brook), and Shing-Tung Yau (Harvard).

    Please click here to register for the event.

    Confirmed Speakers:

  • CMSA EVENT: Workshop on Optimization in Image Processing
    9:00 am-12:30 pm
    11/01/2019-06/30/2016

    The Center of Mathematical Sciences and Applications will be hosting a workshop on Optimization in Image Processing on June 27 – 30, 2016. This 4-day workshop aims to bring together researchers to exchange and stimulate ideas in imaging sciences, with a special focus on new approaches based on optimization methods. This is a cutting-edge topic with crucial impact in various areas of imaging science including inverse problems, image processing and computer vision. 16 speakers will participate in this event, which we think will be a very stimulating and exciting workshop. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Titles, abstracts and schedule will be provided nearer to the event.

    Speakers:

    1. Antonin Chambolle, CMAP, Ecole Polytechnique
    2. Raymond Chan, The Chinese University of Hong Kong
    3. Ke Chen, University of Liverpool
    4. Patrick Louis Combettes, Université Pierre et Marie Curie
    5. Mario Figueiredo, Instituto Superior Técnico
    6. Alfred Hero, University of Michigan
    7. Ronald Lok Ming Lui, The Chinese University of Hong Kong
    8. Mila Nikolova, Ecole Normale Superieure Cachan
    9. Shoham Sabach, Israel Institute of Technology
    10. Martin Benning, University of Cambridge
    11. Jin Keun Seo, Yonsei University
    12. Fiorella Sgallari, University of Bologna
    13. Gabriele Steidl, Kaiserslautern University of Technology
    14. Joachim Weickert, Saarland University
    15. Isao Yamada, Tokyo Institute of Technology
    16. Wotao Yin, UCLA

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

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

    Please click here for registration – Registration Deadline: June 7, 2016; Registration is capped at 70 participants.

    Schedule:

    June 27 – Day 1
    9:00amBreakfast
    9:20amOpening remarks
    9:30am – 10:20amJoachim Weickert, “FSI Schemes: Fast Semi-Iterative Methods for Diffusive or Variational Image Analysis Problems”
    10:20am – 10:50amBreak
    10:50am – 11:40pmPatrick Louis Combettes“Block-Iterative Asynchronous Variational Image Recovery”
    11:40am – 12:30pmIsao Yamada“Spicing up Convex Optimization for Certain Inverse Problems”
    12:30pm – 2:00pmLunch
    2:30pm – 3:20pmFiorella Sgallari, “Majorization-Minimization for Nonconvex Optimization”
    3:20pm – 3:50pmBreak
    3:50pm – 4:40pmShoham Sabach“A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Problems”
    June 28 – Day 2
    9:00amBreakfast
    9:30am – 10:20amAntonin Chambolle“Acceleration of alternating minimisations”
    10:20am – 10:50amBreak
    10:50am – 11:40amMario Figueiredo“ADMM in Image Restoration and Related Problems: Some History and Recent Advances”
    11:40am – 12:30pmKe Chen“Image Restoration and Registration Based on Total Fractional-Order Variation Regularization”
    12:30pm – 2:30pmLunch
    2:30pm – 4:40pmDiscussions
    June 29 – Day 3
    9:00amBreakfast
    9:30am – 10:20amAlfred Hero“Continuum relaxations for discrete optimization”
    10:20am – 10:50amBreak
    10:50am – 11:40amWotao Yin“Coordinate Update Algorithms for Computational Imaging and Machine Learning”
    11:40am – 12:30pmMila Nikolova“Limits on noise removal using log-likelihood and regularization”
    12:30pm – 2:30pmLunch
    2:30pm – 3:20pmMartin Benning, “Nonlinear spectral decompositions and the inverse scale space method”
    3:20pm – 3:50pmBreak
    3:50pm – 4:40pmRonald Ming Lui“TEMPO: Feature-endowed Teichmuller extremal mappings of point cloud for shape classification”
    June 30 – Day 4
    9:00amBreakfast
    9:30am – 10:20amJin Keun Seo“Mathematical methods for biomedical impedance imaging”
    10:20am – 10:50amBreak
    10:50am – 11:40amGabriele Steidl, “Iterative Multiplicative Filters for Data Labeling”
    11:40am – 12:30pmRaymond Chan, “Point-spread function reconstruction in ground-based astronomy”
    * This event is sponsored by CMSA Harvard University.

    Organizers: Raymond Chan and Shing-Tung Yau

  • CMSA EVENT: Machine Learning for Multiscale Model Reduction Workshop
    9:00 am-11:55 am
    11/01/2019-03/29/2019
    Machine-Learning-Poster

    The Machine Learning for Multiscale Model Reduction Workshop will take place on March 27-29, 2019. This is the second of two workshops organized by Michael BrennerShmuel Rubinstein, and Tom Hou.  The first, Fluid turbulence and Singularities of the Euler/ Navier Stokes equations, will take place on March 13-15, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

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

    List of registrants

    Speakers:

  • CMSA EVENT: Simons Collaboration Workshop, Jan. 10-13, 2018
    9:00 am-12:00 pm
    11/01/2019-01/13/2017
    banner-image-1

    The CMSA will be hosting a four-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on January 10-13, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

    We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

     

    Confirmed Participants:

  • CMSA EVENT: Mini-school on Nonlinear Equations, December 3-4, 2016
    9:00 am-5:00 pm
    11/01/2019-12/04/2016

    The Center of Mathematical Sciences and Applications will be hosting a Mini-school on Nonlinear Equations on December 3-4, 2016. The conference will have speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138.

    The mini-school will consist of lectures by experts in geometry and analysis detailing important developments in the theory of nonlinear equations and their applications from the last 20-30 years.  The mini-school is aimed at graduate students and young researchers working in geometry, analysis, physics and related fields.

    Please click here to register for this event.

    Speakers:

    1. Cliff Taubes (Harvard University)
    2. Valentino Tosatti (Northwestern University)
    3. Pengfei Guan (McGill University)
    4. Jared Speck (MIT)

    Schedule:

    December 3rd – Day 1
    9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
    10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
    12:15pm – 1:45pmLUNCH
    1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
    3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”
    December 4th – Day 2
    9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
    10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
    12:15pm – 1:45pmLUNCH
    1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
    3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”

    Please click Mini-School Program for a downloadable schedule with talk abstracts.

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

    * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

  • CMSA EVENT: Workshop on Coding and Information Theory
    9:00 am-3:30 pm
    11/01/2019-04/13/2018

    The workshop on coding and information theory will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

    Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory.  One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program.  Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities.  Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics.  All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    Click here for a list of registrants. 

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

  • CMSA EVENT: Topology and Dynamics in Quantum Matter Workshop
    9:15 am-3:25 pm
    11/01/2019-09/11/2019
    Topology-Poster

    On September 10-11, 2019, the CMSA will be hosting a second workshop on Topological Aspects of Condensed Matter.

    New ideas rooted in topology have recently had a major impact on condensed matter physics, and have led to new connections with high energy physics, mathematics and quantum information theory.  The aim of this program will be to deepen these connections and spark new progress by fostering discussion and new collaborations within and across disciplines.

    Topics include i) the classification of topological states  ii) topological orders in two and three dimensions including quantum spin liquids, quantum Hall states and fracton phases and iii)  interplay of symmetry and topology in quantum many body systems, including symmetry protected topological phases, symmetry fractionalization and anomalies iv) topological phenomena in quantum systems  driven far from equlibrium v) quantum field theory approaches to topological matter.

    This workshop is part of the CMSA’s program on Program on Topological Aspects of Condensed Matterand is the second of two workshops, in addition to a visitor program and seminars.

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

    Click here for a list of restaurants in the area. 

    Organizers: Michael Hermele (CU Boulder) and Ashvin Vishwanath (Harvard)

    Partial list of speakers:

    Videos of the lectures can be found in the Youtube playlist below. Links to talks are also available on the schedule below.

  • CMSA EVENT: Workshop on Invariance and Geometry in Sensation, Action and Cognition
    9:15 am-10:00 am
    11/01/2019-04/17/2019

    As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

    Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, it has traditionally not been an important part of biology, except in the context of aspects of structural biology. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use.

    This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines? The aim is to revisit these old neuro-cognitive problems using a series of modern lenses experimentally, theoretically and computationally, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models.

    In addition to talks, there will be a set of tutorial talks on the mathematical description of invariance (P.J. Olver), the computer vision aspects of invariant algorithms (S. Soatto), and the neuroscientific and cognitive aspects of invariance (TBA). The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by L. Mahadevan (Harvard), Talia Konkle (Harvard), Samuel Gershman (Harvard), and Vivek Jayaraman (HHMI).

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

    List of registrants

    Videos

    Tentative Speaker List:

    Schedule:

    Monday, April 15

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:15amWelcome and Introduction
    9:15 – 10:00amVivek JayaramanTitle: Insect cognition: Small tales of geometry & invariance

    Abstract: Decades of field and laboratory experiments have allowed ethologists to discover the remarkable sophistication of insect behavior. Over the past couple of decades, physiologists have been able to peek under the hood to uncover sophistication in insect brain dynamics as well. In my talk, I will describe phenomena that relate to the workshop’s theme of geometry and invariance. I will outline how studying insects —and flies in particular— may enable an understanding of the neural mechanisms underlying these intriguing phenomena.

    10:00 – 10:45amElizabeth TorresTitle: Connecting Cognition and Biophysical Motions Through Geometric Invariants and Motion Variability

    Abstract: In the 1930s Nikolai Bernstein defined the degrees of freedom (DoF) problem. He asked how the brain could control abundant DoF and produce consistent solutions, when the internal space of bodily configurations had much higher dimensions than the space defining the purpose(s) of our actions. His question opened two fundamental problems in the field of motor control. One relates to the uniqueness or consistency of a solution to the DoF problem, while the other refers to the characterization of the diverse patterns of variability that such solution produces.

    In this talk I present a general geometric solution to Bernstein’s DoF problem and provide empirical evidence for symmetries and invariances that this solution provides during the coordination of complex naturalistic actions. I further introduce fundamentally different patterns of variability that emerge in deliberate vs. spontaneous movements discovered in my lab while studying athletes and dancers performing interactive actions. I here reformulate the DoF problem from the standpoint of the social brain and recast it considering graph theory and network connectivity analyses amenable to study one of the most poignant developmental disorders of our times: Autism Spectrum Disorders.

    I offer a new unifying framework to recast dynamic and complex cognitive and social behaviors of the full organism and to characterize biophysical motion patterns during migration of induced pluripotent stem cell colonies on their way to become neurons.

    10:45 – 11:15amCoffee Break
    11:15 – 12:00pmPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

    Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical prerequisites will be kept to a bare minimum.

    12:00 – 12:45pmStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

    Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

    While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

    12:45 – 2:00pmLunch
    2:00 – 2:45pmAnitha PasupathyTitle: Invariant and non-invariant representations in mid-level ventral visual cortex

    My laboratory investigates how visual form is encoded in area V4, a critical mid-level stage of form processing in the macaque monkey. Our goal is to reveal how V4 representations underlie our ability to segment visual scenes and recognize objects. In my talk I will present results from two experiments that highlight the different strategies used by the visual to achieve these goals. First, most V4 neurons exhibit form tuning that is exquisitely invariant to size and position, properties likely important to support invariant object recognition. On the other hand, form tuning in a majority of neurons is also highly dependent on the interior fill. Interestingly, unlike primate V4 neurons, units in a convolutional neural network trained to recognize objects (AlexNet) overwhelmingly exhibit fill-outline invariance. I will argue that this divergence between real and artificial circuits reflects the importance of local contrast in parsing visual scenes and overall scene understanding.

    2:45 – 3:30pmJacob FeldmanTitle: Bayesian skeleton estimation for shape representation and perceptual organization

    Abstract: In this talk I will briefly summarize a framework in which shape representation and perceptual organization are reframed as probabilistic estimation problems. The approach centers around the goal of identifying the skeletal model that best “explains” a given shape. A Bayesian solution to this problem requires identifying a prior over shape skeletons, which penalizes complexity, and a likelihood model, which quantifies how well any particular skeleton model fits the data observed in the image. The maximum-posterior skeletal model thus constitutes the most “rational” interpretation of the image data consistent with the given assumptions. This approach can easily be extended and generalized in a number of ways, allowing a number of traditional problems in perceptual organization to be “probabilized.” I will briefly illustrate several such extensions, including (1) figure/ground and grouping (3) 3D shape and (2) shape similarity.

    3:30 – 4:00pmTea Break
    4:00 – 4:45pmMoira DillonTitle: Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development

    Abstract: Formal geometry lies at the foundation of millennia of human achievement in domains such as mathematics, science, and art. While formal geometry’s propositions rely on abstract entities like dimensionless points and infinitely long lines, the points and lines of our everyday world all have dimension and are finite. How, then, do we get to abstract geometric thought? In this talk, I will provide evidence that evolutionarily ancient and developmentally precocious sensitivities to the geometry of our everyday world form the foundation of, but also limit, our mathematical reasoning. I will also suggest that successful geometric reasoning may emerge through development when children abandon incorrect, axiomatic-based strategies and come to rely on dynamic simulations of physical entities. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations.

    4:45 – 5:30pmMichael McCloskeyTitle: Axes and Coordinate Systems in Representing Object Shape and Orientation

    Abstract: I describe a theoretical perspective in which a) object shape is represented in an object-centered reference frame constructed around orthogonal axes; and b) object orientation is represented by mapping the object-centered frame onto an extrinsic (egocentric or environment-centered) frame.  I first show that this perspective is motivated by, and sheds light on, object orientation errors observed in neurotypical children and adults, and in a remarkable case of impaired orientation perception. I then suggest that orientation errors can be used to address questions concerning how object axes are defined on the basis of object geometry—for example, what aspects of object geometry (e.g., elongation, symmetry, structural centrality of parts) play a role in defining an object principal axis?

    5:30 – 6:30pmReception

     

    Tuesday, April 16

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:45amPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

    Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical pre

    9:45 – 10:30amStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

    Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

    While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

    10:30 – 11:00amCoffee Break
    11:00 – 11:45amJeannette BohgTitle: On perceptual representations and how they interact with actions and physical representations

    Abstract: I will discuss the hypothesis that perception is active and shaped by our task and our expectations on how the world behaves upon physical interaction. Recent approaches in robotics follow this insight that perception is facilitated by physical interaction with the environment. First, interaction creates a rich sensory signal that would otherwise not be present. And second, knowledge of the regularity in the combined space of sensory data and action parameters facilitate the prediction and interpretation of the signal. In this talk, I will present two examples from our previous work where a predictive task facilitates autonomous robot manipulation by biasing the representation of the raw sensory data. I will present results on visual but also haptic data.

    11:45 – 12:30pmDagmar SternadTitle: Exploiting the Geometry of the Solution Space to Reduce Sensitivity to Neuromotor Noise

    Abstract: Control and coordination of skilled action is frequently examined in isolation as a neuromuscular problem. However, goal-directed actions are guided by information that creates solutions that are defined as a relation between the actor and the environment. We have developed a task-dynamic approach that starts with a physical model of the task and mathematical analysis of the solution spaces for the task. Based on this analysis we can trace how humans develop strategies that meet complex demands by exploiting the geometry of the solution space. Using three interactive tasks – throwing or bouncing a ball and transporting a “cup of coffee” – we show that humans develop skill by: 1) finding noise-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, and 3) optimizing predictability of the object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, attractors with few invariant types that overcome substantial delays and noise in the neuro-mechanical system.

    12:30 – 2:00pmLunch
    2:00 – 2:45pmSam OckoTitle: Emergent Elasticity in the Neural Code for Space

    Abstract: To navigate a novel environment, animals must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such internal maps, and how are these maps used to maintain representations of an animal’s position within an environment. We demonstrate analytically how a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent internal map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network during exploration. Moreover, we verify several experimentally testable predictions of our model, including: (1) systematic deformations of grid cells in irregular environments, (2) path-dependent shifts in grid cells towards the most recently encountered landmark, (3) a dynamical phase transition in which grid cells can break free of landmarks in altered virtual reality environments and (4) the creation of topological defects in grid cells. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

    2:45 – 3:30pmTatyana SharpeeTitle: Hyperbolic geometry of the olfactory space

    Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the production of a specific poison by a plant or bacteria will be accompanied by the emission of certain sets of volatile compounds. An animal can therefore judge the presence of poisons in the food by how the food smells. This perspective suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendrograms, and more generally between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

    3:30 – 4:00pmTea Break
    4:00 – 4:45pmEd ConnorTitle: Representation of solid geometry in object vision cortex

    Abstract: There is a fundamental tension in object vision between the 2D nature of retinal images and the 3D nature of physical reality. Studies of object processing in the ventral pathway of primate visual cortex have focused mainly on 2D image information. Our latest results, however, show that representations of 3D geometry predominate even in V4, the first object-specific stage in the ventral pathway. The majority of V4 neurons exhibit strong responses and clear selectivity for solid, 3D shape fragments. These responses are remarkably invariant across radically different image cues for 3D shape: shading, specularity, reflection, refraction, and binocular disparity (stereopsis). In V4 and in subsequent stages of the ventral pathway, solid shape geometry is represented in terms of surface fragments and medial axis fragments. Whole objects are represented by ensembles of neurons signaling the shapes and relative positions of their constituent parts. The neural tuning dimensionality of these representations includes principal surface curvatures and their orientations, surface normal orientation, medial axis orientation, axial curvature, axial topology, and position relative to object center of mass. Thus, the ventral pathway implements a rapid transformation of 2D image data into explicit representations 3D geometry, providing cognitive access to the detailed structure of physical reality.

    4:45 – 5:30pmL. MahadevanTitle: Simple aspects of geometry and probability in perception

    Abstract: Inspired by problems associated with noisy perception, I will discuss two questions: (i) how might we test people’s perception of probability in a geometric context ? (ii) can one construct invariant descriptions of 2D images using simple notions of probabilistic geometry? Along the way, I will highlight other questions that the intertwining of geometry and probability raises in a broader perceptual context.


    Wednesday, April 17

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:45amGily GinosarTitle: The 3D geometry of grid cells in flying bats

    Abstract: The medial entorhinal cortex (MEC) contains a variety of spatial cells, including grid cells and border cells. In 2D, grid cells fire when the animal passes near the vertices of a 2D spatial lattice (or grid), which is characterized by circular firing-fields separated by fixed distances, and 60 local angles – resulting in a hexagonal structure. Although many animals navigate in 3D space, no studies have examined the 3D volumetric firing of MEC neurons. Here we addressed this by training Egyptian fruit bats to fly in a large room (5.84.62.7m), while we wirelessly recorded single neurons in MEC. We found 3D border cells and 3D head-direction cells, as well as many neurons with multiple spherical firing-fields. 20% of the multi-field neurons were 3D grid cells, exhibiting a narrow distribution of characteristic distances between neighboring fields – but not a perfect 3D global lattice. The 3D grid cells formed a functional continuum with less structured multi-field neurons. Both 3D grid cells and multi-field cells exhibited an anatomical gradient of spatial scale along the dorso-ventral axis of MEC, with inter-field spacing increasing ventrally – similar to 2D grid cells in rodents. We modeled 3D grid cells and multi-field cells as emerging from pairwise-interactions between fields, using an energy potential that induces repulsion at short distances and attraction at long distances. Our analysis shows that the model explains the data significantly better than a random arrangement of fields. Interestingly, simulating the exact same model in 2D yielded a hexagonal-like structure, akin to grid cells in rodents. Together, the experimental data and preliminary modeling suggest that the global property of grid cells is multiple fields that repel each other with a characteristic distance-scale between adjacent fields – which in 2D yields a global hexagonal lattice while in 3D yields only local structure but no global lattice.

    Gily Ginosar 1 , Johnatan Aljadeff 2 , Yoram Burak 3 , Haim Sompolinsky 3 , Liora Las 1 , Nachum Ulanovsky 1

    (1) Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel

    (2) Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK

    (3) The Edmond and Lily Safra Center for Brain Sciences, and Racah Institute of Physics, The Hebrew

    University of Jerusalem, Jerusalem, 91904, Israel

    9:45 – 10:30amSandro RomaniTitle: Neural networks for 3D rotations

    Abstract: Studies in rodents, bats, and humans have uncovered the existence of neurons that encode the orientation of the head in 3D. Classical theories of the head-direction (HD) system in 2D rely on continuous attractor neural networks, where neurons with similar heading preference excite each other, while inhibiting other HD neurons. Local excitation and long-range inhibition promote the formation of a stable “bump” of activity that maintains a representation of heading. The extension of HD models to 3D is hindered by complications (i) 3D rotations are non-commutative (ii) the space described by all possible rotations of an object has a non-trivial topology. This topology is not captured by standard parametrizations such as Euler angles (e.g. yaw, pitch, roll). For instance, with these parametrizations, a small change of the orientation of the head could result in a dramatic change of neural representation. We used methods from the representation theory of groups to develop neural network models that exhibit patterns of persistent activity of neurons mapped continuously to the group of 3D rotations. I will further discuss how these networks can (i) integrate vestibular inputs to update the representation of heading, and (ii) be used to interpret “mental rotation” experiments in humans.

    This is joint work with Hervé Rouault (CENTURI) and Alon Rubin (Weizmann Institute of Science).

    10:30 – 11:00amCoffee Break
    11:00 – 11:45amSam GershmanTitle: The hippocampus as a predictive map

    Abstract: A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. I approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? I show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, I argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning.

    11:45 – 12:30pmLucia JacobsTitle: The adaptive geometry of a chemosensor: the origin and function of the vertebrate nose

    Abstract: A defining feature of a living organism, from prokaryotes to plants and animals, is the ability to orient to chemicals. The distribution of chemicals, whether in water, air or on land, is used by organisms to locate and exploit spatially distributed resources, such as nutrients and reproductive partners. In animals, the evolution of a nervous system coincided with the evolution of paired chemosensors. In contemporary insects, crustaceans, mollusks and vertebrates, including humans, paired chemosensors confer a stereo olfaction advantage on the animal’s ability to orient in space. Among vertebrates, however, this function faced a new challenge with the invasion of land. Locomotion on land created a new conflict between respiration and spatial olfaction in vertebrates. The need to resolve this conflict could explain the current diversity of vertebrate nose geometries, which could have arisen due to species differences in the demand for stereo olfaction. I will examine this idea in more detail in the order Primates, focusing on Old World primates, in particular, the evolution of an external nose in the genus Homo.

    12:30 – 1:30pmLunch
    1:30 – 2:15pmTalia KonkleTitle: The shape of things and the organization of object-selective cortex

    Abstract: When we look at the world, we effortlessly recognize the objects around us and can bring to mind a wealth of knowledge about their properties. In part 1, I’ll present evidence that neural responses to objects are organized by high-level dimensions of animacy and size, but with underlying neural tuning to mid-level shape features. In part 2, I’ll present evidence that representational structure across much of the visual system has the requisite structure to predict visual behavior. Together, these projects suggest that there is a ubiquitous “shape space” mapped across all of occipitotemporal cortex that underlies our visual object processing capacities. Based on these findings, I’ll speculate that the large-scale spatial topography of these neural responses is critical for pulling explicit content out of a representational geometry.

    2:15 – 3:00pmVijay BalasubramanianTitle: Becoming what you smell: adaptive sensing in the olfactory system

    Abstract: I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors.  In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors.  The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules.  I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors.  The resulting algorithm for “estimation by elimination” can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain.  The theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans.   It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb.

    3:00 – 3:45pmIla FeiteTitle: Invariance, stability, geometry, and flexibility in spatial navigation circuits

    Abstract: I will describe how the geometric invariances or symmetries of the external world are reflected in the symmetries of neural circuits that represent it, using the example of the brain’s networks for spatial navigation. I will discuss how these symmetries enable spatial memory, evidence integration, and robust representation. At the same time, I will discuss how these seemingly rigid circuits with their inscribed symmetries can be harnessed to represent a range of spatial and non-spatial cognitive variables with high flexibility.

    3:45 – 4:00pmL Mahadevan – summary
  • CMSA EVENT: The 2017 Charles River Lectures
    9:15 am-5:30 pm
    11/01/2019

    The 2017 Charles River Lectures

    Charles River with Bench at Sunset

    Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community.

    The 2017 lectures will take place 9:15am – 5:30pm on Monday, October 2 at Harvard University  in the Harvard Science Center.


    ***************************************************

    UPDATED LOCATION

    Harvard University

    Harvard Science Center (Halls C & E)

    1 Oxford Street, Cambridge, MA 02138 (Map)

    Monday, October 2, 2017

    9:15 AM – 5:30 PM

    **************************************************

    Please note that registration has closed.

    Speakers:

    Agenda:

    In Harvard Science Center Hall C:

    8:45 am – 9:15 amCoffee/light breakfast

    9:15 am – 10:15 am: Ofer Zeitouni

    Title: Noise stability of the spectrum of large matrices

    Abstract: The spectrum of large non-normal matrices is notoriously sensitive to perturbations, as the example of nilpotent matrices shows. Remarkably, the spectrum of these matrices perturbed by polynomially (in the dimension) vanishing additive noise is remarkably stable. I will describe some results and the beginning of a theory.

    The talk is based on joint work with Anirban Basak and Elliot Paquette, and earlier works with Feldheim, Guionnet, Paquette and Wood.

    10:20 am – 11:20 am: Andrea Montanari

    Title: Algorithms for estimating low-rank matrices 

    Abstract: Many interesting problems in statistics can be formulated as follows. The signal of interest is a large low-rank matrix with additional structure, and we are given a single noisy view of this matrix. We would like to estimate the low rank signal by taking into account optimally the signal structure. I will discuss two types of efficient estimation procedures based on message-passing algorithms and semidefinite programming relaxations, with an emphasis on asymptotically exact results.

    11:20 am – 11:45 amBreak

    11:45 am – 12:45 pm: Paul Bourgade

    Title: Random matrices, the Riemann zeta function and trees

    Abstract: Fyodorov, Hiary & Keating have conjectured that the maximum of the characteristic polynomial of random unitary matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the typical size of local maxima of the Riemann zeta function along the critical axis. I will first explain the origins of this conjecture, and then outline the proof for the leading order of the maximum, for unitary matrices and the zeta function. This talk is based on joint works with Arguin, Belius, Radziwill and Soundararajan.

    1:00 pm – 2:30 pm: Lunch

    In Harvard Science Center Hall E:

    2:45 pm – 3:45 pm: Roman Vershynin

    Title: Deviations of random matrices and applications

    Abstract: Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This lecture will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science.

    3:45 pm – 4:15 pm: Break

    4:15 pm – 5:15 pm: Massimiliano Gubinelli

    Title: Weak universality and Singular SPDEs

    Abstract: Mesoscopic fluctuations of microscopic (discrete or continuous) dynamics can be described in terms of nonlinear stochastic partial differential equations which are universal: they depend on very few details of the microscopic model. This universality comes at a price: due to the extreme irregular nature of the random field sample paths, these equations turn out to not be well-posed in any classical analytic sense. I will review recent progress in the mathematical understanding of such singular equations and of their (weak) universality and their relation with the Wilsonian renormalisation group framework of theoretical physics.

    Poster:

    2017 Charles River Lectures Poster

    Organizers:

     Alexei BorodinHenry CohnVadim GorinElchanan MosselPhilippe RigolletScott Sheffield, and H.T. Yau

  • CMSA EVENT: Kickoff Workshop on Topology and Quantum Phases of Matter
    9:20 am-3:15 pm
    11/01/2019-08/28/2018
    Topological-1

    Screen-Shot-2018-08-13-at-2.28.22-PM

    On August 27-28, 2018, the CMSA will be hosting a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines.

    This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter,  and will be the first of two workshops, in addition to a visitor program and seminars.

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

    Please register here

    Speakers: 

  • Special Seminar
    9:30 am-11:00 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/18/2019 General Relativity Seminar

    9:30 am-10:30 am
    11/01/2019
  • CMSA EVENT: Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
    9:30 am-5:00 pm
    11/01/2019-03/01/2019

    From February 25 to March 1, the CMSA will be hosting a workshop on Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations. 

    Key participants of this workshop include David Jerison (MIT), Alexander Logunov (IAS), and Eugenia Malinnikova (IAS).  This workshop will have morning sessions on Monday-Friday of this week from 9:30-11:30am, and afternoon sessions on Monday, Tuesday, and Thursday from 3:00-5:00pm.
    The sessions will be held in  \(G02\) (downstairs) at 20 Garden, except for Tuesday afternoon, when the talk will be in \(G10\).

  • Special Seminar
    9:30 am
    11/01/2019
  • Seminars
    9:50 am-10:50 am
    11/01/2019

    The seminar for evolution equations, hyperbolic equations, and fluid dynamics will be held on Thursdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule of speakers is below. Titles for the talks will be added as they are received.

    DateNameTitle
    09-03-2015Long JinScattering Resonances for Convex Obstacles
    09-10-2015Chunjing XieWell/ill-posedness for the rotating shallow water system
    09-17-2015Xiangdi HuangGlobal classical and weak Solutions to the 3D fully compressible Navier-Stokes-Fourier system
    09-24-2015Felix FinsterCausal fermion systems and the causal action principle
    10-01-2015Pin YuConstruction of Cauchy data of vacuum Einstein field equations evolving to black holes
    10-08-2015Chunjing XieSteady Euler flows past a wall or through a nozzle
    10-15-2015Zhou Ping XinOn Global Well-Posedness of The Compressible Navier-Stokes Systems with Large Oscillations
    10-22-2015Xiangdi HuangOn Nash’s problem for compressible flows
    10-29-2015Pin YuShock formations for 3 dimensional wave equations
    11-05-2015No talk 
    11-12-2015Zhou Ping Xin (9:30am-10:30am) Nicolai Krylov (10:30am-11:30am)Nonlinear Asymptotic Stability of Lane-Emden Solutions for The Viscous Gaseous Star ProblemOn the existence of $\bf W^{2}_{p}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions
    11-19-2015Nicolai KrylovTo the theory of viscosity solutions for uniformly parabolic Isaacs equations
    11-26-2015ThanksgivingNo seminar
    12-4-2015John Loftin (@11:00am)Moduli of Equivariant Minimal Surfaces in CH^2$
    01-28-2016Xiaoli HanThe symplecitic and Lagrangian mean curvature flow 
    02-04-2016Pranav PanditCategorical Kähler Geometry
    02-11-2016Lydia BieriEinstein’s Equations, Energy and Gravitational Radiation
    02-18-2016Zuoqiang ShiLow dimensional manifold model for image processing
    02-25-2016Chun Peng WangSmooth Transonic Flows of Meyer Type in De Laval Nozzles
    03-03-2016Piotr ChruscielSingularities in general relativity
    03-10-2016Feimin HuangIsometric immersion of complete surface with slowly decaying negative Gauss curvature
    03-17-2016Spring BreakNo Talk
    03-24-2016Michael EichmairMinimal surfaces, isoperimetry, and non-negative scalar curvature in asymptotically flat manifolds
    03-31-2016Felix FinsterLorentzian spectral geometry and the fermionic signature operator
    04-07-2016(Room 232, Science Center)Stefano Bianchini, SISSAConcentration of entropy dissipation for scalar conservation laws
    04-14-2016Tai-peng TsaiStability of periodic waves of the 1D nonlinear Schr\”odinger equations
    04-21-2016Stefano Bianchini, SISSAQuadratic interaction functional for system of conservation laws
    04-28-2016Mihalis Dafermos, PrincetonThe linear stability of the Schwarzschild solution to gravitational perturbations
    05-05-2016Xu-Jia WangMonge-Ampere equations arising in geometric optics
    05-12-2016Stefano Bianchini
  • Special Seminar
    9:50 am-10:50 am
    11/01/2019-04/26/2016

    The seminar on geometric analysis will be held on Tuesdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule can be found below. Titles will be added as they are provided.

    DayNameTitle
    09-08-2015Binglong ChenOn the geometry of complete positively curved Kahler manifolds
    09-15-2015Hongwei XuMean Curvature Flow and Sphere Theorem
    09-22-2015Teng FeiSome new solutions to the Strominger system
    09-29-2015Xuqian FanThe Steklov eigenvalues on annuli
    10-06-2015Binglong ChenRicci flow and the moduli spaces of positive isotropic curvature metrics on four-manifolds
    10-13-2015Pengfei GuanIsometric embeddings of $(S^2,g)$ to general warped product space $(N^3,\bar g)$.
    10-20-2015Ovidiu SavinSmoothness of the eigenfunction for the Monge-Ampere equation
    10-27-2015Tom IlmanenFlow of curves by curvature in R^n
    11-03-2015Tom Hou (Caltech)Existence and stability of self-similar singularities for a 1D model of the 3D axisymmetric Euler equations
    11-10-2015Jerome Darbon (9:30am-10:30am) Adam Jacob (10:30am-11:30am)On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton-Jacobi Equations(1,1) forms with specified Lagrangian phase
    11-17-2015Ovidiu SavinExamples of singular minimizers in the calculus of variations
    11-24-2015Hongwei XuMean curvature flow meets Ricci flow:  Convergence and sphere theorems of sub manifolds arising from Yau rigidity theory
    12-01-2015Tom Ilmanen
    01-26-2016Mao ShengUniformization of p-adic curves
    02-02-2016Yi ZhangHodge Bundles on Smooth Compactifications of Siegel Varieties
    02-09-2016Valentino TosattiNon-Kahler Calabi-Yau manifolds
    02-16-2016Camillo De LellisApproaching Plateau’s problem with minimizing sequences of sets
    02-23-2016Junbin LiConstruction of black hole formation spacetimes
    03-01-2016Ben WeinkoveMonge-Ampere equations and metrics on complex manifolds
    03-08-2016Albert ChauSurvey on Kahler Ricci flow on non-negatively curved non-compact manifolds
    03-15-2016Spring Break 
    03-22-2016Richard Schoen (Standford)The geometry of eigenvalue extremal problems
    03-29-2016Piotr ChruscielMass of characteristic surfaces
    04-05-2016 (Room 232, Science Center)Niky Kamran, McGill UniversityNon-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets
    04-12-2016Connor Mooney, UT AustinFinite time blowup for parabolic systems in the plane
    04-19-2016 (Room 232, Science Center)Xu-Jia WangBoundary behaviour of solutions to singular elliptic equations
    04-26-2016Andre NevesA path to Yau’s conjecture
  • Seminars

    Seminars Colloquia & Seminar
    13/3/2018 Topology Seminar

    10:00 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/22/2018 Topology Seminar

    10:00 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/18/2019 General Relativity

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/24/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/10/18 Topology Seminar

    10:30 am-12:00 am
    11/01/2019-09/11/2018
  • Seminars
    10:30 am-11:42 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/26/2019 Topology

    10:30 am-12:40 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/16/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/11/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/13/2019 General Relativity

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/25/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/18/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars
    10:30 am-12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/20/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars
    10:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/9/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    11/1/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/30/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/2/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/1/2020 Quantum Matter seminar

    10:30 am-12:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-02-2016 Random Matrix & Probability Theory Seminar

    10:32 am
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    10:36 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-07-16 Mathematical Physics Seminar

    10:38 am
    11/01/2019

    No additional detail for this event.

  • Special Seminar

    Special Seminar
    11-04-16 Special Seminar

    10:42 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    10:43 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-09-2016 Random Matrix & Probability Theory Seminar

    10:44 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    10:46 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    10:56 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    10:57 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-14-16 Mathematical Physics Seminar

    10:58 am
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
  • General Relativity Seminar
  • Seminars

    Seminars Colloquia & Seminar
    02-09-2018 Mirror Symmetry Seminar

    11:00 am
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-16-2016 Random Matrix & Probability Theory Seminar

    11:00 am
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/19/2018 Mirror Symmetry Seminar

    11:00 am-11:00 pm
    11/01/2019
  • General Relativity Seminar
  • General Relativity Seminar
  • Seminars

    Seminars Colloquia & Seminar
    2-16-2018 Mirror Symmetry Seminar

    11:00 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2-23-2018 Mirror Symmetry Seminar

    11:00 am
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3-2-2018 Mirror Symmetry Seminar

    11:00 am-12:00 am
    11/01/2019-03/03/2018
  • General Relativity Seminar
  • Seminars

    Seminars Colloquia & Seminar
    4-13-2018 Mirror Symmetry Seminar

    11:00 am-12:00 am
    11/01/2019-04/14/2018
  • Member Seminar
    11:01 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-21-16 Mathematical Physics Seminar

    11:02 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:03 am-11:04 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    11:03 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:04 am
    11/01/2019

    The  CMSA Colloquium will take place every Wednesday from 4:30-5:30pm in CMSA Building, 20 Garden Street, G10.

    Spring 2020

    DateSpeakerTitle/Abstract
    1/29/2020David Yang (Harvard)

    Abstract: Data-intensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in data-intensive economies: first, states are key collectors and repositories of data; second, data is a non-rival input in innovation. We document the importance of state-collected data for innovation using comprehensive data on Chinese facial recognition AI firms and government contracts. Firms produce more commercial software and patents, particularly data-intensive ones, after receiving government public security contracts. Moreover, effects are largest when contracts provide more data. We then build a directed technical change model to study the state’s role in three applications: autocracies demanding AI for surveillance purposes, data-driven industrial policy, and data regulation due to privacy concerns. When the degree of non-rivalry is as strong as our empirical evidence suggests, the state’s collection and processing of data can shape the direction of innovation and growth of data-intensive economies.

    2/5/2020Scott Aaronson (UT Austin)

    Video

    Title: Gentle Measurement of Quantum States and Differential Privacy

    Abstract: I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography”
    of quantum states (that is, answering a large number of questions about a quantum state given few copies of it).

    Based on joint work with Guy Rothblum (arXiv:1904.08747)

    2/12/2020Scott Kominers (Harvard)Title: A Compact, Logical Approach to Large-Market Analysis

    Abstract: In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

    2/19/2020Peter Shor (MIT)Title: Quantum Money from Lattices

    Abstract: Quantum money is  a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.

    2/26/2020Daneil Wise (McGill)Title: The Cubical Route to Understanding Groups

    Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds and simultaneously dramatically extended our understanding of many infinite groups.
    3/4/2020

    4:45 – 5:45pm

    Salil Vadhan (Harvard)Title: Derandomizing Algorithms via Spectral Graph Theory

    Abstract: Randomization is a powerful tool for algorithms; it is often easier to design efficient algorithms if we allow the algorithms to “toss coins” and output a correct answer with high probability. However, a longstanding conjecture in theoretical computer science is that every randomized algorithm can be efficiently “derandomized” — converted into a deterministic algorithm (which always outputs the correct answer) with only a polynomial increase in running time and only a constant-factor increase in space (i.e. memory usage).

    In this talk, I will describe an approach to proving the space (as opposed to time) version of this conjecture via spectral graph theory. Specifically, I will explain how randomized space-bounded algorithms are described by random walks on directed graphs, and techniques in algorithmic spectral graph theory (e.g. solving Laplacian systems) have yielded deterministic space-efficient algorithms for approximating the behavior of such random walks on undirected graphs and Eulerian directed graphs (where every vertex has the same in-degree as out-degree). If these algorithms can be extended to general directed graphs, then the aforementioned conjecture about derandomizing space-efficient algorithms will be resolved.

    3/11/2020

    Postponed

    Jose Scheinkman

    (Columbia)

    This colloquium will be rescheduled at a later date. 

    Title: Menu Costs and the Volatility of Inflation

    Abstract: We present a state-dependent equilibrium pricing model that generates inflation rate fluctuations from idiosyncratic shocks to the cost of price changes of individual firms.  A firm’s nominal price increase lowers other firms’ relative prices, thereby inducing further nominal price increases. We first study a mean-field limit where the equilibrium is characterized by a variational inequality and exhibits a constant rate of inflation. We use the limit model to show that in the presence of a large but finite number n of firms the snowball effect of repricing causes fluctuations to the aggregate price level  and these fluctuations converge to zero slowly as n grows. The fluctuations caused by this mechanism are larger when the density of firms at the repricing threshold is high, and the density at the threshold is high when the trend inflation level is high. However a calibration to US data shows that this mechanism is quantitatively important even at modest levels of trend inflation and  can account for the positive relationship between inflation level and volatility that has been observed empirically.

    3/12/2020

    4:00 – 5:00pm

    Daniel Forger (University of Michigan)This meeting will be taking place virtually on Zoom.

    Title: Math, Music and the Mind; Mathematical analysis of the performed Trio Sonatas of J. S. Bach

    Abstract: I will describe a collaborative project with the University of Michigan Organ Department to perfectly digitize many performances of difficult organ works (the Trio Sonatas by J.S. Bach) by students and faculty at many skill levels. We use these digitizations, and direct representations of the score to ask how music should encoded in the mind. Our results challenge the modern mathematical theory of music encoding, e.g., based on orbifolds, and reveal surprising new mathematical patterns in Bach’s music. We also discover ways in which biophysical limits of neuronal computation may limit performance.

    Daniel Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan. He is also a visiting scholar at Harvard’s NSF-Simons Center and an Associate of the American Guild of Organists.

    3/25/2020Cancelled
    4/1/2020Mauricio Santillana (Harvard)This meeting will be taking place virtually on Zoom.

    Title: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring

    Abstract: I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.

    4/8/2020Juven Wang (CMSA)This meeting will be taking place virtually on Zoom.

    Title: Quantum Matter Adventure to Fundamental Physics and Mathematics (Continued)

    Abstract: In 1956, Parity violation in Weak Interactions is confirmed in particle physics. The maximal parity violation now is a Standard Model physics textbook statement, but it goes without any down-to-earth explanation for long. Why? We will see how the recent physics development in Quantum Matter may guide us to give an adventurous story and possibly a new elementary
    explanation.  We will see how the topology and cobordism in mathematics may come into play of anomalies and non-perturbative interactions in
    fundamental physics. Perhaps some of you (geometers,  string theorists, etc.) can team up with me to understand the “boundary conditions” of the Standard Model and Beyond

    4/15/2020
    Lars Andersson (Max-Planck Institute for Gravitational Physics)
    This meeting will be taking place virtually on Zoom.

    Title: Stability of spacetimes with supersymmetric compactifications

    Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and Shing-Tung Yau.

    4/22/2020William Minicozzi (MIT)This meeting will be taking place virtually on Zoom.

    Title: Mean curvature flow in high codimension

    Abstract: I will talk about joint work with Toby Colding on higher codimension mean curvature flow.  Some of the ideas come from function theory on manifolds with Ricci curvature bounds.

    4/29/2020Gerhard Huisken (Tübingen University / MFO)This meeting will be taking place virtually on Zoom.

    Title: Mean curvature flow of mean-convex embedded 2-surfaces in 3-manifolds

    Abstract: The lecture describes joint work with Simon Brendle on the deformation of embedded surfaces with positive mean curvature in Riemannian 3-manifolds in direction of their mean curvature vector. It is described how to find long-time solutions of this flow, possibly including singularities that are overcome by surgery, leading to a comprehensive description of embedded mean-convex surfaces and the regions they bound in a 3-manifold. The flow can be used to sweep out the region between space-like infinity and the outermost horizon in asymptotically flat 3-manifolds arising in General Relativity. (Joint with Simon Brendle.)

    5/6/2020Lydia Bieri (UMich)This meeting will be taking place virtually on Zoom.

    Title: Energy, Mass and Radiation in General Spacetimes

    Abstract: In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. Isolated gravitating systems such as binary stars, black holes or galaxies can be described in GR by asymptotically flat (AF) solutions of these equations. These are solutions that look like flat Minkowski space outside of spatially compact regions. There are well-defined notions for energy and mass for such systems. The energy-matter content as well as the dynamics of such a system dictate the decay rates at which the solution tends to the flat one at infinity. Interesting questions occur for very general AF systems of slow decay. We are also interested in spacetimes with pure radiation. In this talk, I will review what is known for these systems. Then we will concentrate on spacetimes with pure radiation. In particular, we will compare the situations of incoming radiation and outgoing radiation under various circumstances and what we can read off from future null infinity.

    5/13/2020Mikhail Lukin (Harvard)

    Video

    This meeting will be taking place virtually on Zoom.

    Title: Exploring New Frontiers of Quantum Science with Programmable Atom Arrays

    Abstract: We will discuss recent work at a new scientific interface between  many-body physics and quantum information science. Specifically, we will  describe the advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Within this system we performed quantum simulations of one dimensional spin models, discovered a new type of non-equilibrium quantum dynamics associated with the so-called many body scars and created large-scale entangled states. We will also describe the most recent developments that now allow the control over 200 atoms in two-dimensional arrays.   Ongoing efforts  to study exotic many-body phenomena and to realize and test quantum optimization algorithms within such systems will be discussed.

    5/20/2020This meeting will be taking place virtually on Zoom.

    Fall 2019

    DateSpeakerTitle/Abstract
    9/18/2019Bill Helton (UC San Diego)Title:  A taste of noncommutative convex algebraic geometry

    Abstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example,

    ◦ A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials.

    ◦ A convex NC semialgebraic set has a linear matrix inequality representation.

    ◦ The natural Nullstellensatz are falling into place.

    The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019.

    9/25/2019Pavel Etingof (MIT)

     

    Title: Double affine Hecke algebras

    Abstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications.

    10/2/2019Spiro Karigiannis (University of Waterloo)Title: Cohomologies on almost complex manifolds and their applications

    Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.

    10/9/2019Hans Lindblad (Johns Hopkins University)Title:  Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition

     

    Abstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition  satisfy the preserved wave coordinate condition.

     

    Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times.

    John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas  lainerman came up with the ‘null condition’, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition.

    Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition.

    Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to afraction and has now been used to prove global existence also with matter fields.

    Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equationsbackwards to obtain global solutions with given data at infinity.

    10/16/2019Aram Harrow (MIT)

    Video

    Title: Monogamy of entanglement and convex geometry

    Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems.

    10/23/2019No talk
    10/30/2019Nima Arkani-Hamed (IAS)

    Video

    Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity
    11/6/2019Kevin Costello (Perimeter Institute)

    Video

    Title: A unified perspective on integrability

     

    Abstract: Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics.   I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu.

    11/13/2019Heather  Harrington (University of Oxford)Title:  Algebra, Geometry and Topology of ERK Enzyme Kinetics

    Abstract: In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

    11/20/2019Xi Yin (Harvard)

    Video

    Title: An Introduction to the Non-Perturbative Bootstrap

    Abstract: I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap

    11/25/2019

    Monday

    Madhu Sudan (Harvard)
    Abstract: The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits.

    In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction.

    Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard).

    12/4/2019Xiao-Gang Wen (MIT)
    Video
    Title: Emergence of graviton-like excitations from a lattice model

    Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases.

    2018-2019

    DateSpeakerTitle/Abstract
    9/26/2018Xiao-Gang Wen (MIT)Title: A classification of low dimensional topological orders and fully extended TQFTs

    Abstract: In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1-dimension, there is no non-trivial topological orders. In 2-dimensions, the topological orders are classified by modular tensor category theory. In 3-dimensions, the topological orders are classified by a simple class of braided fusion 2-categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs.

    10/03/2018Richard Schoen (Stanford)Title: Perspectives on the scalar curvature

    Abstract: This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied.

    10/10/2018Justin Solomon (MIT)Title: Correspondence and Optimal Transport for Geometric Data Processing

    Abstract: Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make large-scale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometrically-structured data.

    10/17/2018Jeremy England (MIT)Title: Wisdom of the Jumble

    Abstract: There are certain, specific behaviors that are particularly distinctive of life. For example, living things self-replicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of life-like phenomena in a wide range of messy systems made of many interacting components.

    In this talk I will discuss some of the recent insights we have gleaned from studying emergent fine-tuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more life-like ways of computing that have the potential to either be cheaper or more powerful than existing means.

    10/31/2018Moon Duchin (Tufts)Title: Exploring the (massive) space of graph partitions

    Abstract: The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts).  I’ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics.

    11/14/2018Dusa McDuff (Columbia)Title: The virtual fundamental class in symplectic geometry

    Abstract: Essential to many constructions and applications of symplectic  geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well  understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so  that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there  are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a  construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim.

    11/19/2018Xiaoqin Wang (Johns Hopkins)Title: Computational Principles of Auditory Cortex

    Abstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication.

    11/28/2018Robert Haslhofer (University of Toronto)Title: Recent progress on mean curvature flow

    Abstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanen’s multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits.

    12/5/2018Robert McCann (University of Toronto)Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity

    Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of  probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics.

    Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf

    12/12/2018Zhiwei Yun (MIT)Title: Shtukas: what and why

    Abstract: This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them.

    1/30/2019Richard Freeman (Harvard)Title:  Innovation in Cell Phones in the US and China: Who Improves Technology Faster?

    Abstract:  Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps.  Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones.  Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality.  The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being.

    2/7/2019

    *Thursday*

    Ulrich Mueller (Princeton)Title: Inference for the Mean

    Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.

    2/13/2019Christian Santangelo (UMass Amherst)Title: 4D printing with folding forms

    Abstract: 4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target three-dimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our group’s efforts to understand and design structures that can fold from an initially flat sheet to target three-dimensional shapes. After reviewing the state-of-the-art in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome.

    2/20/2019Michael Woodford (Columbia)Title: Optimally Imprecise Memory and Biased Forecasts

    Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings.

    [authors: Rava Azeredo da Silveira (ENS) and Michael Woodford (Columbia)]

    2/27/2019

    2:30pm

    Ian Martin (LSE)Title: Sentiment and Speculation in a Market with Heterogeneous Beliefs

    Abstract: We present a dynamic model featuring risk-averse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so “the market” is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou]

    3/6/2019

    2:30pm

    Philippe Sosoe (Cornell)Title:  A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation

    Abstract:  In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS’s result, and discuss a sharp transition in the construction of the Gibbs-type invariant measures considered by these authors.  (Joint work with Tadahiro Oh and Leonardo Tolomeo)

    3/13/2019

    5:15pm

    Greg Galloway (University of Miami)Title:  On the geometry and topology of initial data sets in General Relativity

    Abstract:  A theme of long standing interest (to the speaker!)  concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness).  Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple.  The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces,  which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack.

    3/20/2019Sonia Jaffe (Microsoft)Title:  Quality Externalities on Platforms:  The Case of Airbnb

    Abstract:  We explore quality externalities on platforms:  when buyers have limited information, a seller’s quality affects whether her buyers return to the platform, thereby impacting other sellers’ future business.  We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller’s customers to return to the platform.  We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higher-GRP sellers, platforms may be able to increase overall seller surplus.  (Joint work with Peter Coles, Steven Levitt, and Igor Popov.)

    3/27/2019

    5:15pm

    Tatyana Sharpee (Salk Institute for Biological Studies)Title: Hyperbolic geometry of the olfactory space.

    Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their co-occurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical tree-like networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

    4/3/2019

    2:30pm

    Sarah Moshary (Chicago Booth)Title:  Deregulation through Direct Democracy:  Lessons from Liquor

    Abstract:  This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool.

    4/10/2019

    2:30pm

    Pietro Veronesi (Chicago Booth)Title: Inequality Aversion, Populism, and the Backlash Against Globalization

    Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model.

    Paper

    Online Appendix

    4/17/2019Yi-Zhuang You (UCSD)Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

    Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

    .

    [1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103

    [2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804

    [3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223

    4/24/2019Shengwu Li (Harvard)
    Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.
    Date…………SpeakerTitle
    02-09-2018 *Friday       Fan Chung

    (UCSD)

    Sequences: random, structured or something in between

    There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns;

    testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems.

    02-14-2018Zhengwei Liu

    (Harvard Physics)

    A new program on quantum subgroups

    Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing.

    02-21-2018Don Rubin

    (Harvard)

    Essential concepts of causal inference — a remarkable history

    Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis.

    02-26-2018 *MondayTom Hou

    (Caltech)

    Computer-assisted analysis of singularity formation of a regularized 3D Euler equation

    Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate self-similar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate self-similar solution, which implies the existence of the finite time blow-up of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu.

    03-07-2018Richard Kenyon

    (Brown)

    Harmonic functions and the chromatic polynomial

    Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam.

    03-14-2018
    03-21-2018
    03-28-2018Andrea Montanari (Stanford)A Mean Field View of the Landscape of Two-Layers Neural Networks

    Abstract: Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD).  Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties?

    We consider a simple case, namely two-layers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to `average-out’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well.
    [Based on joint work with Song Mei and Phan-Minh Nguyen]

    03-30-2018
    04-04-2018Ramesh Narayan 

    (Harvard)

    Black Holes and Naked Singularities

    Abstract: Black Hole solutions in General Relativity contain Event Horizons and
    Singularities. Astrophysicists have discovered two populations of
    black hole candidates in the Universe: stellar-mass objects with
    masses in the range 5 to 30 solar masses, and supermassive objects
    with masses in the range million to several billion solar
    masses. There is considerable evidence that these objects have Event
    Horizons. It thus appears that astronomical black hole candidates are
    true Black Holes. Direct evidence for Singularities is much harder to
    obtain since, at least in the case of Black Holes, the Singularities
    are hidden inside the Event Horizon. However, General Relativity also
    permits Naked Singularities which are visible to external
    observers. Toy Naked Singularity models have been constructed, and
    some observational features of accretion flows in these spacetimes
    have been worked out.

    04-11-2018Pablo Parrilo

    (MIT)

    Graph Structure in Polynomial Systems: Chordal Networks

    Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).

    04-18-2018Washington Taylor

    (MIT)

    On the fibration structure of known Calabi-Yau threefolds

    Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds.

    04-25-2018 Xi Yin

    (Harvard)

    How we can learn what we need to know about M-theory

    Abstract: M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory.

    05-02-2018
    05-09-2018

    2016-2017

    DateNameTitle/Abstract
    01-25-17Sam Gershman, Harvard Center for Brain Science, Department of Psychology

    Title: Spectral graph theory of cognitive maps

    Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory.

    02-01-17Sean Eddy, Harvard Department of Molecular and Cellular Biology

    Sean_Eddy

    Title: Biological sequence homology searches: the future of deciphering the past 

    Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK.

    02-08-17Matthew Headrick, Brandeis University

    matthew_headrick

    Title: Quantum entanglement, classical gravity, and convex programming: New connections

    Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differential-geometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way.

    02-15-17Masahito Yamazaki, IMPU

    Masahito Yamazaki

     Title: Geometry of 3-manifolds and Complex Chern-Simons Theory

    Abstract: The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras.

    Video

    02-22-17Steven Rayan, University of Saskatchewan

    Title: Higgs bundles and the Hitchin system

    Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics.  As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence.  From this point of view, the Hitchin map and spectral curves emerge.  We’ll use these to form an impression of what the moduli space “looks like”.  I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry.

    Video

    03-01-17Jun Liu, Harvard University

    Jun liu

    Title: Expansion of biological pathways by integrative Genomics

    Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays.

    Based on the joint work with Yang Li and the Vamsi Mootha lab.

    Video

    03-08-17Gabor Lippner, Northeastern University

    ---

    Title: Evolution of cooperation in structured populations

    Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics.  Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies.  It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution.

    In this talk I will present new results about the model where the population is represented by an interaction network.  We study the likelihood of a random mutation spreading through the entire population.  The main question is to understand how the network influences this likelihood.  After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks.
    03-15-17 Spring Break: No session
    03-22-17Gunther Uhlmann, University of Washington

    guntherUhlman

    Abstract We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of
    waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others.
    The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.
    We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.
    03-29-17Leslie Greengard, Courant InstituteLeslie_GreengardTitle: Inverse problems in acoustic scattering and cryo-electron microscopy

    Abstract: A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy.

    NOTE: This talk will begin at 4:00pm

    04-05-17Gongjie Li, Harvard University

    GongjieLi

    Title: Unveiling the Origin of Planetary Systems by Dynamical and Statistical Approaches

    Abstract: The unexpected diversity of observed extrasolar planetary systems has posed new challenges to our classical understanding of planetary formation. A lot of these challenges can be addressed by a deeper understanding of the dynamics in planetary systems, which will also allow us to construct more accurate planetary formation theories consistent with observations. In this talk, I will first explain the origin of counter orbiting planets using a new dynamical mechanism I discovered, which also has wide implications in other astrophysical systems, such as the enhancement of tidal disruption rates near supermassive black hole binaries. In addition, I will discuss the architectural properties of circumbinary planetary systems from selection biases using statistical methods, and infer the origin of such systems.

    Video

    04-12-17Shlomo Razamat, Israel Institute of Technology

    ShlomoRazamat

    Title: Complicated four-dimensional physics and simple mathematics

    Abstract: We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index,  of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of Ruijsenaars-Schneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven.

    Video

    04-19-17Cumrun Vafa, Harvard University

    CumrunVafa

    Title: String Swampland

    Abstract: In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a no-go theorem for non-supersymmetric AdS/CFT holography.

    04-27-17Mehran Kardar, MIT

    MehranKardar

    Title: Levitation by Casimir forces in and out of equilibrium

    Abstract: Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw’s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint.

    Note: This talk will begin at 3:00pm

    05-02-17Simona Cocco, Laboratoire de Physique Statistique de l’ENSTitle: Reverse modeling of protein sequence data: from graphical models to structural and functional predictions

    Body: A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing
    similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models
    have led to substantial progress in protein structural and functional
    predictions.

    Note:  This talk will begin at 4:00pm

    05-03-17Xue-Mei Li, University of WarwickTitle: Perturbation to conservation law and stochastic averaging

    Abstract: A deterministic or random system with a conservation law is often used to
    approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces.

    Note: This talk will be held in the Science Center, Room 507

    05-10-17
    05-17-17Kwok Wai Chan, Chinese University of Hong KongTitle: Scattering diagrams from asymptotic analysis on Maurer-Cartan equations

    Abstract:  In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on Maurer-Cartan equations. In this talk, I will explain some results which implement part of Fukaya’s program. More precisely, I will show how semi-classical limits of Maurer-Cartan solutions give rise naturally to consistent scattering diagrams, which are known to encode Gromov-Witten data on the mirror side and have played an important role in the works of Kontsevich-Soibelman and Gross-Siebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015).

    05-24-17 NO COLLOQUIUM
    05-31-17Peter Michor, University of Vienna

     Title: Geometry of shape spaces and diffeomorphism groups and some of their uses

    Abstract: This talk is devoted to shape spaces, Riemannian metrics on them, their geodesics and distance functions, and some of their uses, mainly in computational anatomy. The simplest Riemannian metrics have vanishing geodesic distance, so one has to use, for example, higher order Sobolev metrics on shape spaces. These have curvature, which complicates statistics on these spaces.

    DateNameTitle
    09-09-16

    Bong Lian, Brandeis

    portrait

    Title: Riemann-Hilbert Problem and Period Integrals

    Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems.

    09-14-16Sze-Man Ngai, Georgia Southern UniversityngaiTitle: The multifractal formalism and spectral asymptotics of self-similar measures with overlaps

    Abstract: Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum.  The asymptotic behavior of the eigenvalue counting function for the associated  Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results.

    09-21-16Prof. L. Mahadevan, Harvard SEAS

    Mahadevan_200x300

    Title: “Morphogenesis: Biology, Physics and Mathematics”

    Abstract:  A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology.  Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains.  I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology.

    09-28-16Hong Liu, MIT

    liu_hong

    Title: A new theory of fluctuating hydrodynamics

    Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate  for capturing  fluctuations.  In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure.

    We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular,  the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations.

    Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anti-commuting variables and the theory exhibits an emergent supersymmetry.

    10-05-16

    Alexander LogunovTel-Aviv University

    alex

    Title: Zeroes of harmonic functions and Laplace eigenfunctions

     Abs: Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete.

    10-12-16 Conan Nai Chung Leung, CUHK

    conan_profile

    Title:  Coisotropic A-branes and their SYZ transform

    Abstract: “Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit.”

    10-19-16Vaughan Jones, UC Berkeley

    vj6

    Title: Are the Thompson groups any good as a model for Diff(S^1)?

    Abstract. The Thompson groups are by definition groups of piecewise linear
    diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can
    be conjugated to a group of smooth diffeomorphisms. That’s the good news.
    The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any
    procedure analogous to the constructions of the central extension of Diff(S^1)?
    I will define all the players in this game, explain this question in detail,and present some failed attempts to answer it.

     10-26-16

    Henry Cohn, Microsoft

    ????????????????????????????????????

    Sums of squares, correlation functions, and exceptional geometric structures

    Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding.  How can we understand and prove their optimality?  In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems.

    11-02-16

    Christian Borgs, Microsoft

    Borgs

    Title:  Graphon processes and limits of   sparse graph sequences

    Abstract:  The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for so-called exchangeable random graphs.   Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection.  While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model.  

    In this talk I describe a new model, where the underlying probability space is replaced by a sigma-finite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits.  The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life.

    11-09-16

    TIME CHANGE: 4PM

    Norden E. HuangNational Central University, (Taiwan)

    member1_clip_image003

    Title: On Holo-Hilbert Spectral Analysis

    Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation.

    11-16-16Tristan Collins, Harvard University

    image

    TIME CHANGE: 3:30PM

    Title: Restricted volumes and finite time singularities of the Kahler-Ricci flow

    Abstract:  I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow.  This is joint work with Valentino Tosatti.

    11-22-16 TUESDAY

    TIME CHANGE: 4-5PM

    Xiangfeng Gu, Stonybrook

    Title: Differential Geometric Methods for Engineering Applications

    Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation.

    11-30-16

    TIME CHANGE: 4:20PM

    Sharad Ramanathan, Harvard MCB & SEAS

    Ramanathan.Sharad_200x300

    Title: Finding co-ordinate systems to monitor the development of mammalian embryos
     12-07-16

    Valentino Tosatti, Northwestern

    Title: Metric limits of hyperkahler manifolds

    Abstract: I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang.

     12-14-16

    2015-2016

    DateNameTitle
    09-02-2015Madhu SudanRobust low-degree testing
    09-09-2015Mithat Unsal
    What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
    09-16-2015Subir SachdevBekenstein-Hawking entropy and strange metals
    09-23-2015Felix FinsterLinear hyperbolic equations in a rotating black hole geometry
    09-30-2015Leslie ValiantHolographic Algorithms
    10-07-2015Christopher RoganExploring the Frontier of Size and Energy with the Large Hadron Collider: sub-atomic particles, the Higgs Boson and beyond
    10-14-2015Boaz Barak, Harvard SEASConvexity, Bayesianism, and the quest towards Optimal Algorithms
    10-21-2015Zhouping XinEntropy and Uniqueness of Weak Solutions to The Multi-Dimensional Compressible Euler Systems
    10-28-2015Cristopher MooreStatistical inference, statistical physics, and the community detection problem
    11-04-2015Tom HouBlowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations
    11-11-2015Stan Osher, UCLAOvercoming the curse of dimensionality for certain Hamilton-Jacobi (HJ) equations arising in control theory and elsewhere
    11-18-2015Xiaole Shirley LiuInference of transcriptional regulation in cancers
    11-25-2015ThanksgivingNo seminar
    12-02-2015Scott KominersGeneralized Matching Market Design: Theory and Practice
    12-09-2015Matthew HolmanDynamical Chaos in Kepler Planetary Systems
    01-27-2016Conan LeungSome modern aspects of Morse theory 
    02-03-2016Camillo De LellisFrom Nash to Onsager, funny coincidences across differential geometry and the theory of turbulence
    02-10-2016Chun Peng Wang
    02-17-2016Samuel Kou, Harvard StatisticsBig data, Google and disease detection: the statistical story
    02-24-2016Dan Xie, Harvard CMSASingularity theory and supersymmetric field theory
    03-02-2016Lydia BieriMathematical General Relativity
    03-09-2016Piotr ChruscielThe mathematics of gravitation
    03-16-2016Spring BreakNo Talk
    03-23-2016Richard Freeman, Harvard EconomicsPulling Apart of Wages and Productivity: why “identical” workers have increasingly different pay and productivity.
    03-30-2016David Garfinkel, Oakland UniversityGravitational Wave Memory
    04-04-2016 (Hall A, Science Center)Xianfeng David Gu, Stony Brook UniversityA Discrete Variational Approach for Solving Monge-Ampere Equation
    04-06-2016Lars Hernquist, HarvardNext Generation Cosmological Simulations: Galaxy Assembly and Evolution
    04-13-2016Jun Zhang, Univ. of Michigan-Ann ArborKahler and Para-Kahler Structure in Information Geometry
    04-20-2016Sijue Wu, Univ. of MichiganOn two dimensional gravity water waves with angled crests
    04-27-2016Paul Seidel, MITTopological quantum field theory and the Gauss-Manin connection
    05-04-2016Hirosi Ooguri, CaltechString Theory And Its Applications in Mathematics and Physics
    05-11-2016      (4pm – 5pm)Juerg Froehlich, ETH and IASImplications of the Chiral Anomaly – From the Quantum Hall Effect to Topological Insulators and Out to Space
  • Colloquium
    11:05 am-11:06 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:07 am-11:08 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:08 am-11:09 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-22-2016 Random Matrix & Probability Theory Seminar

    11:12 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-07-2016 Random Matrix & Probability Theory Seminar

    11:16 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12-05-16 Mathematical Physics Seminar

    11:17 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:21 am-11:22 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    11:21 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-14-2016 Random Matrix & Probability Theory Seminar

    11:22 am
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    11:24 am
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    11:25 am
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Learning from health data in the million genome era
    11:26 am
    11/01/2019

    On November 12019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system.

    Speakers: 

    • Heidi Rehm, Ph.D.
      Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform.
    • Saiju Pyarajan, Ph.D.
      Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS
    • Tianxi Cai, Sci.D
      John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health
    • Susan Redline, M.D., M.P.H
      Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center
    • Avinash Sahu, Ph.D.
      Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health
    • Peter J. Park, Ph.D.
      Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School
    • David Roberson
      Community Engagement Manager, Seven Bridges

    Registration & Schedule

  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 Quantum Field Theory Seminar

    11:30 am-12:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    01-30-2017 Mathematical Physics Seminar

    11:30 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    11:32 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    02-06-2017 Mathematical Physics Seminar

    11:33 am
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    02-13-2017, Mathematical Physics Seminar

    11:34 am
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    11:35 am
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Spacetime and Quantum Mechanics Master Class Workshop
    11:36 am
    11/01/2019-10/30/2019
    Space-Time-poster-5

    As part of the program on Spacetime and Quantum Mechanics, Total Positivity and Motives, the CMSA will host a “Master Class Workshop”  on October 28-30, 2019. Each day of the workshop will feature an intensive full day of pedagogical lectures, with the aim of bringing actively interested but non-expert physicists and mathematicians up to speed on the featured topics.

    Everyone is welcome to attend the lectures.

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

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

    Photos of the event

    Organizers:

  • Member Seminar
    11:37 am
    11/01/2019

    Hansol Hong, Harvard

    Title: Homological Mirror Functors

    Abstract: I will first give a brief introduction to mirror symmetry, which intertwines symplectic geometry and complex geometry of a pair of Kahler manifolds, and explain mirror construction using formal deformation of a Lagrangian submanifold.  We will see that counting of holomorphic discs bounding Lagrangian naturally gives rise to a mirror space (Landau-Ginzburg model) and  a functor from Fukaya category to its mirror matrix factorization category. I will mainly focus on one specific example to give a concrete description of the construction.

  • Colloquium
    11:39 am-11:40 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:40 am-11:41 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    11:42 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:43 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:45 am
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/24/2019 Quantum Matter Seminar

    11:50 am-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/31/2019 Condensed Matter Seminar

    11:50 am-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/10/2019 Condensed Matter Seminar

    11:50 am-1:00 pm
    11/01/2019
  • CMSA EVENT: Quantum Information Workshop
    11:52 am-11:53 am
    11/01/2019
    Asset-6-600x338

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

    The CMSA will host a workshop on Quantum Information. This workshop will be held virtually using Zoom.

    The workshop on Quantum information is organized by Mikhail LukinHorng-Tzer Yau, and Norman Yao.

    More information to follow.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-12-2017 Random Matrix & Probability Theory Seminar

    11:56 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:56 am
    11/01/2019

    No additional detail for this event.

  • Colloquium
    11:58 am
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-22-2017 Random Matrix & Probability Theory Seminar

    11:58 am
    11/01/2019

    No additional detail for this event.

  • Seminars
    11:59 am
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    5/6/2019 Math Physics

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars
    12:00 pm-1:30 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/19/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12/3/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/8/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/29/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/26/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/25/2019 Fluid Dynamics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 Condensed Matter Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/5/2018 Math Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/7/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/22/2019 Math Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/29/2018 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/15/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/9/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    1/28/2018 Mathematical Physics Seminar

    12:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2/4/2019 Math Physics Seminar

    12:00 pm-2:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/25/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • General Relativity Seminar
    12:00 pm-1:00 pm
    11/01/2019

    The Seminar on General Relativity will take place every Wednesday from 12pm – 1pm in CMSA Building, 20 Garden Street, G10.

    The list of speakers is below and will be updated as details are confirmed.

    DateNameTitle
    04-06-2016Mihalis Dafermos (Princeton)The black hole stability problem: the inside story
    04-13-2016Felix Finster, University of RegensburgLinear stability of Kerr black holes
    04-20-2016Paul Chesler, Harvard PhysicsNumerical relativity in asymptotically anti-de Sitter spacetime
    04-27-2016Andy Strominger (Harvard Physics) & Mihalis Dafermos (Princeton University)The Scattering Problem in General Relativity
    05-04-2016Robert Penna, MITBMS invariance and the membrane paradigm
    05-11-2016Piotr T. Chruściel, University of ViennaGluing things in general relativity
    05-18-2016Achilleas Porfyriadis, Harvard PhysicsGravitational waves from the Kerr/CFT correspondence
    05-25-2016Scott Hughes, MITThe gravitational-wave event GW150914: What we learned, and how we learned it
  • Seminars

    Seminars Colloquia & Seminar
    3/4/2019 Mathematical Physics Seminar

    12:00 pm-2:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    1-5-2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Quantum Matter Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/28/2019 Math Physics

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/16/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-2-2018 Mathematical Physics Seminar

    12:00 pm-1:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2/25/2019 Math Physics Seminar

    12:00 pm-2:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/1/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2/11/2019 Mathematical Physics Seminar

    12:00 pm-2:00 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3/19/2018 Mathematical Physics Seminar

    12:00 pm-1:30 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-26-2018 Math Physics Seminar

    12:00 pm-1:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Condensed Matter Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/30/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-22-2017 Random Matrix & Probability Theory Seminar

    12:01 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:03 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Cosmic Road to New Physics
    12:04 pm
    11/01/2019
    The colourful star cluster NGC 3532

    The CMSA will host a 3-day workshop on cosmological signatures of fundamental physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

    The next decade will see a wealth of new cosmological data, which can lead to new insights for fundamental physics. This upcoming data will span the entire history of the cosmos, from the era prior to big-bang nucleosynthesis to the inner Galactic structure today, including the intervening eras of recombination and cosmic dawn. Often, beyond-standard-model (BSM) physics will leave imprints in more than one of these eras. Thus, it is timely to gather experts in BSM physics across the entire cosmic history to exchange ideas and develop joint and powerful probes of new physics. For this program, it will be crucial to have an overlap of particle physicists, astrophysicists and cosmologists. There are a number of tools and techniques being actively developed across these disciplines. The workshop aims to provide a platform for efficient exchange of these new ideas.

    The first day we will discuss sub-Galactic probes, including Gaia data and gravitational waves. The second day we will cover cosmological probes, such as the cosmic microwave background and the 21-cm line. The third day we will discuss early Universe probes, such as inflation and phase transitions. Every day the meeting will begin with a pedagogical blackboard talk plus an overview talk, followed by about 4 talks on more specific topics.

    Organizers:

    Scientific Advisory:

    Speakers: 

    CosmicRoad_Poster

  • Colloquium
    12:05 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:06 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:08 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:09 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar
    12:10 pm-1:10 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

     

    Speaker: Man-Wai Cheung

    Title: Compactification for cluster varieties without frozen variables of finite type

    Abstract: Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev–Borisov construction.

  • CMSA EVENT: 2019 Ding Shum Lecture
    12:11 pm
    11/01/2019
    DingShum-2019

    DSC_0468-e1568985499370

    On October 22, 2019, the CMSA will be hosting our third annual Ding Shum lecture. This year’s lecture will be a talk on “Election Security” by Ronald L. Rivest (MIT). The lecture will take place from 4:30-5:30pm in Science Center, Hall A.

    Ronald L. Rivest is an Institute Professor at the Massachusetts Institute of Technology. He is a member of the Electrical Engineering and Computer Science Department and the Computer Science and Artificial Intelligence Laboratory (CSAIL) and a founder of the Cryptography and Information Security research group within CSAIL. His research has been in the areas of algorithms, machine learning, cryptography, and election security, for which he has received multiple awards, including: the ACM Turing Award (with Adleman and Shamir), the BBVA Frontiers of Knowledge Award, National Inventor’s Hall of Fame membership, and the Marconi Prize.

    Prof. Rivest is also well-known as a co-author of the textbook “Introduction to Algorithms” (with Cormen, Leiserson, and Stein), and as a co-inventor of the RSA public-key cryptosystem (with Adleman and Shamir). He is a co-founder of RSA and of Verisign.He has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), in charge of the Security subcommittee. He is a member of the CalTech/MIT Voting Technology Project, on the Board of Verified Voting, and an advisor to the Electronic Privacy Information Center. Additionally, he has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), as a member of the CalTech/MIT Voting Technology Project, and as an advisor to the Electronic Privacy Information Center.

    Last year featured Eric Maskin, who spoke on “How to Improve Presidential Elections: the Mathematics of Voting.” The first Ding Shum lecture took place on October 10, 2017, featuring Leslie Valiant on “Learning as a Theory of Everything.”

    This event is made possible by the generous funding of Ding Lei and Harry Shum.

    DingShum-2019

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-1-2017 Random Matrix & Probability Seminar

    12:11 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Special Lecture Series on Donaldson-Thomas and Gromov-Witten Theories
    12:11 pm
    11/01/2019-04/19/2017

    From March 8 to April 19, the Center of Mathematical Sciences and Applications will be hosting a special lecture series on Donaldson-Thomas and Gromov-Witten Theories. Artan Sheshmani (QGM Aarhus and CMSA Harvard) will give eight talks on the topic on Wednesdays and Fridays from 9:00-10:30 am, which will be recorded and promptly available on CMSA’s Youtube Channel.

  • Colloquium
    12:12 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:13 pm-12:14 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2-27-2017 Mathematical Physics Seminar

    12:14 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-7-2017 Social Science Applications Forum

    12:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/13/2019 Special Seminar

    12:15 pm-1:05 pm
    11/01/2019
  • Colloquium
    12:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-8-2017 CMSA Special Lecture Series

    12:16 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Noncommutative Analysis, Computational Complexity, and Quantum Information
    12:19 pm
    11/01/2019-10/18/2019
    Noncommutative-Analysis-Poster-3

    On October 16-18, 2019 the CMSA will be hosting a workshop on Noncommutative Analysis, Computational Complexity, and Quantum Information.

    This workshop will focus on  linking three different rapidly developing areas: noncommutative real algebraic geometry (RAG), theory of computation and quantum information theory. This mix of overlapping but independently developing topics should lead to a stimulating flow of tools and important problems into several disciplines.  Given the different communities there will be an emphasis on tutorials and making the lectures broadly understandable.

    The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by Boaz Barak, Bill Helton, Pablo Parrilo, Tselil Schramm.

    Please register here

    Speakers:

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

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-8-2017 Random Matrix & Probability Theory Seminar

    12:21 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-6-2017 Mathematical Physics Seminar

    12:24 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    12:25 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-10-2017 Special Lecture Series

    12:27 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
    12:28 pm
    11/01/2019-05/05/2019
    1 Oxford Street, Cambridge MA 02138
    Differential Geometry, Calabi-Yau theory and General Relativity

    Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau

    On May 2-5, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the  Science Center, Lecture Hall C. 

    Organizers:

    • Horng-Tzer Yau (Harvard)
    • Wilfried Schmid (Harvard)
    • Clifford Taubes (Harvard)
    • Cumrun Vafa (Harvard)

    Speakers:

    • Lydia Bieri, University of Michigan
    • Tristan Collins, MIT
    • Simon Donaldson, Imperial College
    • Fan Chung Graham, UC San Diego
    • Nigel Hitchin, Oxford University
    • Jun Li, Stanford University
    • Kefeng Liu, UCLA
    • Chiu-Chu Melissa Liu, Columbia University
    • Alina Marian, Northeastern University
    • Xenia de la Ossa, Oxford University
    • Duong H. Phong, Columbia University
    • Richard Schoen, UC Irvine
    • Andrew Strominger, Harvard University
    • Nike Sun, MIT
    • Clifford Taubes, Harvard University
    • Chuu-Lian Terng, UC Irvine
    • Valentino Tosatti, Northwestern University
    • Karen Uhlenbeck, University of Texas
    • Cumrun Vafa, Harvard University
    • Mu Tao Wang, Columbia University
    • Edward Witten, IAS
    • Stephen Yau, Tsinghua University, P.R. China
  • Seminars

    Seminars Colloquia & Seminar
    3-21-2017 Social Science Applications Forum

    12:28 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:30 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-20-2017 Mathematical Physics Seminar

    12:30 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-5-2017 Random Matrix & Probability Theory Seminar

    12:31 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:32 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Conference on Algebraic Geometry, Representation theory and Mathematical Physics
    12:33 pm
    11/01/2019-05/01/2019

    From April 29 to May 1, 2019 the CMSA will be hosting a Conference on Algebraic Geometry, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.  

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

    List of registrants

    Videos

    Speakers: 

     

    Monday, April 29

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amWei Zhang, MITTitle: The arithmetic fundamental lemma for diagonal cycles

    Abstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization, the arithmetic Gan-Gross-Prasad conjecture, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions.  The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.

    10:00 – 10:30amBreak
    10:30 – 11:30amYuri Tschinkel, NYUTitle: Equivariant birational geometry and modular symbols

    Abstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).

    11:30 – 1:30pmLunch
    1:30 – 2:30pmAlexander Efimov, MoscowTitle: Torsionness for regulators of canonical extensions

    Abstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.

    2:30 – 3:00pmBreak
    3:00 – 4:00pmAmin Gholampour, MarylandTitle: Euler Characteristics of punctual quot schemes on threefolds

    Abstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F, n) and Quot(G,n), where Quot(-,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.

    4:00 – 4:30pmBreak
    4:30 – 5:30pmMaksym Fedorchuck, BCTitle:  Stability of one-parameter families of weighted hypersurfaces

    Abstract:  We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space.  The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions, and, if time permits, examples where this machinery can be used to produce birational models with good properties.  Joint work with Hamid Ahmadinezhad and Igor Krylov.

     

    Tuesday, April 30

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amBrendan Hassett, BrownTitle: Rationality for geometrically rational threefolds

    Abstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure, like smooth complete intersections of two quadrics.  (joint with Tschinkel)

    10:00 – 10:30amBreak
    10:30 – 11:30amDennis Gaitsgory, HarvardTitle: The Fundamental Local Equivalence in quantum geometric Langlands

    Abstract: The Fundamental Local Equivalence is statement that relates the q-twisted  Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its  dual is combinatorial, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra, which in itself is a geometric device that concisely encodes the root data.

    11:30 – 1:00pmLunch
    1:00- 2:00pmAndrei Negut, MITTitle: AGT relations in geometric representation theory

    Abstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces, and the goal is to connect them with the W-algebra of type gl_n.

    2:00 – 2:15pmBreak
    2:15 – 3:15pmDan Abramovich, BrownTitle: Resolution in characteristic 0 using weighted blowing up

    Abstract: Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved.

    Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop.

    We show that there is a functorial way to resolve varieties using \emph{weighted} blowings up, in the stack-theoretic sense. To an embedded variety $X \subset Y$ one functorially assigns an invariant $(a_1,\ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , \ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.

    This is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.

    3:15 – 3:30pmBreak
    3:30 – 4:30pmFedor Bogomolov, NYUTitle: On the base of a Lagrangian fibration for a compact hyperkahler manifold.

    Abstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of  Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.

    4:30 – 4:45pmBreak
    4:45 – 5:45pmDawei Chen, BCTitle: Volumes and intersection theory on moduli spaces of Abelian differentials

    Abstract: Computing volumes of moduli spaces has significance in many fields. For instance, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

     

    Wednesday, May 1

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amPavel Etingof, MITTitle: Short star-products for filtered quantizations

    Abstract: PDF

    This is joint work with Eric Rains and Douglas Stryker.

    10:00 – 10:30amBreak
    10:30 – 11:30amRoman Bezrukavnikov, MITTitle: Stability conditions and representation theory

    Abstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)
    and its relation to modular Lie algebra representations. I will also address a potential generalization of that picture
    to modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.

    11:30 – 11:45amBreak
    11:45 – 12:45pmQile Chen, BCTitle: Counting curves in critical locus via logarithmic compactification

    Abstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles, the non-compactness of the R-maps moduli makes such powerful torus action useless.

    In this talk, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action.

    This is a joint work with Felix Janda and Yongbin Ruan.

    12:45 – 2:30pmLunch
    2:30 – 3:30pmSi Li, TsinghuaTitle: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry

    Abstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.

    3:30 – 4:00pmBreak
    4:00 – 5:00pmLudmil Katzarkov, MoscowTitle: PDE’s non commutative  motives and HMS.

    Abstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir.  Geometry will be discussed.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-29-2017 Random Matrix & Probability Theory Seminar

    12:35 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-24-2017 Random Matrix & Probability Theory Seminar

    12:37 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-30-2017 CMSA Special Seminar

    12:38 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    03-27-2017 Mathematical Physics Seminar

    12:40 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:41 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-5-2017 Special Lecture Series

    12:42 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-7-2017 Special Lecture Series

    12:43 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:43 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-12-2017 Special Lecture Series

    12:44 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:45 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-14-2017 Special Lecture Series

    12:46 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-3-2017 Mathematical Physics Seminar

    12:50 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    12:51 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-12-2017 Social Science Applications Forum

    12:53 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Workshop on Mirror Symmetry and Stability
    12:55 pm
    11/01/2019-03/20/2019
    HMS-2019-1

    This three-day workshop will take place at Harvard University on March 18-20, 2019 in Science Center room 507. The main topic will be stability conditions in homological mirror symmetry. This workshop is funded by the Simons Collaboration in Homological Mirror Symmetry.

    Organizers: Denis Auroux, Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau, Bong Lian, Shing-Tung Yau, Jingyu Zhao

    Speakers:

    Dylan Allegretti (Sheffield)
    Tristan Collins (MIT)
    Naoki Koseki (Tokyo)
    Chunyi Li (Warwick)
    Jason Lo (CSU Northridge)
    Emanuele Macrì (NEU & IHES)
    Genki Ouchi (Riken iTHEMS)
    Pranav Pandit (ICTS)
    Laura Pertusi (Edinburgh)
    Jacopo Stoppa (SISSA)
    Alex Takeda (UC Berkeley)
    Xiaolei Zhao (UC Santa Barbara)

    More details will be added later.

    Visit the event page for more information. 

     

    HMS-2019-1

  • Colloquium
    12:55 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    12:57 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Simons Collaboration Workshop, April 5-7, 2018
    1:00 pm-6:00 pm
    11/01/2019-04/07/2018
    banner-image-1

    The CMSA will be hosting a three-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 5-7, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

    We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

    Confirmed Speakers:

  • Seminars

    Seminars Colloquia & Seminar
    4-11-2017 Social Science Applications Forum

    1:00 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    Combinatorics & Complexity Seminar, Fridays

    1:00 pm-4:00 pm
    11/01/2019

    The seminar on Combinatorics and Complexity will be held every Friday from 1:00-4:00pm in CMSA Building, 20 Garden Street, Room G10.

    The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

    Additional information on CMSA’s Combinatorics and Complexity program can be found here.

     

    DateNameTitle/Abstract
    09-08-17TBA
    09-15-2017TBA
    09-22-17TBA
    09-29-17TBA
    10-06-17 TBA
    10-13-2017TBA
    10-20-2017TBA
    10-27-2017TBA
    11-03-2017TBA
    11-10-2017TBA
    11-17-2017TBA
    11-24-2017TBA
    12-01-2017TBA
    12-08-2017 TBA
  • CMSA EVENT: Second Annual STAR Lab Conference
    1:01 pm-1:02 pm
    11/01/2019

    The second annual STAR Lab conference is running 10/29/-10/30/2015 at the Harvard Business School.  This event is co-sponsored by the Center of Mathematical Sciences and Applications.

    For more information, please consult the event’s website.

  • Colloquium
    1:02 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:07 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-10-2017 Mathematical Physics Seminar

    1:07 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-21-2015 Mathematical Physics Seminar

    1:09 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    1:10 pm-3:00 pm
    11/01/2019
  • Colloquium
    1:10 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    08-31-2015 Mathematical Physics Seminar

    1:10 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:11 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-01-2015 Differential Geometry Seminar

    1:12 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-12-2017 Random Matrix & Probability Theory Seminar

    1:12 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:13 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-01-2015 Evolution Equation Seminar

    1:13 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-14-2015 Mathematical Physics Seminar

    1:14 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-17-2017 Mathematical Physics Seminar

    1:14 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-18-2017 Social Science Applications Forum

    1:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-08-2015 Geometric Analysis Seminar

    1:16 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-06-2015 Geometric Analysis Seminar

    1:17 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:18 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-08-2015 Evolution Equations Seminar

    1:18 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:20 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:21 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    1:21 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-13-2015 Geometric Analysis Seminar

    1:22 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-19-2017 Random Matrix & Probability Theory Seminar

    1:22 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-10-2015 Evolution Equations Seminar

    1:23 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: 2016 Big Data Conference & Workshop
    1:24 pm
    11/01/2019-08/23/2016
    1 Oxford Street, Cambridge MA 02138

    ! LOCATION CHANGE: The conference will be in Science Center Hall C on Tuesday, Aug.23, 2016.

    The Center of Mathematical Sciences and Applications will be hosting a workshop on Big Data from August 12 – 21, 2016 followed by a two-day conference on Big Data from August 22 – 23, 2016.

    Big Data Conference features many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the second conference on Big Data the Center will host as part of our annual events. The 2015 conference was a huge success.

    The conference will be hosted at Harvard Science Center Hall A (Monday, Aug.22) & Hall C (Tuesday, Aug.23): 1 Oxford Street, Cambridge, MA 02138.

    The 2016 Big Data conference is sponsored by the Center of Mathematical Sciences and Applications at Harvard University and the Alfred P. Sloan Foundation.

    Conference Speakers:

    1. Jörn Boehnke, Harvard CMSA
    2. Joan Bruna, UC Berkeley [Video]
    3. Tamara Broderick, MIT [Video]
    4. Justin Chen, MIT [Video]
    5. Yiling Chen, Harvard University [Video]
    6. Amir Farbin, UT Arlington [Video]
    7. Doug Finkbeiner, Harvard University [Video]
    8. Andrew Gelman, Columbia University [Video]
    9. Nina Holden, MIT [Video]
    10. Elchanan Mossel, MIT
    11. Alex Peysakhovich, Facebook
    12. Alexander Rakhlin, University of Pennsylvania [Video]
    13. Neal Wadhwa, MIT [Video]
    14. Jun Yin, University of Wisconsin
    15. Harry Zhou, Yale University [Video]

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

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

    Please click here for registration.

    Conference Schedule:

    August 22 – Day 1
    8:30amBreakfast
    8:55amOpening remarks
    9:00am – 9:50amYiling Chen, “Machine Learning with Strategic Data Sources” [Video]
    9:50am – 10:40amAndrew Gelman, “Taking Bayesian Inference Seriously” [Video]
    10:40am – 11:10amBreak
    11:10am – 12:00pmHarrison Zhou, “A General Framework for Bayes Structured Linear Models” [Video]
    12:00pm – 1:30pmLunch
    1:30pm – 2:20pmDouglas Finkbeiner, “Mapping the Milky Way in 3D with star colors” [Video]
    2:20pm – 3:10pmNina Holden, “Sparse exchangeable graphs and their limits” [Video]
    3:10pm – 3:40pmBreak
    3:40pm – 4:30pmAlex Peysakhovich, “How social science methods inform personalization on Facebook News Feed” [Video]
    4:30pm – 5:20pmAmir Farbin, “Deep Learning in High Energy Physics” [Video]
    August 23 – Day 2
    8:45amBreakfast
    9:00am – 9:50amJoan Bruna Estrach, “Addressing Computational and Statistical Gaps with Deep Networks” [Video]
    9:50am – 10:40amJustin Chen & Neal Wadhwa, “Smaller Than the Eye Can See: Big Engineering from Tiny Motions in Video” [Video]
    10:40am – 11:10amBreak
    11:10am – 12:00pmAlexander Rakhlin, “How to Predict When Estimation is Hard: Algorithms for Learning on Graphs” [Video]
    12:00pm – 1:30pmLunch
    1:30pm – 2:20pmTamara Broderick, “Fast Quantification of Uncertainty and Robustness with Variational Bayes” [Video]
    2:20pm – 3:10pmElchanan Mossel, “Phylogenetic Reconstruction – a Rigorous Model of Deep Learning”
    3:10pm – 3:40pmBreak
    3:40pm – 4:30pmJörn Boehnke, “Amazon’s Price and Sales-rank Data: What can one billion prices on 150 thousand products tell us about the economy?”

    Workshop Participants:

    Richard Freeman’s Group:

    1. Sen Chai, ESSEC
    2. Brock Mendel, Harvard University
    3. Raviv Muriciano-Goroff, Stanford University
    4. Sifan Zhou, CMSA

    Scott Kominer’s Group:

    1. Bradly Stadie, UC Berkeley
    2. Neal Wadhwa, MIT [Video]
    3. Justin Chen

    Christopher Rogan’s Group:

    1. Amir Farbin, UT Arlington [Video]
    2. Paul Jackson, University of Adelaide

    For more information about the workshops, please reach out directly to the individual group leaders.

    This event is sponsored by CMSA Harvard University and the Alfred P. Sloan Foundation.

  • Seminars

    Seminars Colloquia & Seminar
    10-01-2015 Evolution Equations Seminar

    1:25 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-15-2015 Geometric Analysis Seminar

    1:26 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-16-2015 Random Matrix & Probability Theory Seminar

    1:27 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-23-2015 Random Matrix & Probability Theory Seminar

    1:29 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    5-3-2017 Random Matrix & Probability Theory Seminar

    1:29 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    1:30 pm-3:00 pm
    11/01/2019
  • Special Seminar
    1:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    5-2-2017 Social Sciences Application Forum

    1:30 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11/28/2018 Hodge Lecture

    1:30 pm
    11/01/2019
  • Seminars
    1:30 pm-3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    1/23/2019 Hodge Seminar

    1:30 pm-3:00 pm
    11/01/2019
  • Special Seminar
    1:30 pm-2:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    12/5/2018 Hodge Seminar

    1:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    11/14/2018 Hodge Seminar

    1:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    11/21/2018 Hodge Seminar

    1:30 pm
    11/01/2019
  • Colloquium
    1:31 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-28-2015 Mathematical Physics Seminar

    1:31 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-24-2017 Mathematical Physics Seminar

    1:31 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    1:32 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:33 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Concluding Conference of the Special Program on Nonlinear Equations, April 8 – 10, 2016
    1:34 pm
    11/01/2019-04/10/2016

    The Center of Mathematical Sciences and Applications will be hosting a concluding conference on April 8-10, 2016 to accompany the year-long program on nonlinear equations. The conference will have 15 speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

    Speakers:

    1. Lydia Bieri (University of Michigan)
    2. Luis Caffarelli (University of Texas at Austin)
    3. Mihalis Dafermos (Princeton University)
    4. Camillo De Lellis (Universität Zürich)
    5. Pengfei Guan (McGill University)
    6. Slawomir Kolodziej (Jagiellonian University)
    7. Melissa Liu (Columbia University)
    8. Duong H. Phong (Columbia University)
    9. Richard Schoen (UC Irvine)
    10. Cliff Taubes (Harvard University)
    11. Blake Temple (UC Davis)
    12. Valentino Tosatti (Northwestern University)
    13. Tai-Peng Tsai (University of British Columbia)
    14. Mu-Tao Wang (Columbia University)
    15. Xu-jia Wang (Australian National University)

    Please click NLE Conference Schedule with Abstracts for a downloadable schedule with talk abstracts.

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

    Schedule:

    April 8 – Day 1
    8:30amBreakfast
    8:45amOpening remarks
    9:00am – 10:00amCamillo De Lellis, “A Nash Kuiper theorem for $C^{1,1:5}$ isometric immersions of disks
    10:00am – 10:15amBreak
    10:15am – 11:15amXu-Jia Wang, “Monge’s mass transport problem
    11:15am – 11:30amBreak
    11:30am – 12:30pmPeng-Fei Guan, “The Weyl isometric embedding problem in general $3$ d Riemannian manifolds
    12:30pm – 2:00pmLunch
    2:00pm – 3:00pmBlake Temple, “An instability in the Standard Model of Cosmology
    3:00pm – 3:15pmBreak
    3:15pm – 4:15pmLydia Bieri, “The Einstein Equations and Gravitational Radiation
    4:15pm – 4:30pmBreak
    4:30pm – 5:30pmValentino Tosatti, “Adiabatic limits of Ricci flat Kahler metrics
    April 9 – Day 2
    8:45amBreakfast
    9:00am – 10:00amD.H. Phong, “On Strominger systems and Fu-Yau equations”
    10:00am – 10:15amBreak
    10:15am – 11:15amSlawomir Kolodziej, “Stability of weak solutions of the complex Monge-Ampère equation on compact Hermitian manifolds”
    11:15am – 11:30amBreak
    11:30am – 12:30pmLuis Caffarelli, “Non local minimal surfaces and their interactions”
    12:30pm – 2:00pmLunch
    2:00pm – 3:00pmMihalis Dafermos, “The interior of dynamical vacuum black holes and the strong cosmic censorship conjecture in general relativity”
    3:00pm – 3:15pmBreak
    3:15pm – 4:15pmMu-Tao Wang, “The stability of Lagrangian curvature flows”
    4:15pm – 4:30pmBreak
    4:30pm – 5:30pmMelissa Liu, “Counting curves in a quintic threefold”
    April 10 – Day 3
    8:45amBreakfast
    9:00am – 10:00amRick Schoen, “Metrics of fixed area on high genus surfaces with largest first eigenvalue”
    10:00am – 10:15amBreak
    10:15am – 11:15amCliff Taubes, “The zero loci of Z/2 harmonic spinors in dimensions 2, 3 and 4”
    11:15am – 11:30amBreak
    11:30am – 12:30pmTai-Peng Tsai, “Forward Self-Similar and Discretely Self-Similar Solutions of the 3D incompressible Navier-Stokes Equations”

    * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    10-22-2015 Evolution Equations Seminar

    1:37 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/11/2017 Mathematical Physics Seminar

    1:38 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9-18-17 Mathematical Physics Seminar

    1:39 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-17-2015 Evolution Equations Seminar

    1:39 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    9-27-17 RM&PT Seminar

    1:41 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9-27-17 Mathematical Physics Seminar

    1:42 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-23-17 Mathematical Physics Seminar

    1:43 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    9/11/2019 Random Matrix

    1:45 pm-2:45 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-25-17 RMPT Seminars

    1:45 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:47 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-10-2017 RM & PT Seminar

    1:48 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:51 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-22-2015 Geometric Analysis Seminar

    1:52 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:52 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-30-2015 Random Matrix & Probability Theory Seminar

    1:53 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-13-2017 Mathematical Physics Seminar

    1:53 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:54 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-21-2015 Mathematical Physics Seminar

    1:54 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-15-17 RM & PT Seminar

    1:55 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-6-2017 RM & PT Seminar

    1:56 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    1:58 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    2/22/2019 Social Science Applications Forum

    2:00 pm
    11/01/2019
  • Math Science Lectures in Honor of Raoul Bott

    Math Science Lectures in Honor of Raoul Bott Event
    Math Science Lectures in Honor of Raoul Bott: Freddy Cachazo

    2:00 pm-5:00 pm
    11/01/2019-04/03/2018
    1 Oxford Street, Cambridge MA 02138
    Math Science Lectures in Honor of Raoul Bott

    DSC_0170-e1525711590120

    On April 2-3, the CMSA will be hosting two lectures by Freddy Cachazo (Perimeter Institute) on “Geometry and Combinatorics in Particle Interactions.”  This will be the first of the new annual Bott Math Science Lecture Series hosted by the CMSA.

    The lectures will take place from 4:30-5:30pm in Science Center, Hall D.

     

    Cachazo-e1519325938458

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-20-2017 RM & PT Seminar

    2:00 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02/26/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    Homological Mirror Symmetry Seminar

    2:00 pm-4:00 pm
    11/01/2019-09/15/2017

    The seminar series, Homological Mirror Symmetry, will be held on selected Thursdays from 2PM – 4pm in CMSA Building, 20 Garden Street, Room G10.

    The list of speakers is below and will be updated as details are confirmed.

    DateNameTitle
    09-15-16
    09-22-16Netanel Blaier, Brandeis  “Intro to HMS.”

    Abstract: This is the first talk of the seminar series. We survey the statement of Homological Mirror Symmetry (introduced by Kontsevich in 1994) and some known results, as well as briefly discussing its importance, and the connection to other formulations of Mirror Symmetry and the SYZ conjecture. Following that, we will begin to review the definition of the A-side (namely, the Fukaya category) in some depth. No background is assumed! Also, in the last half hour, we will divide papers and topics among participants.

    Lecture Slides

    09-29-16Netanel Blaier, Brandeisblaier4“Intro to HMS 2.”

    Abstract: In the second talk, we review (some) of the nitty-gritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of J-holomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya’s differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$-structures. We will try to demonstrate all concepts in the Morse theory ‘toy model’.

    Lecture Slides

    10-06-16

    Hansol Hong, CMSAhong

    Title: Homological mirror symmetry for elliptic curves

    Abstract:
    We survey the proof of homological mirror symmetry by Polishchuk and Zaslow. Some of more recent methods to prove HMS for elliptic curves will be discussed also,
    which use homological algebra techniques and formal deformation theory of Lagrangians etc.

    Notes

    Notes (Baris)

    10-13-16

    Yu-Wei Fan, Harvard

    s_yuwei_fan

    Title: Semi-flat mirror symmetry and Fourier-Mukai transform

    Abstract: We will review the semi-flat mirror symmetry setting in Strominger-Yau-Zaslow, and discuss the correspondence between special Lagrangian sections on the A-side and deformed Hermitian-Yang-Mills connections on the B-side using real Fourier-Mukai transform, following Leung-Yau-Zaslow.

     10-20-16

    Tim Large, MIT

    Title: “Symplectic cohomology and wrapped Fukaya categories”

    Abstract: While mirror symmetry was originally conjectured for compact manifolds, the phenomenon applies to non-compact manifolds as well. In the setting of Liouville domains, a class of open symplectic manifolds including affine varieties, cotangent bundles and Stein manifolds, there is an A-infinity category called the wrapped Fukaya category, which is easier to define and often more amenable to computation than the original Fukaya category. In this talk I will construct it, along with symplectic cohomology (its closed-string counterpart), and compute some examples. We will then discuss how compactifying a symplectic manifold corresponds, on the B-side of mirror symmetry, to turning on a Landau-Ginzburg potential.

    Notes

     10-27-16

    Philip Engel, Columbia

    picture

    Title: Mirror symmetry in the complement of an anticanonical divisor”

    According to the SYZ conjecture, the mirror of a Calabi-Yau variety can be constructed by dualizing the fibers of a special Lagrangian fibration. Following Auroux, we consider this rubric for an open Calabi-Yau variety X-D given as the complement of a normal crossings anticanonical divisor D in X. In this talk, we first define the moduli space of special Lagrangian submanfiolds L with a flat U(1) connection in X-D, and note that it locally has the structure of a Calabi-Yau variety. The Fukaya category of such Lagrangians is obstructed, and the degree 0 part of the obstruction on L defines a holomorphic function on the mirror. This “superpotential” depends on counts of holomorphic discs of Maslov index 2 bounded by L. We then restrict to the surface case, where there are codimension 1 “walls” consisting of Lagrangians which bound a disc of Maslov index 0. We examine how the superpotential changes when crossing a wall and discuss how one ought to “quantum correct” the complex structure on the moduli space to undo the discontinuity introduced by these discs.

    Notes

    11-03-16

    Yusuf Baris Kartal, MIT

    HMS for Del Pezzo surfaces

    I will present Auroux-Katzarkov-Orlov’s proof of one side of the homological mirror symmetry for Del Pezzo surfaces. Namely I will prove their derived categories are equivalent to the categories of vanishing cycles for certain LG-models together with B-fields. I plan to show how the general B-field corresponds to non-commutative Del Pezzo surfaces and time allowing may mention HMS for simple degenerations of Del Pezzo surfaces. The tools include exceptional collections( and mutations for degenerate case), explicit description of NC deformations, etc.

    11-10-16No seminar this week
     12-08-16

    Lino Amorim, Boston University

    Title: The Fukaya category of a compact toric manifold

    Abstract: In this talk I will discuss the Fukaya category of a toric manifold following the work of Fukaya-Oh-Ohta-Ono. I will start with an overview of the general structure of the Fukaya category of a compact symplectic manifold. Then I will consider toric manifolds in particular the Fano case and construct its mirror.

    Video

  • CMSA EVENT: Topological Insulators and Mathematical Science – Conference and Program
    2:00 pm-7:00 pm
    11/01/2019-09/17/2014

    The CMSA will be hosting a conference on the subject of topological insulators and mathematical science on September 15-17.  Seminars will take place each day from 2:00-7:00pm in Science Center Hall D, 1 Oxford Street, Cambridge, MA.

  • Seminars
    2:00 pm-4:00 pm
    11/01/2019

    References: 

    • D. Auroux, A beginner’s introduction to Fukaya categories. arXiv:1301.7056
    • I. Smith, A symplectic prolegomenon. arXiv:1401.0269
    • D. Auroux, “Topics in geometry: mirror symmetry”, Fall 2009 (MIT Math 18.969)
    • Nick Sheridan’s IAS and Jussieu lectures. 
    • Sheel Gantara “Topics in symplectic topology”, Spring 2016 (Stanford Math 257B)
  • Seminars

    Seminars Colloquia & Seminar
    1/8/2019 Topology Seminar

    2:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-29-17 RM & PT Seminar

    2:03 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Seminars

    Seminars Colloquia & Seminar
    09-24-2015 Evolution Equations Seminar

    2:03 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-28-2015 Special Random Matrix & Probability Theory Seminar

    2:05 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-18-2015 Random Matrix & Probability Theory Seminar

    2:07 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 RM&PT Seminar

    2:08 pm
    11/01/2019
  • Colloquium
    2:08 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:10 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-29-2017 Mathematical Physics Seminar

    2:11 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Colloquium
    2:11 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-29-2015 Geometric Analysis Seminar

    2:14 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:14 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-28-2015 CMSA Special Seminar

    2:15 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-05-2015 Mathematical Physics Seminar

    2:16 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-6-2017 RM & PT Seminar

    2:16 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-15-2015 Evolution Equations Seminar

    2:17 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12-6-2017 Mathematical Physics Seminar

    2:17 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-07-2015 Random Matrix & Probability Theory Seminar

    2:19 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:20 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-29-2015 Evolution Equations Seminar

    2:20 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-14-2015 Random Matrix & Probability Theory Seminar

    2:21 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    2:21 pm
    11/01/2019-03/06/2018

    During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th, from 1:00 to 3:00pm in room G10, CMSA Building.

    You can watch Prof. Sheshmani describe the series here.

    The Syllabus is as follows:

    Date………..TopicVideo/Audio
    1-25-2018Gromov-Witten invariants 

    Definition, examples via algebraic geometry I

    Video / Audio / Combined 


    *due to technical difficulties the audio and video are split for this lecture.

     2-01-2018Gromov-Witten invariants 

    Virtual Fundamental Class I (definition)

    Video Audio / Combined 


    *due to technical difficulties the audio and video are split for this lecture

    2-13-2018Gromov-Witten invariants 

    Virtual Fundamental Class II (computation in some cases)

     2-15-2018Computing GW invariants 

    Three level GW classes

    Genus zero invariants of the projective plane

     2-20-2018Quantum Cohomology 

    Small Quantum Cohomology (Definition and Properties) I

    2-22-2018Quantum Cohomology 

    Small Quantum Cohomology (Definition and Properties) II

    2-27-2018Quantum Cohomology 

    Big Quantum Cohomology I

     3-1-2018Quantum Cohomology 

    Big Quantum Cohomology II

    GW potential

    WDVV equation

    3-6-2018GW invariants via Quantum Cohomology 

    The Quintic threefold case

    The P^2 case

    GW invariants via Quantum Cohomology 

    Dubrovin (quantum) connection

    Nakajima varieties 

    -Algebraic and symplectic reduction

    Nakajima varieties 

    Quasi maps to Nakajima varieties

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) I

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) II

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) III

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) I

     
    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) II

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) III

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) IV

     
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-21-2015 Random Matrix & Probability Theory Seminar

    2:22 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:23 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:24 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:29 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-28-2015 Random Matrix & Probability Theory Seminar

    2:30 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11/31/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/18/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/3/2019 Colloquium

    2:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Social Science Applications Forum

    2:30 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/19/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/7/2019 Social Science Applications Forum

    2:30 pm-3:00 pm
    11/01/2019
  • Colloquium

    Colloquium Colloquia & Seminar
    4/10/2019 Colloquium

    2:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/12/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    11/01/2019
  • Colloquium

    Colloquium Colloquia & Seminar
    2/27/2019 Colloquium

    2:30 pm-4:00 pm
    11/01/2019
  • General Relativity Seminar
    2:30 pm-3:30 pm
    11/01/2019-04/26/2020
  • Colloquium
    2:30 pm-3:00 pm
    11/01/2019
  • Colloquium
    2:32 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-19-2015 Mathematical Physics Seminar

    2:33 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-20-2015 Geometric Analysis Seminar

    2:35 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-26-2015 Mathematical Physics Seminar

    2:36 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    01-26-2018 Mirror Symmetry Seminar

    2:37 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-02-2015 Mathematical Physics Seminar

    2:37 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-03-2015 Geometric Analysis Seminar

    2:39 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-04-2015 Random Matrix & Probability Theory Seminar

    2:40 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    1-29-2018 Mathematical Physics Seminar

    2:42 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    2:43 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    2:44 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    2-2-2018 Mirror Symmetry Seminar

    2:44 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    2:45 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:47 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    2:48 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-19-2015 Evolution Equations Seminar

    2:50 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-09-2015 CMSA Special Lecture

    2:51 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:54 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-09-2015 Mathematical Physics Seminar

    2:54 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    2:55 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:56 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-19-2015 Random Matrix and Probability Theory Seminar

    2:57 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    2:59 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-16-2015 Mathematical Physics Seminar

    2:59 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    2-27-2018 HMS Lecture

    3:00 pm-4:00 pm
    11/01/2019-03/01/2018
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12/5/2018 Random Matrix and Probability Theory Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/17/2019 Fluid Dynamics Seminar

    3:00 pm
    11/01/2019
  • CMSA EVENT: 2018 Ding Shum Lecture
    3:00 pm-4:00 pm
    11/01/2019
    ding-shum-2018

     

    Screen-Shot-2018-06-14-at-1.41.25-PM

    On October 24, 2018, the CMSA will be hosting our second annual Ding Shum lecture. This event was made possible by the generous funding of Ding Lei and Harry Shum. Last year featured Leslie Valiant, who spoke on “learning as a Theory of Everything.”

    This year will feature Eric Maskin, who will speak on “How to Improve Presidential Elections: the Mathematics of Voting.” This lecture will take place from 5:00-6:00pm in Science Center, Hall D. 

    Pictures of the event can be found here.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/24/2018 RM & PT Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/7/2018 Random Matrix and Probability Theory Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/14/2018 RM & PT Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/28/2018 Random Matrix and Probability Theory Seminar

    3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    1/31/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Special Seminar
    3:00 pm-4:30 pm
    11/01/2019-05/09/2019

    In the Spring 2019 Semester, the CMSA will be hosting a special lecture series on Derived algebraic/differential geometry run by Artan Sheshmani, with lectures given by Prof. Sheshmani and Dr. Dennis Borisov. The seminar will be held on Tuesdays and Thursdays from 3:00-4:30pm in CMSA, room G10.

    Click here for reference material

    Click here for a syllabus

    Schedule:

    Section 1: Basic setting of derived geometry

    The goal: To collect the minimum set of tools needed to do algebraic geometry in the derived context.

    2/05/2019Lecture 1: Model and с-categoriesVideo
    2/07/2019Lecture 2: Grothendieck topologies and homotopy descentVideo
    2/12/2019Lecture 3: Derived Artin stacksVideo 
    2/14/2019Lecture 4: Cotangent complexes

    Section 2: Loop spaces and differential forms

    The goal: This is the algebraic heart of the course – here we learn the homological techniques that are needed for shifted symplectic forms.

    2/19/2019Lecture 5: De Rham complexes and S1-equivariant schemes (loop spaces)Video
    2/21/2019Lecture 6: Chern characterVideo
    2/26/2019

    Room G02

    Lecture 7: Local structure of closed differential forms in the derived sense Part IVideo
    2/28/2019Lecture 8: Local structure of closed differential forms in the derived sense Part IIVideo
    3/05/2019Lecture 9: Cyclic homologyVideo

    Section 3: Shifted symplectic structures
    Goal: To see applications of the algebraic techniques from above in the geometric context of the actual moduli spaces.

    3/07/2019Lecture 10: Definition and existence resultsVideo
    3/12/2019Lecture 11: Lagrangians and Lagrangian fibrationsVideo
    3/14/2019

    Room G02

    Lecture 12: Lagrangians and Lagrangian fibrationsVideo
    3/26/2019Lecture 13: Intersections of LagrangiansVideo
    3/28/2019

    Room G02

    Lecture 14: Examples and applications 2 (Part I)Video
    4/02/2019Lecture 15: Examples and applications 2 (Part II)Video

    Section 4: Uhlenbeck–Yau construction and correspondence

    4/04/2019Lecture 16: Examples and applications 2 (Part III)Video
    4/09/2019

    Room G02

    Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)Video
  • Seminars

    Seminars Colloquia & Seminar
    2/7/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars
    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2/14/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2/20/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/6/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/8/2019 Special Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/20/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    Algebraic Geometry Seminar, Thursdays

    3:00 pm-4:00 pm
    11/01/2019

    This seminar will not be held in the Spring 2018 Semester.

    The Algebraic Geometry Seminar will be every Thursday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

    The schedule will be updated as details are confirmed.

     

     

    DateNameTitle/Abstract
    09-14-17 Yu-Wei Fan (Harvard Math)

    Entropy of an autoequivalence on Calami-Yau manifolds

    Abstract:  We will recall the notion of entropy of an autoequivalence on triangulated categories, and provide counterexamples of a conjecture by Kikuta-Takahashi.

    11-1-17

    *5:00pm, G10*

     Shamil Shakirov, Harvard Math

    Undulation invariants of plane curves

    Abstract: “One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem, described by Cayley and Salmon in 1852, is to determine whether or not a given plane curve of degree r > 3 has undulation points — the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r – 3)(3 r – 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries, and we conjecture a generalization for r = 5

    11-2-17

     

    Alexander Moll, IHES

    Hilbert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves

    ABSTRACT: By Grojnowski and Nakajima, Fock spaces are cohomology rings of Hilbert scheme of points in the plane.  On the other hand, by Pressley-Segal, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the Kähler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J.  First, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this Kähler structure.  Second, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = – e_1 e_2 that is invariant under e_2 <-> e_1.  As a corollary of Lehn’s theorem, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element.  Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin.  As time permits, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov’s BPS/CFT Correspondence.

    11-9-17  TBD  TBD
    11-16-17 TBD TBD
    11-23-17  TBD  TBD
    11-30-17  TBD  TBD
    12-7-17  TBD  TBD
    12-15-17  TBD  TBD
  • Seminars

    Seminars Colloquia & Seminar
    4/24/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Fluid Dynamics Seminar

    Fluid Dynamics Seminar
    10/9/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/03/2018 RMPT Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    5/22/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    5/15/2019 Fluid Dynamics

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    5/1/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Special Seminar
    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    Dmytro Shklyrov HMS Focused Lecture Series

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/4/2019 Special Seminar

    3:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    11-17-2015 Geometric Analysis Seminar

    3:00 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    9/18/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    11-23-2015 Mathematical Physics Seminar

    3:01 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    Random Matrix & Probability Theory Seminar (2016-2017)

    3:01 pm
    11/01/2019-12/14/2017
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    DSC_0025-768x512

    The random matrix and probability theory will be every Wednesday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

  • CMSA EVENT: Working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017
    3:02 pm-3:03 pm
    11/01/2019-01/13/2017

    The Center of Mathematical Sciences and Applications will be hosting a working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Participants:

    Gerard Ben Arous, Courant Institute of Mathematical Sciences

    Alex Bloemendal, Broad Institute

    Arup Chakraburty, MIT

    Zhou Fan, Stanford University

    Alpha Lee, Harvard University

    Matthew R. McKay, Hong Kong University of Science and Technology (HKUST)

    David R. Nelson, Harvard University

    Nick Patterson, Broad Institute

    Marc Potters, Capital Fund management

    Yasser Roudi, IAS

    Tom Trogdon, UC Irvine

    Organizers:

    Michael Brenner, Lucy Colwell, Govind Menon, Horng-Tzer Yau

    Please click Program for a downloadable schedule with talk abstracts.

    Please note that breakfast & lunch will be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants should you need recommendations for dinner.

    Schedule:

    January 9 – Day 1
    9:30am – 10:00amBreakfast & Opening remarks
    10:00am – 11:00amMarc Potters, “Eigenvector overlaps and the estimation of large noisy matrices”
    11:00am – 12:00pmYasser Roudi
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 10 – Day 2
    8:30am – 9:00amBreakfast
    9:00am – 10:00amArup Chakraburty, “The mathematical analyses and biophysical reasons underlying why the prevalence of HIV strains and their relative fitness are simply correlated, and pose the challenge of building a general theory that encompasses other viruses where this is not true.”
    10:00am – 11:00amTom Trogdon, “On the average behavior of numerical algorithms”
    11:00am – 12:00pmDavid R. Nelson, “Non-Hermitian Localization in Neural Networks”
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 11 – Day 3
    8:30am – 9:00amBreakfast
    9:00am – 10:00amNick Patterson
    10:00am – 11:00amLucy Colwell
    11:00am – 12:00pmAlpha Lee
    12:00pm – 2:00pmLunch
    2:00pm-4:00pmAfternoon Discussion
    4:00pmGerard Ben Arous (Public Talk), “Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms
    January 12 – Day 4
    8:30am – 9:00amBreakfast
    9:00am – 10:00amGovind Menon
    10:00am – 11:00amAlex Bloemendal
    11:00am – 12:00pmZhou Fan, “Free probability, random matrices, and statistics”
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 13 – Day 5
    8:30am – 9:00amBreakfast
    9:00am – 12:00pmFree for Working
    12:00pm – 2:00pmLunch
    2:00pmFree for Working

    * This event is sponsored by CMSA Harvard University.

  • Colloquium
    3:03 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-24-2015 Geometric Analysis Seminar

    3:03 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-04-2016 Evolution Equations Seminar

    3:04 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    Hodge and Noether-Lefschetz Loci Seminar

    3:06 pm
    11/01/2019

    In the Fall 2018 Semester the CMSA will be hosting a seminar on Hodge and Noether-Lefschetz loci, with lectures given by Hossein Movasati (IMPA). The seminar will occur weekly on Wednesday at 1:30 in room G10 of the CMSA.

    The schedule below will be updated as talks are confirmed.

    DateTitle/Abstract
    11/7/2018

    Video

    Title: Hodge and Noether-Lefschetz loci

    Abstract: Hodge cycles are topological cycles which are conjecturally (the millennium Hodge conjecture) supported in algebraic cycles of a given smooth projective complex manifold. Their study in families leads to the notion of Hodge locus, which is also known as Noether-Lefschetz locus in the case of surfaces. The main aim of this mini course is to introduce a computational approach to the study of Hodge loci for hypersurfaces and near the Fermat hypersurface. This will ultimately lead to the verification of the variational Hodge conjecture for explicit examples of algebraic cycles inside hypersurfaces and also the verification of integral Hodge conjecture for examples of Fermat hypersurfaces. Both applications highly depend on computer calculations of rank of huge matrices. We also aim to review some classical results on this topic, such as Cattani-Deligne-Kaplan theorem on the algebraicity of the components of the hodge loci, Deligne’s absolute Hodge cycle theorem for abelian varieties etc.

    In the theoretical side another aim is to use the available tools in algebraic geometry and construct the moduli space of projective varieties enhanced with elements in their algebraic de Rham cohomology ring. These kind of moduli spaces have been useful in mathematical physics in order to describe the generating function of higher genus Gromov-Witten invariants, and it turns out that the Hodge loci in such moduli spaces are well-behaved, for instance, they are algebraic leaves of certain holomorphic foliations. Such foliations are constructed from the underlying Gauss-Manin connection. This lectures series involves many reading activities on related topics, and contributions by participants are most welcome.

    11/14/2018

    Video

    Title:  Integral Hodge conjecture for Fermat varieties

    Abstract: We describe an algorithm which verifies whether  linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this  confirms the integral Hodge conjecture for quartic and quintic Fermat fourfolds. Our algorithm is based on computation of the list of elementary divisors of both the lattice of linear algebraic cycles, and the lattice of Hodge cycles written in terms of  vanishing cycles, and observing that these two lists are the same. This is a joint work with E. Aljovin and R. Villaflor.

    11/21/2018

    Video

    Title:  Periods of algebraic cycles

    Abstract: The tangent space of the Hodge locus at a point can be described by the so called infinitesimal variation of Hodge structures and the cohomology class of Hodge cycles. For hypersurfaces of dimension $n$ and degree $d$ it turns out that one can describe it without any knowledge of cohomology theories and in a fashion which E. Picard in 1900’s wanted to study integrals/periods. The data of cohomology class is replaced with periods of Hodge cycles, and explicit computations of these periods, will give us a computer implementable description of the tangent space.  As an application of this we show that for examples of $n$ and $d$, the locus of hypersurfaces containing two linear cycles whose intersection is of low dimension, is a reduced component of the Hodge locus in the underlying parameter space.

    11/28/2018

    Video

    Title: Periods of Complete Intersection Algebraic Cycles

    Speaker: Roberto Villaflor

    Abstract: In order to compute periods of algebraic cycles inside even dimensional smooth degree d hypersurfaces of the projective space, we restrict ourselves to cycles supported in a complete intersection subvariety. When the description of the complete intersection is explicit, we can compute its periods, and furthermore its cohomological class. As an application, we can use this data to describe the Zariski tangent space of the corresponding Hodge locus, as the degree d part of some Artinian Gorenstein ideal of the homogeneous coordinate ring of the projective space. Using this description, we can show that for d>5, the locus of hypersurfaces containing two linear cycles, is a reduced component of the Hodge locus in the underlying parameter space.

    12/05/2018

    Room G02

    Title: Some explicit Hodge cycles

    Abstract: Explicit examples of Hodge cycles are due to D. Mumford and A. Weil in the case of CM abelian varieties. In this talk, I will describe few other examples for the Fermat variety. Effective verification of the Hodge conjecture for these cycles is not known.

    12/12/2018

    Video

    Title: A conjectural Hodge locus for cubic tenfold

    Abstract: In this talk we will consider the difference  of two linear algebraic cycles of dimension 5 inside a smooth cubic tenfold and such that the dimension of their intersection is 3. We will show some computer assisted evidences to the fact that the corresponding Hodge locus is bigger than the expected locus of algebraic deformations of the cubic tenfold together with its linear cycles. A similar discussion will be also presented for cubic six and eightfold,  for which we will prove that the corresponding second and third order infinitesimal Hodge loci are smooth. The main ingredient is a computer implementation of power series of periods of hypersurfaces.

    1/16/2019Title: Algebraic BCOV anomaly equation

    Abstract: We introduce the moduli space T of  non-rigid compact Calabi-Yau threefolds enhanced with differential forms and a Lie algebra of vector fields in T. This will be used in order to give a purely algebraic interpretation of topological string partition functions and the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation (joint work with M. Alim, E. Scheidegger, S.-T. Yau).  We will also define similar moduli spaces for even dimensional Calabi-Yau varieties, where we have the notion of Hodge locus.

    1/23/2019

    Video

    Title: A new model for modular curves

    Abstract: One of the non-trivial examples of a Hodge locus is the modular curve X_0(N), which is due to isogeny of elliptic curves (a Hodge/algebraic cycle in the product of two elliptic curves). After introducing the notion of enhanced moduli of elliptic curves, I will describe a new model for X_0(N) in the weighted projective space of dimension 4 and with weights (2,3,2,3,1). I will also introduce some elements in the defining ideal of such a model.

    The talk is based on the article arXiv:1808.01689.

    1/30/2019

    Video

    Title: Constant Yukawa couplings

    Abstract: In this talk I will first introduce algebraic Yukawa couplings for any moduli of enhanced Calabi-Yau n-folds. Then I will list many examples in support of the following conjecture. A moduli of Calabi-Yau n-folds is a quotient of a Hermitian symmetric domain (constructed from periods) by an arithmetic group if and only if the corresponding Yukawa couplings are constants.

    2/6/2019

    Video

    Title: Integrality properties of CY modular forms

    Abstract: The integrality of the coefficients of the mirror map is a central problem in the arithmetic of Calabi-Yau varieties and it has been investigated  by Lian-Yau (1996, 1998), Hosono-Lian-Yau (1996), Zudilin (2002), Kontsevich-Schwarz-Vologodsky (2006) Krattenthaler-Rivoal (2010). The central tool in most of these works has been the so called Dwork method.  In this talk we use this method and classify all hypergeometric differential equations with a maximal unipotent monodromy whose mirror map has integral coefficients.

    We also  give a computable condition on the parameters of a hypergeometric function which conjecturally computes all the primes which appear in the denominators of the coefficients of the mirror map. This is a joint work with Kh. Shokri.

    2/13/2019Title: Foliations and Hodge loci

    Abstract: In this talk I will introduce a holomorphic foliation in a larger parameter space attached to families of enhanced projective varieties. Irreducible components of the Hodge locus with constant periods are algebraic leaves of such a foliation. Under the hypothesis that these are all the algebraic leaves,  we get the fact that such algebraic leaves are defined over the algebraic closure of the base field and that Hodge classes are weak absolute in the sense of C. Voisin.

     

    References:

  • Seminars

    Seminars Colloquia & Seminar
    02-02-2016 Geometric Analysis Seminar

    3:06 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    3:06 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Data Analysis Workshop, April 4 – 8, 2016
    3:09 pm-3:10 pm
    11/01/2019-04/08/2016

    The Center of Mathematical Sciences and Applications will be hosting a 5-day workshop on Data Analysis and related areas on April 4 – 8, 2016.

    Workshop Locations:

    April 4 – 7 (Monday ~ Thursday)

    Room G10,
    20 Garden Street, Cambridge, MA 02138 

    April 8 (Friday)

    EPS Faculty Lounge, Room 409, 4th floor, Hoffman Lab
    20 Oxford Street, Cambridge, MA 02138

     Participants:

    • Peter Hubyers (Harvard University)
    • Eli Tziperman (Harvard University)
    • Andrew Rhines (University of Washington)
    • Karen McKinnon (UCAR)
    • Douglas MacMartin (Caltech)
    • Thomas Laepple (Alfred Wegener Institute)
    • Yossi Ashkenazy (Ben-Gurion University)
    • Marlene Kretschamer (Potsdam Institute for Climate Impact Research)
    • Natesh Pillai (Harvard University)
    • Judah Cohen (Atmospheric and Environmental Research)
    • Cristian Proistosescu (Harvard University)

    Please click Workshop Agenda for a downloadable agenda.

    * This event is sponsored by CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    02-11-2016 Evolution Equations Seminar

    3:09 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    3:09 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2-16-2018 RM & PT Seminar

    3:09 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Colloquium
    3:11 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-03-2016 Random Matrix & Probability Theory Seminar

    3:11 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    3:13 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 RMPT Seminar

    3:15 pm-4:15 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/9/2019 RM & PT Seminar

    3:15 pm-4:15 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/30/2019 Random Matrix and Probability Theory Seminar

    3:15 pm-4:15 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/16/2019 RM & PT Seminar

    3:15 pm
    11/01/2019
  • Colloquium
    3:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-16-2016 Geometric Analysis Seminar

    3:16 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-15-2016 Mathematical Physics Seminar

    3:17 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-18-2016 Evolution Equations Seminar

    3:19 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-22-2016 Mathematical Physics Seminar

    3:20 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-23-2016 Geometric Analysis Seminar

    3:22 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-24-2016 Random Matrix & Probability Theory

    3:23 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Mini-workshop on SYZ and Homological Mirror Symmetry
    3:23 pm
    11/01/2019-12/02/2016

    The Center of Mathematical Sciences and Applications will be hosting a 4-day workshop on SYZ and Homological Mirror Symmetry and related areas on November 28 – December 2, 2016 at Harvard CMSA Building: Room G10, 20 Garden Street, Cambridge, MA 02138.

    Organizers:

    Bong Lian (Brandeis University), Siu-Cheong Lau (Boston University), Shing-Tung Yau (Harvard University)

    Speakers:

    1. Conan Leung, Chinese University of Hong Kong
    2. Junwu Tu, University of Missouri
    3. Jingyu Zhao, Columbia University
    4. David Treumann, Boston College
    5. Hiro Lee Tanaka, Harvard University
    6. Fabian Haiden, Harvard University
    7. Hansol Hong, Harvard CMSA/Brandeis University
    8. Netanel Blaier, Harvard CMSA/Brandeis University
    9. Garret Alston, The University of Oklahoma

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

    Conference Schedule:

    Monday, November 28 – Day 1
    10:30am –11:30amHiro Lee Tanaka“Floer theory through spectra”
    Lunch
    1:00pm – 2:30pmFabian Haiden“Categorical Kahler Geometry”
     2:30pm-2:45pm Break
    2:45pm – 4:15pmFabian Haiden“Categorical Kahler Geometry”
    4:30pm – 5:15pmGarret Alston“Potential Functions of Non-exact fillings”
    Tuesday, November 29 – Day 2
    10:30am –11:30amConan Leung, “Remarks on SYZ”
    Lunch
    1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
     2:30pm-2:45pm Break
    2:45pm – 4:15pmHiro Lee Tanaka“Floer theory through spectra”
    4:30pm – 5:15pmHansol Hong, “Mirror Symmetry for punctured Riemann surfaces and gluing construction”
    Wednesday, November 30 – Day 3
    10:30am –11:30amJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
    Lunch
    1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
     2:30-2:45pm Break
    2:45pm – 4:15pmDavid Treumann, “Invariants of Lagrangians via microlocal sheaf theory”
    Thursday, December 1 – Day 4
    10:30am –11:30amDavid Treumann“Some examples in three dimensions”
    Lunch
    1:00pm – 2:30pmJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
     2:30-2:45pm Break
    2:45pm – 3:30pmNetanel Blaier, “The quantum Johnson homomorphism, and the symplectic mapping class group of 3-folds”

    * This event is sponsored by the Simons Foundation and CMSA Harvard University.

  • Colloquium
    3:25 pm
    11/01/2019

    During the Spring 2021 semester, and until further notice, all seminars will take place virtually.

    The 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually, using zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed.

    To learn how to attend, please fill out this form.

    Information on previous colloquia can be found here.

    Spring 2021:

    DateSpeakerTitle/Abstract
    1/27/2021Evelyn Tang (Max Planck Institute for Dynamics and Self-Organization)

    Slides

    Video

    Title: Topology protects chiral edge currents in stochastic systems

    Abstract: Living systems can exhibit time-scales much longer than those of the underlying components, as well as collective dynamical behavior. How such global behavior is subserved by stochastic constituents remains unclear. I will present two-dimensional stochastic networks that consist of out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. I will discuss the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, stochastic growth and shrinkage, and synchronization.

    2/3/2021André Luiz de Gouvêa (Northwestern)

    Video

    Title: The Brave Nu World

    Abstract: Neutrinos are the least understood of the fundamental particles that make up the so-called Standard Model of Particle Physics. Measuring neutrino properties and identifying how they inform our understanding of nature at the smallest distant scales is among the highest priorities of particle physics research today. I will discuss our current understanding of neutrinos, concentrating on the observation of neutrino oscillations and neutrino masses, along with all the open questions that came of these discoveries from the end of the 20th century.

    2/10/2021Mykhaylo Shkolnikov (Princeton)

    Video

    Title: Probabilistic approach to free boundary problems and applications

    Abstract: We will discuss a recently developed probabilistic approach to (singular) free boundary problems, such as the supercooled Stefan problem. The approach is based on a new notion of solution, referred to as probabilistic, which arises naturally in the context of large system limits of interacting particle systems. In the talk, I will give an example of how such interacting particle systems arise in applications (e.g., finance), then obtain a solution of a free boundary problem in the large system limit, and discuss how this solution can be analyzed mathematically (thereby answering natural questions about the systemic risk in financial systems and neural synchronization in the brain). The talk is based on recent and ongoing joint works with Sergey Nadtochiy, Francois Delarue, Jiacheng Zhang and Xiling Zhang

    2/17/2021
    9:00 – 10:00PM ET
    C. Seshadhri (UC Santa Cruz)

    Video

    Title: Studying the (in)effectiveness of low dimensional graph embeddings

    Abstract: Low dimensional graph embeddings are a fundamental and popular tool used for machine learning on graphs. Given a graph, the basic idea is to produce a low-dimensional vector for each vertex, such that “similarity” in geometric space corresponds to “proximity” in the graph. These vectors can then be used as features in a plethora of machine learning tasks, such as link prediction, community labeling, recommendations, etc. Despite many results emerging in this area over the past few years, there is less study on the core premise of these embeddings. Can such low-dimensional embeddings effectively capture the structure of real-world (such as social) networks? Contrary to common wisdom, we mathematically prove and empirically demonstrate that popular low-dimensional graph embeddings do not capture salient properties of real-world networks. We mathematically prove that common low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, which have been widely established to be empirically true for real-world networks. Empirically, we observe that the embeddings generated by popular methods fail to recreate the triangle structure of real-world networks, and do not perform well on certain community labeling tasks. (Joint work with Ashish Goel, Caleb Levy, Aneesh Sharma, and Andrew Stolman.)

    2/24/2021David Ben-Zvi (U Texas)

    Video

    Title: Electric-Magnetic Duality for Periods and L-functions

    Abstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory.
    A fundamental aspect of the Langlands correspondence — the relative Langlands program — studies the representation of L-functions of Galois representations as integrals of automorphic forms. However, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don’t seem to line up.
    We present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely, we rewrite the relative Langlands program as duality in the presence of supersymmetric boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.

    3/3/2021

    9:00pm ET

    Omer Tamuz (Caltech)Title: Monotone Additive Statistics

    Abstract: How should a random quantity be summarized by a single number? We study mappings from random variables to real numbers, focussing on those with the following two properties: (1) monotonicity with respect to first-order stochastic dominance, and (2) additivity for sums of independent random variables. This problem turns out to be connected to the following question: Under what conditions on the random variables X and Y does there exist an independent Z so that X + Z first-order stochastically dominates Y + Z?

    (Joint work with Tobias Fritz, Xiaosheng Mu, Luciano Pomatto and Philipp Strack.)

    3/10/2021

    9:00pm ET

    Piotr Indyk (MIT)Title: Learning-Based Sampling and Streaming

    Abstract: Classical algorithms typically provide “one size fits all” performance, and do not leverage properties or patterns in their inputs. A recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. In this talk I will present two examples of this type, in the context of streaming and sampling algorithms. In particular, I will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (ICLR’19), and (b) sampling algorithms for estimating the support size of a distribution (ICLR’21). Both algorithms use an ML-based predictor that, given a data item, estimates the number of times the item occurs in the input data set. (The talk will cover material from papers co-authored with T Eden, CY Hsu, D Katabi, S Narayanan, R Rubinfeld, S Silwal, T Wagner and A Vakilian.

    3/17/2021
    9:00pm ET
    Chiu-Chu Melissa Liu (Columbia)Title: Topological Recursion and Crepant Transformation Conjecture

    Abstract: The Crepant Transformation Conjecture (CTC), first proposed by Yongbin Ruan and later refined/generalized by others, relates Gromov-Witten (GW) invariants of K-equivalent smooth varieties or smooth Deligne-Mumford stacks. We will outline a proof of all-genus open and closed CTC for symplectic toric Calabi-Yau 3-orbifolds based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong. Our proof relies on the Remodeling Conjecture (proposed by Bouchard-Klemm-Marino-Pasquetti and proved in full generality by Fang, Zong and the speaker) relating open and closed GW invariants of a symplectic toric Calabi-Yau 3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin Topological Recursion.

    3/24/2021Weinan E (Princeton)

    Video

    Title: Machine Learning and PDEs

    Abstract: I will discuss two topics:
    (1) Machine learning-based algorithms and “regularity” theory for very high dimensional PDEs;
    (2) Formulating machine learning as PDE (more precisely, integral-differental equation) problems.

    3/31/2021Thore Graepel (DeepMind/UCL)

    Video

    Title: From AlphaGo to MuZero – Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model

    Abstract: Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a perfect simulator is available. However, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. MuZero learns a model that, when applied iteratively, predicts the quantities most directly relevant to planning: the reward, the action-selection policy, and the value function. When evaluated on 57 different Atari games – the canonical video game environment for testing AI techniques, in which model-based planning approaches have historically struggled – our new algorithm achieved a new state of the art. When evaluated on Go, chess and shogi, without any knowledge of the game rules, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.

    4/7/2021Kui Ren (Columbia)Title: Inversion via Optimization: Revisiting the Classical Least-Squares Formulation of Inverse Problems

    Abstract: The classical least-squares formulation of inverse problems has provided a successful framework for the computational solutions of those problems. In recent years, modifications and alternatives have been proposed to overcome some of the disadvantages of this classical formulation in dealing with new applications. This talk intends to provide an (likely biased) overview of the recent development in constructing new least-squares formulations for model and data-driven solutions of inverse problems.

    4/14/2021Siu-Cheong Lau (Boston U)Title: An algebro-geometric formulation of computing machines

    Abstract: Neural network in machine learning has obvious similarity with quiver representation theory.  The main gap between the two subjects is that network functions produced from two isomorphic quiver representations are not equal, due to the presence of non-linear activation functions which are not equivariant under the automorphism group.  This violates the important math/physics principle that isomorphic objects should produce the same results.  In this talk, I will introduce a general formulation using moduli spaces of framed modules of (noncommutative) algebra and fix this gap.  Metrics over the moduli space are crucial.  I will also explain uniformization between spherical, Euclidean and hyperbolic moduli.

    4/21/2021Vasco Carvalho (Cambridge)Title: The Economy as a Complex Production Network
    Abstract: A modern economy is an intricately linked web of specialized production units, each relying on the flow of inputs from their suppliers to produce their own output, which in turn is routed towards other downstream units. From this production network vantage point we: (i) present the theoretical foundations for the role of such input linkages as a shock propagation channel and as a mechanism for transforming micro-level shocks into macroeconomic, economy-wide fluctuations (ii) selectively survey both empirical and simulation-based studies that attempt to ascertain the relevance and quantitative bite of this argument and (time permitting) (iii) discuss a range of domains where this networked production view is currently being extended to.
    4/28/2021

    9:00 – 10:00pm ET

    Shamit Kachru (Stanford)

    Slides

    Title: K3 Metrics from String Theory

    Abstract: Calabi-Yau manifolds have played a central role in important developments in string theory and mathematical physics.  Famously, they admit Ricci flat metrics — but the proof of that fact is not constructive, and the metrics remain mysterious.  K3 is perhaps the simplest non-trivial compact Calabi-Yau space.  In this talk, I describe two different methods of constructing (smooth, Ricci flat) K3 metrics, and a string theory duality which relates them.  The duality re-sums infinite towers of disc instanton corrections via a purely classical infinite-dimensional hyperkahler quotient construction, which can be practically implemented.


    Fall 2020:

    DateSpeakerTitle/Abstract
    9/23/2020David Kazhdan (Hebrew University)Title: On Applications of Algebraic Combinatorics to Algebraic Geometry

    Abstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.

    10/7/2020

    10:00am

    Mariangela Lisanti (Princeton University)

    Video

    Title: Mapping the Milky Way’s Dark Matter Halo with Gaia

    Abstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium, as typically assumed, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments, which search for the interactions of these particles in terrestrial targets.

    10/14/2020Gil Kalai (Hebrew University and IDC Herzliya)

    Video

    Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers

    Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to
    a) My general argument “against” quantum computers,
    b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
    Relevant papers:
    Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.
    wordpress.com/2019/11/stat-quantum2.pdf

    Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.
    wordpress.com/2020/08/laws-blog2.pdf

    Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.
    wordpress.com/2019/09/main-pr.pdf

    10/21/2020Marta Lewicka (University of Pittsburgh)

    Video

    Title: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models

    Abstract: We propose results that relate the following two contexts:
    (i) Given a Riemann metric G on a thin plate, we study the question of what is its closest isometric immersion, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.
    (ii) We perform the full scaling analysis of E^h, in the context of dimension reduction as the plate’s thickness h goes to 0, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).
    For each n, we identify conditions for the validity of the corresponding scaling, in terms of the vanishing of Riemann curvatures of G up to appropriate orders, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth, swelling, shrinkage, plasticity, etc. Our results display the interaction of calculus of variations,
    geometry and mechanics of materials in the prediction of patterns and shape formation.

    10/28/2020Jonathan Heckman (University of Pennsylvania)

    Video

    Title: Top Down Approach to Quantum Fields

    Abstract: Quantum Field theory (QFT) is the common language of particle physicists, cosmologists, and condensed matter physicists. Even so, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory, highlighting in particular the special role of seemingly “exotic”  higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs, and are now using this to extra observables from strongly correlated systems in theories with more than four spacetime dimensions, as well as in spacetimes with four or fewer spacetime dimensions. Along the way, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems

    11/4/2020
    9:00pm ET
    Surya Ganguli (Stanford)

    Video

    Title: Weaving together machine learning, theoretical physics, and neuroscience through mathematics

    Abstract: An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning, theoretical physics, and neuroscience.  The unification of these fields will likely enable us to exploit the power of complex systems analysis, developed in theoretical physics and applied mathematics, to elucidate the design principles governing neural systems, both biological and artificial, and deploy these principles to develop better algorithms in machine learning.  We will give several vignettes in this direction, including:  (1) determining the best optimization problem to solve in order to perform regression in high dimensions;  (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) developing interpretable machine learning to derive and understand state of the art models of the retina; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) delineating fundamental theoretical limits on the energy, speed and accuracy with which non-equilibrium sensors can detect signals
    Selected References:
    M. Advani and S. Ganguli, Statistical mechanics of optimal convex inference in high dimensions, Physical Review X, 6, 031034, 2016.
    M. Advani and S. Ganguli, An equivalence between high dimensional Bayes optimal inference and M-estimation, NeurIPS, 2016.
    A.K. Lampinen and S. Ganguli, An analytic theory of generalization dynamics and transfer learning in deep linear networks, International Conference on Learning Representations (ICLR), 2019.
    H. Tanaka, A. Nayebi, N. Maheswaranathan, L.M. McIntosh, S. Baccus, S. Ganguli, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction, NeurIPS 2019.
    S. Deny, J. Lindsey, S. Ganguli, S. Ocko, The emergence of multiple retinal cell types through efficient coding of natural movies, Neural Information Processing Systems (NeurIPS) 2018.
    B. Sorscher, G. Mel, S. Ganguli, S. Ocko, A unified theory for the origin of grid cells through the lens of pattern formation, NeurIPS 2019.
    Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
    S.E. Harvey, S. Lahiri, and S. Ganguli, A universal energy accuracy tradeoff in nonequilibrium cellular sensing, https://arxiv.org/abs/2002.10567

    11/11/2020Kevin Buzzard (Imperial College London)

    Video

    Title: Teaching proofs to computers

    Abstract: A mathematical proof is a sequence of logical statements in a precise language, obeying some well-defined rules. In that sense it is very much like a computer program. Various computer tools have appeared over the last 50 years which take advantage of this analogy by turning the mathematical puzzle of constructing a proof of a theorem into a computer game. The newest tools are now capable of understanding some parts of modern research mathematics. In spite of this, these tools are not used in mathematics departments, perhaps because they are not yet capable of telling mathematicians *something new*.
    I will give an overview of the Lean theorem prover, showing what it can currently do. I will also talk about one of our goals: using Lean to make practical tools which will be helpful for future researchers in pure mathematics.

    11/18/2020Jose A. Scheinkman (Columbia)

    Video

    Title: Re-pricing avalanches

    Abstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive.  Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper, we show that a state-dependent  pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment.  These fluctuations, in turn, cause fluctuations  in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)

    11/25/2020

    10:45am

    Eric J. Heller (Harvard)

    Video

    Title: Branched Flow

    Abstract: In classical and quantum  phase space flow, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In  evolution under smooth, random, weakly deflecting  but persistent perturbations, a remarkable regime develops, called branched flow. Lying between the first cusp catastrophes at the outset, leading to fully chaotic  statistical flow much later, lies the visually beautiful regime of branched flow.  It applies to tsunami wave propagation, freak wave formation, light propagation, cosmic microwaves arriving from pulsars, electron flow in metals and devices, sound propagation in the atmosphere and oceans, the large scale structure of the universe, and much more. The mathematical structure of this flow is only partially understood, involving exponential instability coexisting with “accidental” stability. The flow is qualitatively universal, but this has not been quantified.  Many questions arise, including the scale(s) of the random medium,  and the time evolution of manifolds and “fuzzy” manifolds in phase space.  The classical-quantum (ray-wave)  correspondence in this flow is only partially understood.  This talk will be an introduction to the phenomenon, both visual and mathematical, emphasizing unanswered questions

    12/2/2020Douglas Arnold (U of Minnesota)

    Video

    Title: Preserving geometry in numerical discretization

    Abstract: An important design principle for numerical methods for differential equations is that the discretizations preserve key geometric, topological, and algebraic structures of the original differential system.  For ordinary differential equations, such geometric integrators were developed at the end of the last century, enabling stunning computations in celestial mechanics and other applications that would have been impossible without them.  Since then, structure-preserving discretizations have been developed for partial differential equations.  One of the prime examples has been the finite element exterior calculus or FEEC, in which the structures to preserve are related to Hilbert complexes underlying the PDEs, the de Rham complex being a canonical example.  FEEC has led to highly successful new numerical methods for problems in fluid mechanics, electromagnetism, and other applications which relate to the de Rham complex.  More recently, new tools have been developed which extend the applications of FEEC far beyond the de Rham complex, leading to progress in discretizations of problems from solid mechanics, materials science, and general relativity.

    12/9/2020Manuel Blum and Lenore Blum (Carnegie Mellon)

    Video

    Title: What can Theoretical Computer Science Contribute to the Discussion of Consciousness?

    Abstract: The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We study consciousness from the perspective of theoretical computer science. This is done by formalizing the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. We give a precise formal definition of a Conscious Turing Machine (CTM), also called Conscious AI, in the spirit of Alan Turing’s simple yet powerful definition of a computer. We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness.
    After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness, the range of related concepts that the model explains easily and naturally, and the extent of the theory’s agreement with scientific evidence

  • Seminars

    Seminars Colloquia & Seminar
    02-25-2016 Evolution Equations Seminar

    3:25 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-03-2016 Evolution Equations Seminar

    3:26 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-29-2016 Geometric Analysis Seminar

    3:27 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-5-2018 Mathematical Physics Seminar

    3:27 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Seminars

    Seminars Colloquia & Seminar
    04-07-2016 Evolution Equations Seminar

    3:28 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: JDG 2017 Conference, April 28 – May 2, 2017
    3:29 pm
    11/01/2019-05/02/2017

    In celebration of the Journal of Differential Geometry’s 50th anniversary, the Harvard Math Department will be hosting the Tenth Conference on Geometry and Topology (JDG 2017) from April 28 – May 2, 2017.

    Registration and additional information on the conference can be found at http://abel.harvard.edu/jdg/index.html.

    Confirmed Speakers

    * This event is co-sponsored by Lehigh University and partially supported by the National Science Foundation.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2-23-2018 RM & PT Seminar

    3:30 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Seminars

    Seminars Colloquia & Seminar
    4/4/2019 General Relativity Seminar

    3:30 pm-4:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    02-29-2016 Social Science Application Forum

    3:30 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/14/2019 General Relativity Seminar

    3:30 pm-4:30 pm
    11/01/2019
  • Colloquium
    3:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/15/2019 Spacetime Seminar

    3:30 pm-5:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/10/2019 Spacetime Seminar

    3:30 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/17/2018 RM & PT Seminar

    3:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    02-29-2016 Mathematical Physics Seminar

    3:31 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-01-2016 Geometric Analysis Seminar

    3:32 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-10-2016 Evolution Equations Seminar

    3:34 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Working Conference on Materials and Data Analysis, March 27-30, 2017
    3:34 pm
    11/01/2019-03/30/2017

    The Center of Mathematical Sciences and Applications will be hosting a 5-day working Conference on Materials and Data Analysis and related areas, March 27-30, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Photos of the event can be found on CMSA’s Blog.

     Participants:

    Organizers:

    * This event is sponsored by CMSA Harvard University.

    Schedule:

    Monday, March 27

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amKieron Burke, University of California, IrvineBackground in DFT and electronic structure calculations
    10:00am – 11:00amKieron Burke, University of California, Irvine

    The density functionals machines can learn

    11:00am – 12:00pmSadasivan Shankar, Harvard UniversityA few key principles for applying Machine Learning to Materials (or Complex Systems) — Scientific and Engineering Perspectives

    Tuesday, March 28

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amRyan Adams, HarvardTBA
    10:00am – 11:00amGábor Csányi, University of Cambridge

    Interatomic potentials using machine learning: accuracy, transferability and chemical diversity

    11:00am – 1:00pmLunch Break
    1:00pm – 2:00pmEvan Reed, Stanford UniversityTBA

     Wednesday, March 29 

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amPatrick Riley, GoogleThe Message Passing Neural Network framework and its application to molecular property prediction
    10:00am – 11:00amJörg Behler, University of GöttingenTBA
    11:00am – 12:00pmEkin Doğuş Çubuk, Stanford UniversTBA
    4:00pmLeslie Greengard, Courant InstituteInverse problems in acoustic scattering and cryo-electron microscopy

    CMSA Colloquium

    Thursday, March 30

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amMatthias Rupp, Fitz Haber Institute of the Max Planck SocietyTBA
    10:00am – 11:00amPetros Koumoutsakos, Radcliffe Institute for Advanced Study, HarvardTBA
    11:00am – 1:00pmLunch Break
    1:00pm – 2:00pmDennis Sheberla, Harvard UniversityRapid discovery of functional molecules by a high-throughput virtual screening
  • CMSA EVENT: Workshop on Discrete and Topological Models for Effective Field Theories, January 9-13, 2017
    3:35 pm-3:36 pm
    11/01/2019-01/13/2017

    The Center of Mathematical Sciences and Applications will be hosting a Workshop on “Discrete and Topological Models for Effective Field Theories,” January 9-13, 2017.  The workshop will be hosted in G02 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Titles, abstracts and schedule will be provided nearer to the event.

    Participants:

    Dan Freed, UT Austin

    Anton Kapustin, California Institute of Technology

    Alexei Y. Kitaev, California Institute of Technology

    Greg Moore, Rutgers University

    Constantin Teleman, University of Oxford

    Organizers:

    Mike Hopkins, Shing-Tung Yau

    * This event is sponsored by CMSA Harvard University.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-09-2016 Random Matrix & Probability Theory

    3:35 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-23-2016 Random Matrix & Probability Theory

    3:37 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    3:38 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Working Conference on Covariance Analysis in Biology, May 1-4, 2017
    3:40 pm-3:41 pm
    11/01/2019-05/02/2017

    The Center of Mathematical Sciences and Applications will be hosting a working Conference on Covariance Analysis in Biology, May 1-4, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    This event is open and free.  If you would like to attend, please register here to help us keep a headcount. A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Speakers:

    Orr Ashenberg, Fred Hutchinson Cancer Research Center

    John Barton, Massachusetts Institute of Technology

    Simona Cocco, Laboratoire de Physique Statistique de l’ENS

    Sean Eddy, Harvard University

    Efthimios Kaxiras, Harvard University

    Michael Laub, Massachusetts Institute of Technology

    Debora S. Marks, Harvard University

    Govind Menon, Brown University

    Rémi Monasson, Laboratoire de Physique Théorique de l’ENS

    Andrew Murray, Harvard University

    Ilya Nemenman, Emory College

    Chris Sander, Dana-Farber Cancer Institute, Harvard Medical School

    Dave Thirumalai, University of Texas at Austin

    Martin Weigt, IBPS, Université Pierre et Marie Curie

    Matthieu Wyart, EPFL

    More speakers will be confirmed soon.

     

    Schedule:

    (Please click here for a downloadable version of the schedule.)

    Please note that the schedule for both days is currently tentative and is subject to change.

    May 1, Monday

    TimeSpeakerTopic
    9:00-10:00amSean EddyTBA
    10:00-11:00amMike LaubTBA
    11:00am-12:00pmIlya NemenmanTBA
    May 2, Tuesday
    TimeSpeakerTopic
    9:00-10:00amOrr AshenbergTBA
    10:00-11:00amDebora MarksTBA
    11:00am-12:00pmMartin WeigtTBA
    4:30pm-5:30pmSimona CoccoCMSA Colloquia

     

    May 3, Wednesday
    TimeSpeakerTopic
    9:00-10:00amAndrew MurrayTBA
    10:00-11:00amMatthieu WyartTBA
    11:00am-12:00pmRémi MonassonTBA

     

    May 4, Thursday
    TimeSpeakerTopic
    9:00-10:00amDavid ThirumalaiTBA
    10:00-11:00amChris SanderTBA
    11:00am-12:00pmJohn BartonTBA

     

    Organizers:

    Michael Brenner, Lucy Colwell, Elena Rivas, Eugene Shakhnovich

    * This event is sponsored by CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    03-07-2016 Mathematical Physics Seminar

    3:41 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2-26-2018 Mathematical Physics Seminar

    3:42 pm
    11/01/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-11-2016 Random Matrix & Probability Theory

    3:42 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: A Celebration of Symplectic Geometry: 15 Years of JSG, June 5-6, 2017
    3:44 pm
    11/01/2019-05/04/2017

    In celebration of the Journal of Symplectic Geometry’s 15th anniversary, the Center of Mathematical Sciences and Applications will be hosting A Celebration of Symplectic Geometry: 15 Years of JSG on June 5-6, 2017.

    To register for this event, please click here.

    Confirmed speakers:

    The conference is co-organized by Denis Auroux and Victor Guillemin. Additional information on the conference will be announced closer to the event.

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

    Schedule:

    The schedule for both days is currently tentative and is subject to change. A pdf version of the schedule can also be downloaded here.

    June 5, Monday (Full day)

    TimeSpeakerTopic
    8:30am – 9:0amBreakfast
    9:00am – 10:00amJonathan WeitsmanTitle: On the geometric quantization of (some) Poisson manifolds
    10:30am – 11:30amEckhard MeinrenkenTitle: On Hamiltonian loop group spaces

    Abstract: Let G be a compact Lie group. We explain a construction of an LG-equivariant spinor module over any Hamiltonian loop group space with proper moment map. It may be regarded as its `canonical spin-c structure’. We show how to reduce to finite dimensions, resulting in actual spin-s structure on transversals, as well as twisted spin-c structures for the associated quasi-hamiltonian space. This is based on joint work with Yiannis Loizides and Yanli Song.

    11:30am – 1:30pmBreak
    1:30pm – 2:30pmAna Rita PiresTitle: Infinite staircases in symplectic embedding problems

    Abstract: McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with Cristofaro-Gardiner, Holm and Mandini.

    Video

    3:00pm – 4:00pmSobhan SeyfaddiniTitle: Rigidity of conjugacy classes in groups of area-preserving homeomorphisms

    Abstract: Motivated by understanding the algebraic structure of groups of area-preserving homeomorphims F. Beguin, S. Crvoisier, and F. Le Roux were lead to the following question: Can the conjugacy class of a Hamiltonian homeomorphism be dense? We will show that one can rule out existence of dense conjugacy classes by simply counting fixed points. This is joint work with Le Roux and Viterbo.

    4:30pm – 5:30pmRoger CasalsTitle: Differential Algebra of Cubic Graphs
    Abstract: In this talk we will associate a combinatorial dg-algebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations and examples. From there we study the Legendrian surfaces behind these constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.Video

    June 6, Tuesday (Full day)

    TimeSpeakerTopic
    8:30am – 9:00amBreakfast
    9:00am – 10:00amAlejandro UribeTitle: Semi-classical wave functions associated with isotropic submanifolds of phase space

    Abstract: After reviewing fundamental ideas on the quantum-classical correspondence, I will describe how to associate spaces of semi-classical wave functions to isotropic submanifolds of phase space satisfying a Bohr-Sommerfeld condition. Such functions have symbols that are symplectic spinors, and they satisfy a symbol calculus under the action of quantum observables. This is the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin, and it is joint work with Victor Guillemin and Zuoqin Wang. I will inlcude applications and open questions.

    Video

    10:30am – 11:30amAlisa KeatingTitle: Symplectomorphisms of exotic discs

    Abstract: It is a theorem of Gromov that the group of compactly supported symplectomorphisms of R^4, equipped with the standard symplectic form, is contractible. While nothing is known in higher dimensions for the standard symplectic form, we show that for some exotic symplectic forms on R^{4n}, for all but finitely n, there exist compactly supported symplectomorphisms that are smoothly non-trivial. The principal ingredients are constructions of Milnor and Munkres, a symplectic and contact version of the Gromoll filtration, and Borman, Eliashberg and Murphy’s work on existence of over-twisted contact structures. Joint work with Roger Casals and Ivan Smith.

    Video

    11:30am – 1:30pmBreak
    1:30pm – 2:30pmChen HeTitle: Morse theory on b-symplectic manifolds

    Abstract: b-symplectic (or log-symplectic) manifolds are Poisson manifolds equipped with symplectic forms of logarithmic singularity. Following Guillemin, Miranda, Pires and Scott’s introduction of Hamiltonian group actions on b-symplectic manifolds, we will survey those classical results of Hamiltonian geometry to the b-symplectic case.

    Video

    3:00pm – 4:00pmYael KarshonTitle: Geometric quantization with metaplectic-c structures

    Abstract: I will present a variant of the Kostant-Souriau geometric quantization procedure that uses metaplectic-c structures to incorporate the “half form correction” into the prequantization stage. This goes back to the late 1970s but it is not widely known and it has the potential to generalize and improve upon recent works on geometric quantization.

    Video


  • Seminars

    Seminars Colloquia & Seminar
    03-08-2016 Geometric Analysis Seminar

    3:44 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-21-2016 Mathematical Physics Seminar

    3:46 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-24-2016 Evolution Equations Seminar

    3:47 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: 2017 Big Data Conference
    3:47 pm
    11/01/2019-08/19/2017
    1 Oxford Street, Cambridge MA 02138

    The Center of Mathematical Sciences and Applications will be hosting a conference on Big Data from August 18 – 19, 2017, in Hall D of the Science Center at Harvard University.

    The Big Data Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the third conference on Big Data the Center will host as part of our annual events, and is co-organized by Richard Freeman, Scott Kominers, Jun Liu, Horng-Tzer Yau and Shing-Tung Yau.

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

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

    Confirmed Speakers:

     

    Following the conference, there will be a two-day workshop from August 20-21. The workshop is organized by Scott Kominers, and will feature:

    • Jörn Boehnke, Harvard University
    • Nikhil Naik, Harvard University
    • Bradly Stadie, Open AI, University of California, Berkeley

     

    Conference Schedule

    A PDF version of the schedule below can also be downloaded here.

    August 18, Friday (Full day)

    TimeSpeakerTopic
    8:30 am – 9:00 amBreakfast
    9:00 am – 9:40 amMohammad Akbarpour

    Video

    Title: Information aggregation in overlapping generations and the emergence of experts

    Abstract: We study a model of social learning with “overlapping generations”, where agents meet others and share data about an underlying state over time. We examine under what conditions the society will produce individuals with precise knowledge about the state of the world. There are two information sharing regimes in our model: Under the full information sharing technology, individuals exchange the information about their point estimates of an underlying state, as well as their sources (or the precision of their signals) and update their beliefs by taking a weighted average. Under the limited information sharing technology, agents only observe the information about the point estimates of those they meet, and update their beliefs by taking a weighted average, where weights can depend on the sequence of meetings, as well as the labels. Our main result shows that, unlike most social learning settings, using such linear learning rules do not guide the society (or even a fraction of its members) to learn the truth, and having access to, and exploiting knowledge of the precision of a source signal are essential for efficient social learning (joint with Amin Saberi & Ali Shameli).

    9:40 am – 10:20 amLucas Janson

    Video

    Title: Model-Free Knockoffs For High-Dimensional Controlled Variable Selection

    Abstract: Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new framework of model-free knockoffs, which reads from a different perspective the knockoff procedure (Barber and Candès, 2015) originally designed for controlling the false discovery rate in linear models. The key innovation of our method is to construct knockoff variables probabilistically instead of geometrically. This enables model-free knockoffs to deal with arbitrary (and unknown) conditional models and any dimensions, including when the dimensionality p exceeds the sample size n, while the original knockoffs procedure is constrained to homoscedastic linear models with n greater than or equal to p. Our approach requires the design matrix be random (independent and identically distributed rows) with a covariate distribution that is known, although we show our procedure to be robust to unknown/estimated distributions. As we require no knowledge/assumptions about the conditional distribution of the response, we effectively shift the burden of knowledge from the response to the covariates, in contrast to the canonical model-based approach which assumes a parametric model for the response but very little about the covariates. To our knowledge, no other procedure solves the controlled variable selection problem in such generality, but in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case-control study of Crohn’s disease in the United Kingdom, making twice as many discoveries as the original analysis of the same data.

    Slides

    10:20 am – 10:50 amBreak
    10:50 pm – 11:30 pmNoureddine El Karoui

    Video

    Title: Random matrices and high-dimensional statistics: beyond covariance matrices

    Abstract: Random matrices have played a central role in understanding very important statistical methods linked to covariance matrices (such as Principal Components Analysis, Canonical Correlation Analysis etc…) for several decades. In this talk, I’ll show that one can adopt a random-matrix-inspired point of view to understand the performance of other widely used tools in statistics, such as M-estimators, and very common methods such as the bootstrap. I will focus on the high-dimensional case, which captures well the situation of “moderately” difficult statistical problems, arguably one of the most relevant in practice. In this setting, I will show that random matrix ideas help upend conventional theoretical thinking (for instance about maximum likelihood methods) and highlight very serious practical problems with resampling methods.

    11:30 am – 12:10 pmNikhil Naik

    Video

    Title: Understanding Urban Change with Computer Vision and Street-level Imagery

    Abstract: Which neighborhoods experience physical improvements? In this work, we introduce a computer vision method to measure changes in the physical appearances of neighborhoods from time-series street-level imagery. We connect changes in the physical appearance of five US cities with economic and demographic data and find three factors that predict neighborhood improvement. First, neighborhoods that are densely populated by college-educated adults are more likely to experience physical improvements. Second, neighborhoods with better initial appearances experience, on average, larger positive improvements. Third, neighborhood improvement correlates positively with physical proximity to the central business district and to other physically attractive neighborhoods. Together, our results illustrate the value of using computer vision methods and street-level imagery to understand the physical dynamics of cities.

    (Joint work with Edward L. Glaeser, Cesar A. Hidalgo, Scott Duke Kominers, and Ramesh Raskar.)

    12:10 pm – 12:25 pmVideo #1

    Video #2

    Data Science Lightning Talks
    12:25 pm – 1:30 pmLunch
    1:30 pm – 2:10 pmTracy Ke

    Video

    Title: A new SVD approach to optimal topic estimation

    Abstract: In the probabilistic topic models, the quantity of interest—a low-rank matrix consisting of topic vectors—is hidden in the text corpus matrix, masked by noise, and Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank matrix and the singular vectors of the text corpus matrix are usually complicated and hard to spell out, so how to use SVD for learning topic models faces challenges.

    We overcome the challenge by revealing a surprising insight: there is a low-dimensional simplex structure which can be viewed as a bridge between the low-rank matrix of interest and the SVD of the text corpus matrix, and which allows us to conveniently reconstruct the former using the latter. Such an insight motivates a new SVD-based approach to learning topic models.

    For asymptotic analysis, we show that under a popular topic model (Hofmann, 1999), the convergence rate of the l1-error of our method matches that of the minimax lower bound, up to a multi-logarithmic term. In showing these results, we have derived new element-wise bounds on the singular vectors and several large deviation bounds for weakly dependent multinomial data. Our results on the convergence rate and asymptotical minimaxity are new. We have applied our method to two data sets, Associated Process (AP) and Statistics Literature Abstract (SLA), with encouraging results. In particular, there is a clear simplex structure associated with the SVD of the data matrices, which largely validates our discovery.

    2:10 pm – 2:50 pmAlbert-László Barabási

    Video

    Title: Taming Complexity: From Network Science to Controlling Networks

    Abstract: The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here we explore the controllability of an arbitrary complex network, identifying the set of driver nodes whose time-dependent control can guide the system’s entire dynamics. We apply these tools to several real networks, unveiling how the network topology determines its controllability. Virtually all technological and biological networks must be able to control their internal processes. Given that, issues related to control deeply shape the topology and the vulnerability of real systems. Consequently unveiling the control principles of real networks, the goal of our research, forces us to address series of fundamental questions pertaining to our understanding of complex systems.

     

    2:50 pm – 3:20 pmBreak
    3:20 pm – 4:00 pmMarena Lin

    Video

    Title: Optimizing climate variables for human impact studies

    Abstract: Estimates of the relationship between climate variability and socio-economic outcomes are often limited by the spatial resolution of the data. As studies aim to generalize the connection between climate and socio-economic outcomes across countries, the best available socio-economic data is at the national level (e.g. food production quantities, the incidence of warfare, averages of crime incidence, gender birth ratios). While these statistics may be trusted from government censuses, the appropriate metric for the corresponding climate or weather for a given year in a country is less obvious. For example, how do we estimate the temperatures in a country relevant to national food production and therefore food security? We demonstrate that high-resolution spatiotemporal satellite data for vegetation can be used to estimate the weather variables that may be most relevant to food security and related socio-economic outcomes. In particular, satellite proxies for vegetation over the African continent reflect the seasonal movement of the Intertropical Convergence Zone, a band of intense convection and rainfall. We also show that agricultural sensitivity to climate variability differs significantly between countries. This work is an example of the ways in which in-situ and satellite-based observations are invaluable to both estimates of future climate variability and to continued monitoring of the earth-human system. We discuss the current state of these records and potential challenges to their continuity.

    4:00 pm – 4:40 pmAlex Peysakhovich Title: Building a cooperator

    Abstract: A major goal of modern AI is to construct agents that can perform complex tasks. Much of this work deals with single agent decision problems. However, agents are rarely alone in the world. In this talk I will discuss how to combine ideas from deep reinforcement learning and game theory to construct artificial agents that can communicate, collaborate and cooperate in productive positive sum interactions.

    4:40 pm – 5:20 pmTze Leung Lai

    Video

    Title: Gradient boosting: Its role in big data analytics, underlying mathematical theory, and recent refinements

    Abstract: We begin with a review of the history of gradient boosting, dating back to the LMS algorithm of Widrow and Hoff in 1960 and culminating in Freund and Schapire’s AdaBoost and Friedman’s gradient boosting and stochastic gradient boosting algorithms in the period 1999-2002 that heralded the big data era. The role played by gradient boosting in big data analytics, particularly with respect to deep learning, is then discussed. We also present some recent work on the mathematical theory of gradient boosting, which has led to some refinements that greatly improves the convergence properties and prediction performance of the methodology.

    August 19, Saturday (Full day)

    TimeSpeakerTopic
    8:30 am – 9:00 amBreakfast
    9:00 am – 9:40 amNatesh Pillai

    Video

    Title: Accelerating MCMC algorithms for Computationally Intensive Models via Local Approximations

    Abstract: We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler’s exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this article: when the likelihood has some local regularity, the number of model evaluations per Markov chain Monte Carlo (MCMC) step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ordinary differential equation (ODE) and partial differential equation (PDE) inference problems, with both synthetic and real data.

    9:40 am – 10:20 amRavi Jagadeesan

    Video

    Title: Designs for estimating the treatment effect in networks with interference

    Abstract: In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring” on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide range of interference functions encountered in applications, we show both by theory and simulations that the classical Neymanian estimator for the direct effect has desirable properties for our designs. This further extends to settings where homophily is present in addition to interference.

    10:20 am – 10:50 amBreak
    10:50 am – 11:30 amAnnie Liang

    Video

    Title: The Theory is Predictive, but is it Complete? An Application to Human Generation of Randomness

    Abstract: When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? This question is difficult to answer, because in general we do not know how much “predictable variation” there is in the problem. In this paper, we consider approaches motivated by machine learning algorithms as a means of constructing a benchmark for the best attainable level of prediction.  We illustrate our methods on the task of predicting human-generated random sequences. Relative to a theoretical machine learning algorithm benchmark, we find that existing behavioral models explain roughly 15 percent of the predictable variation in this problem. This fraction is robust across several variations on the problem. We also consider a version of this approach for analyzing field data from domains in which human perception and generation of randomness has been used as a conceptual framework; these include sequential decision-making and repeated zero-sum games. In these domains, our framework for testing the completeness of theories provides a way of assessing their effectiveness over different contexts; we find that despite some differences, the existing theories are fairly stable across our field domains in their performance relative to the benchmark. Overall, our results indicate that (i) there is a significant amount of structure in this problem that existing models have yet to capture and (ii) there are rich domains in which machine learning may provide a viable approach to testing completeness (joint with Jon Kleinberg and Sendhil Mullainathan).

    11:30 am – 12:10 pmZak Stone

    Video

    Title: TensorFlow: Machine Learning for Everyone

    Abstract: We’ve witnessed extraordinary breakthroughs in machine learning over the past several years. What kinds of things are possible now that weren’t possible before? How are open-source platforms like TensorFlow and hardware platforms like GPUs and Cloud TPUs accelerating machine learning progress? If these tools are new to you, how should you get started? In this session, you’ll hear about all of this and more from Zak Stone, the Product Manager for TensorFlow on the Google Brain team.

    12:10 pm – 1:30 pmLunch
    1:30 pm – 2:10 pmJann Spiess

    Video

    Title: (Machine) Learning to Control in Experiments

    Abstract: Machine learning focuses on high-quality prediction rather than on (unbiased) parameter estimation, limiting its direct use in typical program evaluation applications. Still, many estimation tasks have implicit prediction components. In this talk, I discuss accounting for controls in treatment effect estimation as a prediction problem. In a canonical linear regression framework with high-dimensional controls, I argue that OLS is dominated by a natural shrinkage estimator even for unbiased estimation when treatment is random; suggest a generalization that relaxes some parametric assumptions; and contrast my results with that for another implicit prediction problem, namely the first stage of an instrumental variables regression.

    2:10 pm – 2:50 pmBradly StadieTitle: Learning to Learn Quickly: One-Shot Imitation and Meta Learning

    Abstract: Many reinforcement learning algorithms are bottlenecked by data collection costs and the brittleness of their solutions when faced with novel scenarios.
    We will discuss two techniques for overcoming these shortcomings. In one-shot imitation, we train a module that encodes a single demonstration of a desired behavior into a vector containing the essence of the demo. This vector can subsequently be utilized to recover the demonstrated behavior. In meta-learning, we optimize a policy under the objective of learning to learn new tasks quickly. We show meta-learning methods can be accelerated with the use of auxiliary objectives. Results are presented on grid worlds, robotics tasks, and video game playing tasks.

    2:50 pm – 3:20 pmBreak
    3:20 pm – 4:00 pmHau-Tieng Wu

    Video

    Title: When Medical Challenges Meet Modern Data Science

    Abstract: Adaptive acquisition of correct features from massive datasets is at the core of modern data analysis. One particular interest in medicine is the extraction of hidden dynamics from a single observed time series composed of multiple oscillatory signals, which could be viewed as a single-channel blind source separation problem. The mathematical and statistical problems are made challenging by the structure of the signal which consists of non-sinusoidal oscillations with time varying amplitude/frequency, and by the heteroscedastic nature of the noise. In this talk, I will discuss recent progress in solving this kind of problem by combining the cepstrum-based nonlinear time-frequency analysis and manifold learning technique. A particular solution will be given along with its theoretical properties. I will also discuss the application of this method to two medical problems – (1) the extraction of a fetal ECG signal from a single lead maternal abdominal ECG signal; (2) the simultaneous extraction of the instantaneous heart/respiratory rate from a PPG signal during exercise; (3) (optional depending on time) an application to atrial fibrillation signals. If time permits, the clinical trial results will be discussed.

    4:00 pm – 4:40 pmSifan Zhou

    Video

    Title: Citing People Like Me: Homophily, Knowledge Spillovers, and Continuing a Career in Science

    Abstract: Forward citation is widely used to measure the scientific merits of articles. This research studies millions of journal article citation records in life sciences from MEDLINE and finds that authors of the same gender, the same ethnicity, sharing common collaborators, working in the same institution, or being geographically close are more likely (and quickly) to cite each other than predicted by their proportion among authors working on the same research topics. This phenomenon reveals how social and geographic distances influence the quantity and speed of knowledge spillovers. Given the importance of forward citations in academic evaluation system, citation homophily potentially put authors from minority group at a disadvantage. I then show how it influences scientists’ chances to survive in the academia and continue publishing. Based on joint work with Richard Freeman.

     

    To view photos and video interviews from the conference, please visit the CMSA blog.

     

  • Seminars

    Seminars Colloquia & Seminar
    12-07-2015 Mathematical Physics Seminar

    3:49 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-22-2016 Geometric Analysis Seminar

    3:51 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/16/2019 Colloquium

    4:00 pm
    11/01/2019
  • Yip Lecture Series

    Yip Lecture Series Event
    Yip Annual Lecture

    4:00 pm-5:00 pm
    11/01/2019
    1 Oxford Street, Cambridge MA 02138

    On April 18, 2019 Harvard CMSA hosted the inaugural Yip lecture. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Peter Galison (Harvard Physics).

    The lecture was held from 4:00-5:00pm in Science Center, Hall A.

    Credit:Bronzwaer/Davelaar/Moscibrodzka/Falcke/Radboud University
  • Seminars
    4:00 pm-5:00 pm
    11/01/2019

  • Math Science Lectures in Honor of Raoul Bott

    Math Science Lectures in Honor of Raoul Bott Event
    Math Science Lectures in Honor of Raoul Bott: Mina Aganagic

    4:00 pm
    11/01/2019-04/10/2019
    1 Oxford Street, Cambridge MA 02138

    On April 9 and 10, 2019 the CMSA hosted two lectures by Mina Aganagic (UC Berkeley).  This was the second annual Math Science Lecture Series held in honor of Raoul Bott.

    The lectures took place in Science Center, Hall C

    “Two math lessons from string theory”

    Lecture 1:

     

     

     

     

     

    April 9, 2019

    Title: “Lesson on Integrability”

     

    Abstract: The quantum Knizhnik-Zamolodchikov (qKZ) equation is a difference generalization of the famous Knizhnik-Zamolodchikov (KZ) equation. The problem to explicitly capture the monodromy of the qKZ equation has been open for over 25 years. I will describe the solution to this problem, discovered jointly with Andrei Okounkov. The solution comes from the geometry of Nakajima quiver varieties and has a string theory origin.

    Part of the interest in the qKZ monodromy problem is that its solution leads to integrable lattice models, in parallel to how monodromy matrices of the KZ equation lead to knot invariants. Thus, our solution of the problem leads to a new, geometric approach, to integrable lattice models. There are two other approaches to integrable lattice models, due to Nekrasov and Shatashvili and to Costello, Witten and Yamazaki. I’ll describe joint work with Nikita Nekrasov which explains how string theory unifies the three approaches to integrable lattice models.

    Lecture 2:

     

     

     

     

     

    April 10, 2019

    Title: “Lesson on Knot Categorification”

     

    Abstract: An old problem is to find a unified approach to the knot categorification problem. The new string theory perspective on the qKZ equation I described in the first talk can be used to derive two geometric approaches to the problem.

    The first approach is based on a category of B-type branes on resolutions of slices in affine Grassmannians. The second is based on a category of A-branes in a Landau-Ginzburg theory. The relation between them is two dimensional (equivariant) mirror symmetry. String theory also predicts that a third approach to categorification, based on counting solutions to five dimensional Haydys-Witten equations, is equivalent to the first two.

    This talk is mostly based on joint work with Andrei Okounkov.

     

    Information about last year’s Math Science Bott lecture can be found here. 

    Aganagic

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    03-28-2016 Mathematical Physics Seminar

    4:08 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-06-2016 Random Matrix & Probability Theory

    4:10 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-30-2016 Random Matrix & Probability Theory Seminar

    4:11 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-14-2016 Evolution Equations Seminar

    4:13 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-12-2016 Geometric Analysis Seminar

    4:14 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Special Seminar

    4:15 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    03-31-2016 Evolution Equations Seminar

    4:15 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    4:15 pm-5:15 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    Duality String Seminar, Thursdays

    4:15 pm-6:00 pm
    11/01/2019-10/12/2016

    The Duality String  Seminar is held every Thursday at 4:15pm in Jefferson Lab, 453.

    For details, please visit the website.

    * The Duality String Seminar is sponsored by the Center of Mathematical Sciences and Applications’ Cheng Yu-Tong Fund, for Research at the Interface of Mathematics and Physics.

  • Seminars

    Seminars Colloquia & Seminar
    04-04-2016 Mathematical Physics Seminar

    4:20 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-05-2016 Geometric Analysis Seminar

    4:21 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-11-2016 Mathematical Physics Seminar

    4:22 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-07-2016 Evolution Equations Seminar

    4:24 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-06-2016 Seminar on General Relativity

    4:25 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-11-2016 Random Matrix & Probability Theory Seminar

    4:28 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-13-2016 General Relativity Seminar

    4:29 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars
    4:30 pm-5:30 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2/14/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium

    Colloquium Colloquia & Seminar
    2/20/2019 Colloquium

    4:30 pm-5:00 pm
    11/01/2019
  • Colloquium

    Colloquium Colloquia & Seminar
    2/13/2019 Colloquium

    4:30 pm-5:00 pm
    11/01/2019
  • Seminars
    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    1/30/2019 Colloquium

    4:30 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/4/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 RM & PT Seminar

    4:30 pm-5:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/24/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/9/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Seminars
    4:30 pm-5:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4/17/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    10/2/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    9/18/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    04-20-2016 General Relativity Seminar

    4:30 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    3/20/2019 Colloquium

    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm-5:30 pm
    11/01/2019
  • Colloquium
    4:30 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3/28/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    04-18-2016 Social Science Application Forum

    4:31 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:33 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-19-2016 Geometric Analysis Seminar

    4:33 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-18-2016 Mathematical Physics Seminar

    4:34 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:34 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-21-2016 Evolution Equations Seminar

    4:35 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:36 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-20-2016 Random Matrix & Probability Theory Seminar

    4:37 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-26-2016 Geometric Analysis Seminar

    4:38 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:39 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-25-2016 Mathematical Physics Seminar

    4:39 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    4:41 pm
    11/01/2019
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-27-2016 Random Matrix & Probability Theory Seminar

    4:42 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-27-2016 General Relativity Seminar

    4:44 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-28-2016 CMSA Special Seminar

    4:45 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-28-2016 Evolution Equations Seminar

    4:46 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-04-2016 General Relativity Seminar

    4:48 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-29-2016 CMSA Special Seminar

    4:49 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    05-02-2016 Mathematical Physics Seminar

    4:50 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-05-2016 Evolution Equations Seminar

    4:51 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-25-2016 General Relativity Seminar

    4:52 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar
    4:54 pm
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
    4:58 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium
    5:00 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    2018 HMS Focused Lecture Series

    5:00 pm
    11/01/2019

    As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester. The lectures will take place  on Tuesdays and Thursdays in the CMSA Building, 20 Garden Street, Room G10.

    The schedule will be updated below.

    DateSpeakerTitle/Abstract
    January 23, 25, 30 and February 1 

    3-5pm

    *Room G10*

    Ivan Losev 

    (Northeastern)

    Title: BGG category O: towards symplectic duality 

    Abstract: We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson, Ginzburg and Soergel on the Koszul duality for such categories, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting.

    Approximate (optimistic) plan of the lectures:

    1) Preliminaries and BGG category O.

    2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem.

    3) Localization theorem continued. Soergel modules.

    4) Koszul algebras and Koszul duality for categories O.

    Time permitting: other instances of Symplectic duality.

    Prerequisites:

    Semi-simple Lie algebras and their finite dimensional representation theory.

    Some  Algebraic geometry. No prior knowledge of category O/ Geometric

    Representation theory is assumed.

    Scanned from a Xerox Multifunction Device

    February 27, 

    and March 1

    3-5pm

    Colin Diemer 

    (IHES)

    Title: Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS. 

    Abstract: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau’s the role of the mirror map is well-appreciated. In these talks I’ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov, Kontsevich, Pantev), the interplay of the topology  of LG models with autoequivalence relations in the Calabi-Yau setting, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we’ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster).

    March 6 and 8 

    4-5pm

    Adam Jacob 

    (UC Davis)

    Title: The deformed Hermitian-Yang-Mills equation 

    Abstract: In this series I will discuss the deformed Hermitian-Yang-Mills equation, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible, and cover joint work with T.C. Collins and S.-T. Yau.

    March 6, 8, 13, 15 

    3-4pm

    Dmytro Shklyarov 

    (TU Chemnitz)

    Title: On categories of matrix factorizations and their homological invariants 

    Abstract: The talks will cover the following topics:

    1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements.

    2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the “classical” mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models.

    3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data, namely, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type, open varieties, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which, just as their non-equivariant cousins, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds.

    April 10 & 12 

    3-4pm

    Mauricio Romo 

    (IAS)

    Title: Gauged Linear Sigma Models, Supersymmetric Localization and Applications 

    Abstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with  CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs).

    Lecture notes

    April 17, 19, 26 

    3-5pm

    Andrew  Harder 

    (University of Miami)

    Title: Perverse sheaves of categories on surfaces 

    Abstract: Perverse sheaves of categories on a Riemann surface S are systems of categories and functors which are encoded by a graphs on S, and which satisfy conditions that resemble the classical characterization of perverse sheaves on a disc.

    I’ll review the basic ideas behind Kapranov and Schechtman’s notion of a perverse schober and generalize this to perverse sheaves of categories on a punctured Riemann surface. Then I will give several examples of perverse sheaves of categories in both algebraic geometry, symplectic geometry, and category theory. Finally, I will describe how one should be able to use related ideas to prove homological mirror symmetry for certain noncommutative deformations of projective 3-space.

     

    May 15, 17 

    1-3pm

    Charles Doran 

    (University of Alberta)

    Lecture One:
    Title: Picard-Fuchs uniformization and Calabi-Yau geometry
    Abstract:
    Part 1:  We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties, with emphasis on Calabi-Yau manifolds.  Specializing to the case of K3 surfaces, we explore general results on “Picard-Fuchs uniformization” of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces.  As an application, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces.
    Part 2:  We next consider families with one natural complex structure modulus, (e.g., elliptic curves, rank 19 K3 surfaces, b_1=4 Calabi-Yau threefolds, …), where the Picard-Fuchs equations are ODEs.  What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces?  Using Hodge theory and parabolic cohomology, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space.  In particular, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau.

     

    Lecture Two:
    Title: Calabi-Yau fibrations: construction and classification
    Abstract:

    Part 1:  Codimension one Calabi-Yau submanifolds induce fibrations, with the periods of the total space relating to those of the fibers and the structure of the fibration.  We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals.

    Part 2:  We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces.  The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces.  When the total space of the fibration is a Calabi-Yau threefold, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations.  The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1.

  • CMSA EVENT: Noga Alon Public Talk, 9-7-17
    5:00 pm-6:00 pm
    11/01/2019

    Noga Alon (Tel Aviv University) will be giving a public talk on September 7, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

    Title: Graph Coloring: Local and Global

    Abstract: Graph Coloring is arguably the most popular subject in Discrete Mathematics, and its combinatorial, algorithmic and computational aspects have been studied intensively. The most basic notion in the area, the chromatic number of a graph, is an inherently global property. This is demonstrated by the hardness of computation or approximation of this invariant as well as by the existence of graphs with arbitrarily high chromatic number and no short cycles. The investigation of these graphs had a profound impact on Graph Theory and Combinatorics. It combines combinatorial, probabilistic, algebraic and topological techniques with number theoretic tools. I will describe the rich history of the subject focusing on some recent results.

  • CMSA EVENT: 2017 Ding Shum Lecture
    5:00 pm-6:00 pm
    11/01/2019
    1 Oxford Street, Cambridge MA 02138

    Leslie Valiant will be giving the inaugural talk of the Ding Shum Lectures on Tuesday, October 10 at 5:00 pm in Science Center Hall D, Cambridge, MA.

    Learning as a Theory of Everything

    Abstract: We start from the hypothesis that all the information that resides in living organisms was initially acquired either through learning by an individual or through evolution. Then any unified theory of evolution and learning should be able to characterize the capabilities that humans and other living organisms can possess or acquire. Characterizing these capabilities would tell us about the nature of humans, and would also inform us about feasible targets for automation. With this purpose we review some background in the mathematical theory of learning. We go on to explain how Darwinian evolution can be formulated as a form of learning. We observe that our current mathematical understanding of learning is incomplete in certain important directions, and conclude by indicating one direction in which further progress would likely enable broader phenomena of intelligence and cognition to be realized than is possible at present.

     

  • CMSA EVENT: Jennifer Chayes Public Talk, 11-02-17
    5:00 pm-6:00 pm
    11/01/2019

    Jennifer Chayes (Microsoft Research) will be giving a public talk on November 02, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

    Title: Network Science: From the Online World to Cancer Genomics

    Abstract: Everywhere we turn these days, we find that networks can be used to describe relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage many human diseases. In this talk, I look quite generally at some of the models we are using to describe these networks, processes we are studying on the networks, algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. I’ll discuss in some detail particular applications to cancer genomics, applying network algorithms to suggest possible drug targets for certain kinds of cancer.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    05-11-2016 Random Matrix & Probability Theory Seminar

    5:00 pm
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
    5:02 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    06-01-2016 Random Matrix & Probability Theory Seminar

    5:03 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    06-08-2016 Random Matrix & Probability Theory Seminar

    5:04 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    07-12-2016 Chinese Economy Seminar

    5:06 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    07-19-2016 Chinese Economy Seminar

    5:07 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    08-02-2016 China Gazetteer Seminar

    5:08 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-12-2016 Mathematical Physics Seminar

    5:10 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-19-2016 Mathematical Physics Seminar

    5:11 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-21-2016 Random Matrix & Probability Theory Seminar

    5:13 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium

    Colloquium Colloquia & Seminar
    3/27/2019 Colloquium

    5:15 pm-6:15 pm
    11/01/2019
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-23-2018 Math Physics

    5:15 pm
    11/01/2019

    No additional detail for this event.

  • Colloquium

    Colloquium Colloquia & Seminar
    2/13/2019 Colloquium

    5:15 pm-6:15 pm
    11/01/2019
  • Seminars

    Seminars Colloquia & Seminar
    4-16-2018 Social Science Applications Forum

    5:16 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-20-2018 Social Science Applications Forum

    5:18 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-26-16 Mathematical Physics Seminar

    5:32 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-28-2016 Random Matrix & Probability Theory Seminar

    5:35 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    5:36 pm
    11/01/2019

    As part of the Program on Topological Aspects of Condensed Mattera weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

    DateSpeakerTitle/Abstract
    8/29/2018Zeng-Cheng GuTitle: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory

    Abstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.

    9/10/2018Dominic Else, MIT

    Video

    Title: Phases and topology in periodically driven (Floquet) systems

    Abstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.

    9/17/2018Adrian Po, MIT

    Video

    Title: A modern solution to the old problem of symmetries in band theory

    Abstract: There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants.

    9/24/2018Maxim MetlitskiTitle: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs

    Abstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.

    10/1/2018Cancelled
    10/9/2018

    Tuesday

    3:00-4:30pm

    Sagar VijayTitle: Fracton Phases of Matter

    Abstract:  Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped, point-like excitations (“fractons”) that are strictly immobile at zero temperature, and by degenerate ground-states that are locally indistinguishable.  Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions, and these states of matter are a gateway for exploring mechanisms for quantum information storage, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases, constructions of these states using well-studied two-dimensional topological phases, and a model in which the fracton excitations carry a protected internal degeneracy, which provides a natural generalization of non-Abelian anyons to three spatial dimensions.  I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.

    10/15/2018Ethan LakeTitle: A primer on higher symmetries

    Abstract: The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.

    10/22/2018

    Room G02

    Yin-Chen He, PerimeterTitle: Emergent QED3 and QCD3 in condensed matter system

    Abstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.

    10/29/2018Dominic Williamson, Yale

    Video

    Title: Symmetry and topological order in tensor networks

    Abstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.

    11/13/2018

    Tuesday

    3:00-4:30pm

    Jason Alicea, CaltechTitle: Time-crystalline topological superconductors
    11/19/2018X. G. Wen, MIT

    Video

    Title: A classification of 3+1D topological orders

    Abstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.

    12/3/2018

    *Room G02*

    Claudio Chamon, Boston UniversityTitle: Many-body scar states with topological properties in 1D, 2D, and 3D.

    Abstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies.

    12/10/2018

    Room G02

    Anders Sandvik, Boston University and Institute of Physics, CAS, BeijingTitle: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets

    Abstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.

    1/8/2019Lukasz Fidkowski, Univ. of Washington

    Video

    Title: Non-trivial quantum cellular automata in 3 dimensions

    Abstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom.  This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.

    3/18/2019Ari Turner, Technion

    Video

    Title:  Trapping Excitations at Phantasmagoric Wave Vectors

    Abstract:  This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this, and also introduce “finite fields”, which are the number systems one needs to define exponentials mod. 2.

    4/1/2019Yi-Zhuang You (UCSD)Title: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points

    Abstract: Noether’s theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s  theorem at the deconfined quantum critical point (DQCP), which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.

    4/8/2019Adam Nahum (Oxford)Title: Emergent statistical mechanics of entanglement in random unitary circuits

    Abstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.

    4/16/2019

    Lyman 425

    1:30pm

    Xie Chen (Calthech)Title: Foliated Fracton Order

    Abstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk, I will present a new framework, which we call the “foliated fracton order”, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models, but also points to the direction of search for interesting new features.

    4/24/2019

    10:30am

    Michael Freedman (Microsoft Station Q)

    Video

    Title: Quantum cellular automata in higher dimensions

    Abstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.

    4/26/2019

    10:30am

    Maissam Barkeshli (University of Maryland)

    Video

    Title: Relative anomalies in (2+1)D symmetry enriched topological states

    Abstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.

    5/3/2019Yuan-Ming Lu (Ohio State)Title: Spontaneous symmetry breaking from anyon condensation

    Abstract: In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

    5/9/2019

    10:30am

    Michael Zaletel (UC Berkeley)Title: Three-partite entanglement in CFTs and chiral topological orders

    Abstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement, multi-partite entanglement is far richer, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure, the “entanglement of purification,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders, and solicit the audience’s help in proving or disproving it.

    5/28/2019

    10:30am

    Masaki Oshikawa (U Tokyo)Title: Gauge invariance, polarization, and conductivity

     

    Abstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors, and also to general constraints on the electric conductivity.

    7/18/2019Eslam Khalaf (Harvard)

    Title: Dynamical correlations in anomalous disordered wires

    Abstract: In a (multichannel) disordered wire, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case, the classical dynamics are described by diffusion + drift, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.
    The problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.
    The mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.
  • Seminars

    Seminars Colloquia & Seminar
    Spacetime and Quantum Mechanics Seminar

    5:38 pm
    11/01/2019

    As part of the program on Spacetime and Quantum Mechanics, the CMSA will be hosting a weekly seminar on Thursdays at 2:30pm in room G10.

    DateSpeakerTitle/Abstract
    9/12/2019Pasha Pylyavskyy (University of Minnesota)Title: Vector-relation configurations and plabic graphs
    19/18/2019

    2:00pm

    G02

    Francis Brown (University of Oxford)Title: Amplitudes, Polylogs and Moduli Spaces
    9/19/2019Chuck Doran (University of Alberta)Title: Calabi-Yau geometry of the N-loop sunset Feynman integrals

    Abstract: I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals.

    Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli.

    These include: (1) an iterated fibration structure which allows one to “bootstrap” both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (“jump loci”) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via “creative telescoping”; and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties.

    Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev.

    9/26/2019Tomasz Taylor (Northeastern)Title: Celestial Amplitudes
    10/3/2019Simon Caron-Huot (McGill)Title: Poincare Duals of Feynman Integrals
    10/10/2019

    3:30pm

    Yutin Huang (National Taiwan University)Title: Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian
    10/15/2019

    Tuesday

    3:30pm

     

    Sergey Fomin (Univ. of Michigan)

     

    Title: “Morsifications and mutations” (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston). 
    10/18/2019

    Friday 

    G02

    Sebastian Franco (The City College of New York)Title: Graded quivers, generalized dimer models, and topic geometry
    10/31/2019Junjie Rao (Albert Einstein Institute)Title: All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
    11/1/2019

    SC 232

    1:30pm

    George Lusztig (MIT)Title: Total positivity in Springer fibres
    11/12/2019

    Tuesday

    G02

    3:30pm

     

    Pierpaolo Mastrolia (University of Padova)

    Title: Feynman Integrals and Intersection Theory
    11/14/2019

    G02

    Pierpaolo Mastrolia (University of Padova)Title: Feynman Integrals and Intersection Theory Pt. II
    11/21/2019Cristian Vergu (Niels Bohr Institute)Title: The Octagonal Alphabet
    11/26/2019Stephan Stieberger (IAS)Title: Strings on the Celestial Sphere
    12/4/2019Hadleigh Frost (Oxford)Title: BCJ numerators, $\mathcal{M}_{0,n}$, and ABHY

    Abstract: We relate the BCJ numerator Jacobi property to the classical fact that the top homology group of $\mathcal{M}_{0,n}$ is isomorphic to a component of the free Lie algebra. We describe ways to get BCJ numerators, and caution that the BCJ Jacobi property doesn’t imply the existence of what has been called a ‘kinematic algebra.’

     12/5/2019David Kosower (IAS)Title: From scattering amplitudes to classical observables
    12/10/2019Ramis Movassagh (MIT)Title: Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law

    Abstract: In recent years, there has been a surge of activities in proposing “exactly solvable” quantum spin chains with surprising high amount of ground state entanglement–exponentially more than the critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $\sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and ‘generic’ aspects of local spin chains.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-05-2016 Random Matrix & Probability Theory Seminar

    5:41 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/10/2018 Math-Physics Seminar

    5:41 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    5:42 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3/14/2019 Random Matrix and Probability Theory Seminar

    5:45 pm
    11/01/2019
  • Seminars
    5:48 pm
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
    5:52 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/17/2018 Math-Physics Seminar

    5:53 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/24/2018 Math-Physics Seminar

    5:55 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    5:56 pm
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
    5:59 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Workshop on Additive Combinatorics, Oct. 2-6, 2017
    6:00 pm-6:01 pm
    11/01/2019-10/06/2017

    The workshop on additive combinatorics will take place October 2-6, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    Additive combinatorics is a mathematical area bordering on number theory, discrete mathematics, harmonic analysis and ergodic theory. It has achieved a number of successes in pure mathematics in the last two decades in quite diverse directions, such as:

    • The first sensible bounds for Szemerédi’s theorem on progressions (Gowers);
    • Linear patterns in the primes (Green, Tao, Ziegler);
    • Construction of expanding sets in groups and expander graphs (Bourgain, Gamburd);
    • The Kakeya Problem in Euclidean harmonic analysis (Bourgain, Katz, Tao).

    Ideas and techniques from additive combinatorics have also had an impact in theoretical computer science, for example

    • Constructions of pseudorandom objects (eg. extractors and expanders);
    • Constructions of extremal objects (eg. BCH codes);
    • Property testing (eg. testing linearity);
    • Algebraic algorithms (eg. matrix multiplication).

    The main focus of this workshop will be to bring together researchers involved in additive combinatorics, with a particular inclination towards the links with theoretical computer science. Thus it is expected that a major focus will be additive combinatorics on the boolean cube (Z/2Z)^n , which is the object where the exchange of ideas between pure additive combinatorics and theoretical computer science is most fruitful. Another major focus will be the study of pseudorandom phenomena in additive combinatorics, which has been an important contributor to modern methods of generating provably good randomness through deterministic methods. Other likely topics of discussion include the status of major open problems (the polynomial Freiman-Ruzsa conjecture, inverse theorems for the Gowers norms with bounds, explicit correlation bounds against low degree polynomials) as well as the impact of new methods such as the introduction of algebraic techniques by Croot–Pach–Lev and Ellenberg–Gijswijt.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Ben GreenSwastik KoppartyRyan O’DonnellTamar Ziegler.

    Monday, October 2

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast 
    9:30-10:20amJacob FoxTower-type bounds for Roth’s theorem with popular differences

    Abstract: A famous theorem of Roth states that for any $\alpha > 0$ and $n$ sufficiently large in terms of $\alpha$, any subset of $\{1, \dots, n\}$ with density $\alpha$ contains a 3-term arithmetic progression. Green developed an arithmetic regularity lemma and used it to prove that not only is there one arithmetic progression, but in fact there is some integer $d > 0$ for which the density of 3-term arithmetic progressions with common difference $d$ is at least roughly what is expected in a random set with density $\alpha$. That is, for every $\epsilon > 0$, there is some $n(\epsilon)$ such that for all $n > n(\epsilon)$ and any subset $A$ of $\{1, \dots, n\}$ with density $\alpha$, there is some integer $d > 0$ for which the number of 3-term arithmetic progressions in $A$ with common difference $d$ is at least $(\alpha^3-\epsilon)n$. We prove that $n(\epsilon)$ grows as an exponential tower of 2’s of height on the order of $\log(1/\epsilon)$. We show that the same is true in any abelian group of odd order $n$. These results are the first applications of regularity lemmas for which the tower-type bounds are shown to be necessary.

    The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

    10:20-11:00amCoffee Break 
    11:00-11:50amYufei ZhaoTower-type bounds for Roth’s theorem with popular differences

    Abstract:  Continuation of first talk by Jacob Fox. The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

    12:00-1:30pmLunch 
    1:30-2:20pmJop BriëtLocally decodable codes and arithmetic progressions in random settings

    Abstract: This talk is about a common feature of special types of error correcting codes, so-called locally decodable codes (LDCs), and two problems on arithmetic progressions in random settings, random differences in Szemerédi’s theorem and upper tails for arithmetic progressions in a random set in particular. It turns out that all three can be studied in terms of the Gaussian width of a set of vectors given by a collection of certain polynomials. Using a matrix version of the Khintchine inequality and a lemma that turns such polynomials into matrices, we give an alternative proof for the best-known lower bounds on LDCs and improved versions of prior results due to Frantzikinakis et al. and Bhattacharya et al. on arithmetic progressions in the aforementioned random settings.

    Joint work with Sivakanth Gopi

    2:20-3:00pmCoffee Break 
    3:00-3:50pmFernando Shao

    Large deviations for arithmetic progressions

    Abstract: We determine the asymptotics of the log-probability that the number of k-term arithmetic progressions in a random subset of integers exceeds its expectation by a constant factor. This is the arithmetic analog of subgraph counts in a random graph. I will highlight some open problems in additive combinatorics that we encountered in our work, namely concerning the “complexity” of the dual functions of AP-counts.

    4:00-6:00pmWelcome Reception

    Tuesday, October 3

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amEmanuele ViolaInterleaved group products

    Authors: Timothy Gowers and Emanuele Viola

    Abstract: Let G be the special linear group SL(2,q). We show that if (a1,a2) and (b1,b2) are sampled uniformly from large subsets A and B of G^2 then their interleaved product a1 b1 a2 b2 is nearly uniform over G. This extends a result of Gowers (2008) which corresponds to the independent case where A and B are product sets. We obtain a number of other results. For example, we show that if X is a probability distribution on G^m such that any two coordinates are uniform in G^2, then a pointwise product of s independent copies of X is nearly uniform in G^m, where s depends on m only. Similar statements can be made for other groups as well.

    These results have applications in computer science, which is the area where they were first sought by Miles and Viola (2013).

    10:20-11:00amCoffee Break
    11:00-11:50amVsevolod LevOn Isoperimetric Stability

    Abstract: We show that a non-empty subset of an abelian group with a small edge boundary must be large; in particular, if $A$ and $S$ are finite, non-empty subsets of an abelian group such that $S$ is independent, and the edge boundary of $A$ with respect to $S$ does not exceed $(1-c)|S||A|$ with a real $c\in(0,1]$, then $|A|\ge4^{(1-1/d)c|S|}$, where $d$ is the smallest order of an element of $S$. Here the constant $4$ is best possible.

    As a corollary, we derive an upper bound for the size of the largest independent subset of the set of popular differences of a finite subset of an abelian group. For groups of exponent $2$ and $3$, our bound translates into a sharp estimate for the additive  dimension of the popular difference set.

    We also prove, as an auxiliary result, the following estimate of possible independent interest: if $A\subseteq{\mathbb Z}^n$ is a finite, non-empty downset, then, denoting by $w(z)$ the number of non-zero components of the vector $z\in\mathbb{Z}^n$, we have   $$ \frac1{|A|} \sum_{a\in A} w(a) \le \frac12\, \log_2 |A|. $$

    12:00-1:30pmLunch
    1:30-2:20pmElena GrigorescuNP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem

    Abstract: I will discuss the complexity of decoding Reed-Solomon codes, and some results establishing NP-hardness for asymptotically smaller decoding radii than the maximum likelihood decoding radius. These results follow from the study of a generalization of the classical Subset Sum problem to higher moments, which may be of independent interest. I will further discuss a connection with the Prouhet-Tarry-Escott problem studied in Number Theory, which turns out to capture a main barrier in extending our techniques to smaller radii.

    Joint work with Venkata Gandikota and Badih Ghazi.

    2:20-3:00pmCoffee Break
    3:00-3:50pmSean PrendivillePartition regularity of certain non-linear Diophantine equations.

    Abstract:  We survey some results in additive Ramsey theory which remain valid when variables are restricted to sparse sets of arithmetic interest, in particular the partition regularity of a class of non-linear Diophantine equations in many variables.

    Wednesday, October 4

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast 
    9:30-10:20amOlof SisaskBounds on capsets via properties of spectra

    Abstract: A capset in F_3^n is a subset A containing no three distinct elements x, y, z satisfying x+z=2y. Determining how large capsets can be has been a longstanding problem in additive combinatorics, particularly motivated by the corresponding question for subsets of {1,2,…,N}. While the problem in the former setting has seen spectacular progress recently through the polynomial method of Croot–Lev–Pach and Ellenberg–Gijswijt, such progress has not been forthcoming in the setting of the integers. Motivated by an attempt to make progress in this setting, we shall revisit the approach to bounding the sizes of capsets using Fourier analysis, and in particular the properties of large spectra. This will be a two part talk, in which many of the ideas will be outlined in the first talk, modulo the proof of a structural result for sets with large additive energy. This structural result will be discussed in the second talk, by Thomas Bloom, together with ideas on how one might hope to achieve Behrend-style bounds using this method.

    Joint work with Thomas Bloom.

    10:20-11:00amCoffee Break 
    11:00-11:50amThomas BloomBounds on capsets via properties of spectra

    This is a continuation of the previous talk by Olof Sisask.

    12:00-1:30pmLunch 
    1:30-2:20pmHamed HatamiPolynomial method and graph bootstrap percolation

    Abstract: We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori and multidimensional grids (in particular hypercubes). The former answers a question of Morrison and Noel, and the latter provides an alternative and simpler proof for one of their main results. This is based on a joint work with Lianna Hambardzumyan and Yingjie Qian.

    2:20-3:00pmCoffee Break
    3:00-3:50pmArnab BhattacharyyaAlgorithmic Polynomial Decomposition

    Abstract: Fix a prime p. Given a positive integer k, a vector of positive integers D = (D_1, …, D_k) and a function G: F_p^k → F_p, we say a function P: F_p^n → F_p admits a (k, D, G)-decomposition if there exist polynomials P_1, …, P_k: F_p^n -> F_p with each deg(P_i) <= D_i such that for all x in F_p^n, P(x) = G(P_1(x), …, P_k(x)). For instance, an n-variate polynomial of total degree d factors nontrivially exactly when it has a (2, (d-1, d-1), prod)-decomposition where prod(a,b) = ab.

    When show that for any fixed k, D, G, and fixed bound d, we can decide whether a given polynomial P(x_1, …, x_n) of degree d admits a (k,D,G)-decomposition and if so, find a witnessing decomposition, in poly(n) time. Our approach is based on higher-order Fourier analysis. We will also discuss improved analyses and algorithms for special classes of decompositions.

    Joint work with Pooya Hatami, Chetan Gupta and Madhur Tulsiani.

    Thursday, October 5

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amMadhur TulsianiHigher-order Fourier analysis and approximate decoding of Reed-Muller codes

     Abstract: Decomposition theorems proved by Gowers and Wolf provide an appropriate notion of “Fourier transform” for higher-order Fourier analysis. I will discuss some questions and techniques that arise from trying to develop polynomial time algorithms for computing these decompositions.

    I will discuss constructive proofs of these decompositions based on boosting, which reduce the problem of computing these decompositions to a certain kind of approximate decoding problem for codes. I will also discuss some earlier and recent works on this decoding problem.

    Based on joint works with Arnab Bhattacharyya, Eli Ben-Sasson, Pooya Hatami, Noga Ron-Zewi and Julia Wolf.

    10:20-11:00amCoffee Break
    11:00-11:50amJulia WolfStable arithmetic regularity

    The arithmetic regularity lemma in the finite-field model, proved by Green in 2005, states that given a subset A of a finite-dimensional vector space over a prime field, there exists a subspace H of bounded codimension such that A is Fourier-uniform with respect to almost all cosets of H. It is known that in general, the growth of the codimension of H is required to be of tower type depending on the degree of uniformity, and that one must allow for a small number of non-uniform cosets.

    Our main result is that, under a natural model-theoretic assumption of stability, the tower-type bound and non-uniform cosets in the arithmetic regularity lemma are not necessary.  Specifically, we prove an arithmetic regularity lemma for k-stable subsets in which the bound on the codimension of the subspace is a polynomial (depending on k) in the degree of uniformity, and in which there are no non-uniform cosets.

    This is joint work with Caroline Terry.

    12:00-1:30pmLunch 
    1:30-2:20pmWill Sawin

    Constructions of Additive Matchings

    Abstract: I will explain my work, with Robert Kleinberg and David Speyer, constructing large tri-colored sum-free sets in vector spaces over finite fields, and how it shows that some additive combinatorics problems over finite fields are harder than corresponding problems over the integers. 

    2:20-3:00pmCoffee Break
    3:00-3:50pmMei-Chu ChangArithmetic progressions in multiplicative groups of finite fields

    Abstract:   Let G be a multiplicative subgroup of the prime field F_p of size |G|> p^{1-\kappa} and r an arbitrarily fixed positive integer. Assuming \kappa=\kappa(r)>0 and p large enough, it is shown that any proportional subset A of G contains non-trivial arithmetic progressions of length r.

    Friday, October 6

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amAsaf FerberOn a resilience version of the Littlewood-Offord problem

    Abstract:  In this talk we consider a resilience version of the classical Littlewood-Offord problem. That is, consider the sum X=a_1x_1+…a_nx_n, where the a_i-s are non-zero reals and x_i-s are i.i.d. random variables with     (x_1=1)= P(x_1=-1)=1/2. Motivated by some problems from random matrices, we consider the question: how many of the x_i-s  can we typically allow an adversary to change without making X=0? We solve this problem up to a constant factor and present a few interesting open problems.

    Joint with: Afonso Bandeira (NYU) and Matthew Kwan (ETH, Zurich).

    10:20-11:00amCoffee Break
    11:00-11:50amKaave HosseiniProtocols for XOR functions and Entropy decrement

    Abstract: Let f:F_2^n –> {0,1} be a function and suppose the matrix M defined by M(x,y) = f(x+y) is partitioned into k monochromatic rectangles.  We show that F_2^n can be partitioned into affine subspaces of co-dimension polylog(k) such that f is constant on each subspace. In other words, up to polynomial factors, deterministic communication complexity and parity decision tree complexity are equivalent.

    This relies on a novel technique of entropy decrement combined with Sanders’ Bogolyubov-Ruzsa lemma.

    Joint work with Hamed Hatami and Shachar Lovett

    12:00-1:30pmLunch
    1:30-2:20pmGuy Kindler

    From the Grassmann graph to Two-to-Two games

    Abstract: In this work we show a relation between the structure of the so called Grassmann graph over Z_2 and the Two-to-Two conjecture in computational complexity. Specifically, we present a structural conjecture concerning the Grassmann graph (together with an observation by Barak et. al., one can view this as a conjecture about the structure of non-expanding sets in that graph) which turns out to imply the Two-to-Two conjecture.

    The latter conjecture its the lesser-known and weaker sibling of the Unique-Games conjecture [Khot02], which states that unique games (a.k.a. one-to-one games) are hard to approximate. Indeed, if the Grassmann-Graph conjecture its true, it would also rule out some attempts to refute the Unique-Games conjecture, as these attempts provide potentially efficient algorithms to solve unique games, that would actually also solve two-to-two games if they work at all.

    These new connections between the structural properties of the Grassmann graph and complexity theoretic conjectures highlight the Grassmann graph as an interesting and worthy object of study. We may indicate some initial results towards analyzing its structure.

    This is joint work with Irit Dinur, Subhash Khot, Dror Minzer, and Muli Safra.

  • CMSA EVENT: Current Developments In Mathematics 2018
    6:00 pm-5:00 pm
    11/01/2019-11/17/2018
    CDM2018

    Current Developments in Mathematics 2018 Conference.

    Friday, Nov. 16, 2018 2:15 pm – 6:00 pm

    Saturday, Nov. 17, 2018  9:00 am – 5:00 pm

    Harvard University Science Center, Hall B

    Visit the conference page here 

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/01/2018 Math-Physics Seminar

    6:01 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Fluid turbulence and Singularities of the Euler/ Navier Stokes equations
    6:02 pm
    11/01/2019-03/15/2018
    Fluid turbulence

    The Workshop on Fluid turbulence and Singularities of the Euler/ Navier Stokes equations will take place on March 13-15, 2019. This is the first of two workshop organized by Michael Brenner, Shmuel Rubinstein, and Tom Hou. The second, Machine Learning for Multiscale Model Reduction, will take place on March 27-29, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

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

    List of registrants

    Speakers: 

  • General Relativity Seminar
    6:03 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/08/2018 Math-Physics Seminar

    6:04 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:05 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Blockchain Conference
    6:05 pm
    11/01/2019-01/25/2018
    Blockchain

    On January 24-25, 2019 the Center of Mathematical Sciences will be hosting a conference on distributed-ledger (blockchain) technology. The conference is intended to cover a broad range of topics, from abstract mathematical aspects (cryptography, game theory, graph theory, theoretical computer science) to concrete applications (in accounting, government, economics, finance, management, medicine). The talks will take place in Science Center, Hall D.

    https://youtu.be/FyKCCutxMYo

    List of registrants

    Photos

    Speakers: 

  • Special Seminar
    6:06 pm
    11/01/2019

    No additional detail for this event.

  • CMSA EVENT: Workshop on Algebraic Methods in Combinatorics
    6:07 pm
    11/01/2019-11/17/2017

    The workshop on Algebraic Methods in Combinatorics will take place November 13-17, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    The main focus of the workshop is the application of algebraic method to study problems in combinatorics.  In recent years there has been a large number of results in which the use of algebraic technique has resulted in significant improvements to long standing open problems. Such problems include the finite field Kakeya problem, the distinct distance problem of Erdos and, more recently, the cap-set problem. The workshop will include talks on all of the above mentioned problem as well as on recent development in related areas combining combinatorics and algebra.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Zeev DvirLarry Guth, and Shubhangi Saraf.

    Click here for a list of registrants.

    Monday, Nov. 13

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Jozsef Solymosi

     

    On the unit distance problem

    Abstract: Erdos’ Unit Distances conjecture states that the maximum number of unit distances determined by n points in the plane is almost linear, it is O(n^{1+c}) where c goes to zero as n goes to infinity. In this talk I will survey the relevant results and propose some questions which would imply that the maximum number of unit distances is o(n^{4/3}). 

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

     

    Orit RazIntersection of linear subspaces in R^d and instances of the PIT problem 

    Abstract: In the talk I will tell about a new deterministic, strongly polynomial time algorithm which can be viewed in two ways. The first is as solving a derandomization problem, providing a deterministic algorithm to a new special case of the PIT (Polynomial Identity Testing) problem. The second is as computing the dimension of the span of a collection of flats in high dimensional space. The talk is based on a joint work with Avi Wigderson.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Andrew Hoon Suk

    Ramsey numbers: combinatorial and geometric

    Abstract:  In this talk, I will discuss several results on determining the tower growth rate of Ramsey numbers arising in combinatorics and in geometry.  These results are joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Janos Pach, and Benny Sudakov.

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Josh Zahl

    Cutting curves into segments and incidence geometry

    4:00-6:00pmWelcome Reception

    Tuesday, Nov. 14

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Péter Pál Pach

    Polynomials, rank and cap sets

    AbstractIn this talk we will look at a new variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like $\mathbb{Z}_4^n$ and $\mathbb{F}_q^n$ are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets and mention further applications of the method.

    10:30-11:00amCoffee Break
    11:00-12:00pmJordan Ellenberg

    The Degeneration Method

    Abstract:  In algebraic geometry, a very popular way to study (nice, innocent, nonsingular) varieties is to degenerate them to (weird-looking, badly singular, nonreduced) varieties (which are actually not even varieties but schemes.)  I will talk about some results in combinatorics using this approach (joint with Daniel Erman) and some ideas for future applications of the method.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Larry GuthThe polynomial method in Fourier analysis

    Abstract: This will be a survey talk about how the polynomial method helps to understand problems in Fourier analysis.  We will review some applications of the polynomial method to problems in combinatorial geometry.  Then we’ll discuss some problems in Fourier analysis, explain the analogy with combinatorial problems, and discuss how to adapt the polynomial method to the Fourier analysis setting.

     

    2:30-3:00pm

    Coffee Break
    3:00-4:00pmOpen Problem

    Wednesday, Nov. 15

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

     

    Avi Wigderson

    The “rank method” in arithmetic complexity: Lower bounds and barriers to lower bounds

    Abstract: Why is it so hard to find a hard function? No one has a clue! In despair, we turn to excuses called barriers. A barrier is a collection of lower bound techniques, encompassing as much as possible from those in use, together with a  proof that these techniques cannot prove any lower bound better than the state-of-art (which is often pathetic, and always very far from what we expect for complexity of random functions).

    In the setting of  Boolean computation of Boolean functions (where P vs. NP is the central open problem),  there are several famous barriers which provide satisfactory excuses, and point to directions in which techniques may be strengthened.

    In the setting of Arithmetic computation of polynomials and tensors (where  VP vs. VNP is the central open problem) we have no satisfactory barriers, despite some recent interesting  attempts.

    This talk will describe a new barrier for the Rank Method in arithmetic complexity, which encompass most lower bounds in this field. It also encompass most lower bounds on tensor rank in algebraic geometry (where the the rank method is called Flattening).

    I will describe the rank method, explain how it is used to prove lower bounds, and then explain its limits via the new barrier result. As an example, it shows that while the best lower bound on the tensor rank of any explicit 3-dimensional tensor of side n (which is achieved by a rank method) is 2n, no rank method can prove a lower bound which exceeds 8n

    (despite the fact that a random such tensor has rank quadratic in n).

    No special background knowledge is assumed. The audience is expected to come up with new lower bounds, or else, with new excuses for their absence.

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Venkat Guruswami

    Subspace evasion, list decoding, and dimension expanders

     Abstract: A subspace design is a collection of subspaces of F^n (F = finite field) most of which are disjoint from every low-dimensional subspace of F^n. This notion was put forth in the context of algebraic list decoding where it enabled the construction of optimal redundancy list-decodable codes over small alphabets as well as for error-correction in the rank-metric. Explicit subspace designs with near-optimal parameters have been constructed over large fields based on polynomials with structured roots. (Over small fields, a construction via cyclotomic function fields with slightly worse parameters is known.) Both the analysis of the list decoding algorithm as well as the subspace designs crucially rely on the *polynomial method*.

    Subspace designs have since enabled progress on linear-algebraic analogs of Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In particular, they yield an explicit construction of constant-degree dimension expanders over large fields. While constructions of such dimension expanders are known over any field, they are based on a reduction to a highly non-trivial form of vertex expanders called monotone expanders. In contrast, the subspace design approach is simpler and works entirely within the linear-algebraic realm. Further, in recent (ongoing) work, their combination with rank-metric codes yields dimension expanders with expansion proportional to the degree.

    This talk will survey these developments revolving around subspace designs, their motivation, construction, analysis, and connections.

    (Based on several joint works whose co-authors include Chaoping Xing, Swastik Kopparty, Michael Forbes, Nicolas Resch, and Chen Yuan.)

    12:00-1:30pmLunch
    1:30-2:30pm

     

    David Conlon

    Finite reflection groups and graph norms

    Abstract: For any given graph $H$, we may define a natural corresponding functional $\|.\|_H$. We then say that $H$ is norming if $\|.\|_H$ is a semi-norm. A similar notion $\|.\|_{r(H)}$ is defined by $\| f \|_{r(H)} := \| | f | \|_H$ and $H$ is said to be weakly norming if $\|.\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. Using results from the theory of finite reflection groups, we identify a much larger class of weakly norming graphs. This result includes all previous examples of weakly norming graphs and adds many more. We also discuss several applications of our results. In particular, we define and compare a number of generalisations of Gowers’ octahedral norms and we prove some new instances of Sidorenko’s conjecture. Joint work with Joonkyung Lee.

     

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Laszlo Miklós Lovasz

    Removal lemmas for triangles and k-cycles.

    Abstract: Let p be a fixed prime. A k-cycle in F_p^n is an ordered k-tuple of points that sum to zero; we also call a 3-cycle a triangle. Let N=p^n, (the size of F_p^n). Green proved an arithmetic removal lemma which says that for every k, epsilon>0 and prime p, there is a delta>0 such that if we have a collection of k sets in F_p^n, and the number of k-cycles in their cross product is at most a delta fraction of all possible k-cycles in F_p^n, then we can delete epsilon times N elements from the sets and remove all k-cycles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in particular, asked whether a polynomial bound holds. Despite considerable attention, prior to our work, the best known bound for any k, due to Fox, showed that 1/delta can be taken to be an exponential tower of twos of height logarithmic in 1/epsilon (for a fixed k).

    In this talk, we will discuss recent work on Green’s problem. For triangles, we prove an essentially tight bound for Green’s arithmetic triangle removal lemma in F_p^n, using the recent breakthroughs with the polynomial method. For k-cycles, we also prove a polynomial bound, however, the question of the optimal exponent is still open.

    The triangle case is joint work with Jacob Fox, and the k-cycle case with Jacob Fox and Lisa Sauermann.

    Thursday, Nov. 16

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Janos PachLet’s talk about multiple crossings

    Abstract: Let k>1 be a fixed integer. It is conjectured that any graph on n vertices that can be drawn in the plane without k pairwise crossing edges has O(n) edges. Two edges of a hypergraph cross each other if neither of them contains the other, they have a nonempty intersection, and their union is not the whole vertex set. It is conjectured that any hypergraph on n vertices that contains no k pairwise crossing edges has at most O(n) edges. We discuss the relationship between the above conjectures and explain some partial answers, including a recent result of Kupavskii, Tomon, and the speaker, improving a 40 years old bound of Lomonosov.

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Misha Rudnev

    Few products, many sums

    Abstract: This is what I like calling “weak Erd\H os-Szemer\’edi conjecture”, still wide open over the reals and in positive characteristic. The talk will focus on some recent progress, largely based on the ideas of I. D. Shkredov over the past 5-6 years of how to use linear algebra to get the best out of the Szemer\’edi-Trotter theorem for its sum-product applications. One of the new results is strengthening (modulo the log term hidden in the $\lesssim$ symbol) the textbook Elekes inequality

    $$

    |A|^{10} \ll |A-A|^4|AA|^4

    $$

    to

    $$|A|^{10}\lesssim |A-A|^3|AA|^5.$$

    The other is the bound 

    $$E(H) \lesssim |H|^{2+\frac{9}{20}}$$ for additive energy of sufficiently small multiplicative subgroups in $\mathbb F_p$.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Adam Sheffer

    Geometric Energies: Between Discrete Geometry and Additive Combinatorics

    Abstract: We will discuss the rise of geometric variants of the concept of Additive energy. In recent years such variants are becoming more common in the study of Discrete Geometry problems. We will survey this development and then focus on a recent work with Cosmin Pohoata. This work studies geometric variants of additive higher moment energies, and uses those to derive new bounds for several problems in Discrete Geometry.  

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Boris Bukh

    Ranks of matrices with few distinct entries

    Abstract: Many applications of linear algebra method to combinatorics rely on the bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these application. I will also present a classification of sets L for which no low-rank matrix with entries in L exists.

    Friday, Nov. 17

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Benny Sudakov

    Submodular minimization and set-systems with restricted intersections

    AbstractSubmodular function minimization is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint types under which it remains efficiently solvable. The arguably most relevant non-trivial constraint class for which polynomial algorithms are known are parity constraints, i.e., optimizing submodular function only over sets of odd (or even) cardinality. Parity constraints capture classical combinatorial optimization problems like the odd-cut problem, and they are a key tool in a recent technique to efficiently solve integer programs with a constraint matrix whose subdeter-minants are bounded by two in absolute value.

    We show that efficient submodular function minimization is possible even for a significantly larger class than parity constraints, i.e., over all sets (of any given lattice) of cardinality r mod m, as long as m is a constant prime power. To obtain our results, we combine tools from Combinatorial Optimization, Combinatorics, and Number Theory. In particular, we establish an interesting connection between the correctness of a natural algorithm, and the non-existence of set systems with specific intersection properties.

    Joint work with M. Nagele and R. Zenklusen

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Robert Kleinberg 

    Explicit sum-of-squares lower bounds via the polynomial method

    AbstractThe sum-of-squares (a.k.a. Positivstellensatz) proof system is a powerful method for refuting systems of multivariate polynomial inequalities, i.e. proving that they have no solutions. These refutations themselves involve sum-of-squares (sos) polynomials, and while any unsatisfiable system of inequalities has a sum-of-squares refutation, the sos polynomials involved might have arbitrarily high degree. However, if a system admits a refutation where all polynomials involved have degree at most d, then the refutation can be found by an algorithm with running time polynomial in N^d, where N is the combined number of variables and inequalities in the system.

    Low-degree sum-of-squares refutations appear throughout mathematics. For example, the above proof search algorithm captures as a special case many a priori unrelated algorithms from theoretical computer science; one example is Goemans and Williamson’s algorithm to approximate the maximum cut in a graph. Specialized to extremal graph theory, they become equivalent to flag algebras. They have also seen practical use in robotics and optimal control.

    Therefore, it is of interest to identify “hard” systems of low-degree polynomial inequalities that have no solutions but also have no low-degree sum-of-squares refutations. Until recently, the only known examples were either not explicit (i.e., known to exist by non-constructive means such as the probabilistic method) or not robust (i.e., a system is constructed which is not refutable by degree d sos polynomials, but becomes refutable when perturbed by an amount tending to zero with d). We present a new family of instances derived from the cap-set problem, and we show a super-constant lower bound on the degree of its sum-of-squares refutations. Our instances are both explicit and robust.

    This is joint work with Sam Hopkins.

    12:00-1:30pmLunch

     

  • Special Seminar
    6:10 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:11 pm-6:12 pm
    11/01/2019-10/25/2016

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/10/2018 RM & PT Seminar

    6:11 pm
    11/01/2019

    No additional detail for this event.

  • General Relativity Seminar
    6:12 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-03-16 Mathematical Physics Seminar

    6:13 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/15/2018 Topology Seminar

    6:14 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/15/2018 Math Physics Seminar

    6:15 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-12-2016 Random Matrix & Probability Theory Seminar

    6:16 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:17 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-24-2016 Random Matrix & Probability Theory Seminar

    6:18 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/30/2018 RM & PT Seminar

    6:19 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:19 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:20 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-19-2016 Random Matrix & Probability Theory Seminar

    6:22 pm
    11/01/2019

    No additional detail for this event.

  • Member Seminar
    6:24 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/22/2018 Mathematical Physics Seminar

    6:24 pm
    11/01/2019
  • Member Seminar
    6:26 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-26-2016 Random Matrix & Probability Theory Seminar

    6:27 pm
    11/01/2019

    No additional detail for this event.

  • Member Seminar
    6:29 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-24-16 Mathematical Physics Seminar

    6:30 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    6:32 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    6:34 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    6:36 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-19-2016 Random Matrix & Probability Theory Seminar

    6:37 pm
    11/01/2019

    No additional detail for this event.

  • Member Seminar
    6:40 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-17-16 Mathematical Physics Seminar

    6:41 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-26-2016 Random Matrix & Probability Theory Seminar

    6:46 pm
    11/01/2019

    No additional detail for this event.

  • Member Seminar
    6:52 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-24-16 Mathematical Physics Seminar

    6:53 pm
    11/01/2019

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    6:54 pm
    11/01/2019

    No additional detail for this event.

  • Special Seminar
    6:59 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    7:00 pm
    11/01/2019

    No additional detail for this event.

  • Seminars
    7:03 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-31-16 Mathematical Physics Seminar

    7:05 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12/10/2018 Mathematical Physics Seminar

    8:42 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    12/10/2018 Topology Seminar

    8:43 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    12/12/2018 Hodge Seminar

    8:43 pm
    11/01/2019

    No additional detail for this event.

  • Mathematical Physics Seminar
    8:45 pm
    11/01/2019

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    1/16/2019 Hodge Seminar

    8:46 pm
    11/01/2019

    No additional detail for this event.

  • Fluid Dynamics Seminar

    Fluid Dynamics Seminar
    4/3/2019 Fluid Dynamics Seminar

    8:54 pm
    11/01/2019

    No additional detail for this event.

  • Program
    9:39 pm
    11/01/2019-12/18/2014

    arge random matrices provide some of the simplest models for large, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a rigorous understanding of universality in the case of orthogonal, Hermitian, or symplectic matrices with independent entries, resolving a conjecture of Wigner-Dyson-Mehta dating back 50 years. These new developments have exploited techniques from a wide range of mathematical areas in addition to probability, including combinatorics, partial differential equations, and hydrodynamic limits. It is hoped that these new techniques will be useful in the analysis of universal behaviour in matrix ensembles with more complicated structure such as random regular graph models, or 2D matrix ensembles, as well as more physically relevant systems such as band matrices and random Schroedinger-type Hamiltonians. For some of these models, results in the direction of universality have already been obtained.

    Here is a partial list of the mathematicians who are participating in this program

  • Program
    9:44 pm
    11/01/2019-12/28/2013

    During Academic year 2018-19, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines.

    As part of the Program, the CMSA will be hosting two workshops:

    .

    Additionally, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

    Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program
    NameTentative Visiting Dates

    Jason Alicea

    11/12/2018-11/16/2018
    Maissam Barkeshli4/22/2019 – 4/26/2019
    Xie Chen4/15-17/2019 4/19-21/2019 4/24-30/2019

    Lukasz Fidkowski

    1/7/2019-1/11/2019

    Zhengcheng Gu

    8/15/2018-8/30/2018 & 5/9/2019-5/19/2019

    Yin Chen He

    10/14/2018-10/27/2018
    Anton Kapustin8/26/2018-8/30/2018 & 3/28/2019-4/5/2019

    Michael Levin

    3/11/2019-3/15/2019
    Yuan-Ming Lu4/29/2019-6/01/2019

    Adam Nahum

    4/2/2019- 4/19/2019

    Masaki Oshikawa

    4/22/2019-5/22/2019
    Chong Wang 10/22/2018-11/16/2018

    Juven Wang

    4/1/2019-4/16/2019
    Cenke Xu 8/26/2018-10/1/2018

    Yi-Zhuang You

    4/1/2019-4/19/2019

    Mike Zaletel

    5/1/2019-5/10/2019
  • Program
    9:45 pm-9:46 pm
    11/01/2019-12/31/2010

    During Academic year 2018-19, the CMSA will be hosting a Program on Mathematical Biology.

    Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape.

    In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. And in mathematics and computation, there has been a revolution in terms of posing and solving problems at the intersection of computational geometry, statistics and inference.  So, how far are we from realizing a descriptive, predictive and controllable theory of biological shape?

    In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems

    The CMSA will be hosting three workshops as part of this program. The Workshop on Morphometrics, Morphogenesis and Mathematics will take place on October 22-26. 

    A workshop on Morphogenesis: Geometry and Physics will take place on December 3-6, 2018.

    A workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

  • Program
    9:48 pm
    11/01/2019-12/31/2010

    Recent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during fall 2019, with between 20-30 participants. They will also invite 10-20 longer-term visitors throughout the semester. Additionally, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10.

    Organizers:

    .

    Workshops:

     

    Here is a partial list of the mathematicians and physicists who have indicated that they will attend part or all of this special program as a visitor:

  • Program
    9:49 pm
    11/01/2019-12/23/2010

    The Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry, Symplectic geometry, Arithmetic geometry, Quantum topology and mathematical aspects of high energy physics, specially string theory with the goal of proving the homological mirror symmetry conjecture (HMS) in full generality and explore its applications. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model). We are happy to announce that the Simons Foundation has agreed to renew funding for the HMS collaboration program for three additional years.

    A brief induction of the Brandeis-Harvard CMSA HMS/SYZ research agenda and team members are as follow:


    Directors:


    Shing-Tung Yau (Harvard University)

    Born in Canton, China, in 1949, S.-T. Yau grew up in Hong Kong, and studied in the Chinese University of Hong Kong from 1966 to 1969. He did his PhD at UC Berkeley from 1969 to 1971, as a student of S.S. Chern. He spent a year as a postdoc at the Institute for Advanced Study in Princeton, and a year as assistant professor at SUNY at Stony Brook. He joined the faculty at Stanford in 1973. On a Sloan Fellowship, he spent a semester at the Courant Institute in 1975. He visited UCLA the following year, and was offered a professorship at UC Berkeley in 1977. He was there for a year, before returning to Stanford. He was a plenary speaker at the 1978 ICM in Helsinki. The following year, he became a faculty member at the IAS in Princeton. He moved to UCSD in 1984. Yau came to Harvard in 1987, and was appointed the Higgins Professor of Mathematics in 1997. He has been at Harvard ever since. Yau has received numerous prestigious awards and honors throughout his career. He was named a California Scientist of the Year in 1979. In 1981, he received a Oswald Veblen Prize in Geometry and a John J. Carty Award for the Advancement of Science, and was elected a member of the US National Academy of Sciences. In 1982, he received a Fields Medal for “his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex MongeAmpre equations”. He was named Science Digest, America’s 100 Brightest Scientists under 40, in 1984. In 1991, he received a Humboldt Research Award from the Alexander von Humboldt Foundation in Germany. He was awarded a Crafoord Prize in 1994, a US National Medal of Science in 1997, and a China International Scientific and Technological Cooperation Award, for “his outstanding contribution to PRC in aspects of making progress in sciences and technology, training researchers” in 2003. In 2010, he received a Wolf Prize in Mathematics, for “his work in geometric analysis and mathematical physics”. Yau has also received a number of research fellowships, which include a Sloan Fellowship in 1975-1976, a Guggenheim Fellowship in 1982, and a MacArthur Fellowship in 1984-1985. Yau’s research interests include differential and algebraic geometry, topology, and mathematical physics. As a graduate student, he started to work on geometry of manifolds with negative curvature. He later became interested in developing the subject of geometric analysis, and applying the theory of nonlinear partial differential equations to solve problems in geometry, topology, and physics. His work in this direction include constructions of minimal submanifolds, harmonic maps, and canonical metrics on manifolds. The most notable, and probably the most influential of this, was his solution of the Calabi conjecture on Ricci flat metrics, and the existence of Kahler-Einstein metrics. He has also succeeded in applying his theory to solve a number of outstanding conjectures in algebraic geometry, including Chern number inequalities, and the rigidity of complex structures of complex projective spaces. Yau’s solution to the Calabi conjecture has been remarkably influential in mathematical physics over the last 30 years, through the creation of the theory of Calabi-Yau manifolds, a theory central to mirror symmetry. He and a team of outstanding mathematicians trained by him, have developed many important tools and concepts in CY geometry and mirror symmetry, which have led to significant progress in deformation theory, and on outstanding problems in enumerative geometry. Lian, Yau and his postdocs have developed a systematic approach to study and compute period integrals of CY and general type manifolds. Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula of Candelas et al for worldsheet instantons on the quintic threefold. In the course of understanding mirror symmetry, Strominger, Yau, and Zaslow proposed a new geometric construction of mirror symmetry, now known as the SYZ construction. This has inspired a rapid development in CY geometry over the last two decades. In addition to CY geometry and mirror symmetry, Yau has done influential work on nonlinear partial differential equations, generalized geometry, Kahler geometry, and general relativity. His proof of positive mass conjecture is a widely regarded as a cornerstone in the classical theory of general relativity. In addition to publishing well over 350 research papers, Yau has trained more than 60 PhD students in a broad range of fields, and mentored dozens of postdoctoral fellows over the last 40 years.


    Professor Bong Lian (Brandeis University)

    BongBorn in Malaysia in 1962, Bong Lian completed his PhD in physics at Yale University under the direction of G. Zuckerman in 1991. He joined the permanent faculty at Brandeis University in 1995, and has remained there since. Between 1995 and 2013, he had had visiting research positions at numerous places, including the National University of Taiwan, Harvard University, and Tsinghua University. Lian received a J.S. Guggenheim Fellowship in 2003. He was awarded a Chern Prize at the ICCM in Taipei in 2013, for his “influential and fundamental contributions in mathematical physics, in particular in the theory of vertex algebras and mirror symmetry.” He has also been co-Director, since 2014, of the Tsinghua Mathcamp, a summer outreach program launched by him and Yau for mathematically talented teenagers in China. Since 2008, Lian has been the President of the International Science Foundation of Cambridge, a non-profit whose stated mission is “to provide financial and logistical support to scholars and universities, to promote basic research and education in mathematical sciences, especially in the Far East.” Over the last 20 years, he has mentored a number of postdocs and PhD students. His research has been supported by an NSF Focused Research Grant since 2009. Published in well over 60 papers over 25 years, Lian’s mathematical work lies in the interface between representation theory, Calabi-Yau geometry, and string theory. Beginning in the late 80’s, Lian, jointly with Zuckerman, developed the theory of semi-infinite cohomology and applied it to problems in string theory. In 1994, he constructed a new invariant (now known as the Lian- Zuckerman algebra) of a topological vertex algebra, and conjectured the first example of a G algebra in vertex algebra theory. The invariant has later inspired a new construction of quantum groups by I. Frenkel and A. Zeitlin, as semi-infinite cohomology of braided vertex algebras, and led to a more recent discovery of new relationships between Courant algebroids, A-algebras, operads, and deformation theory of BV algebras. In 2010, he and his students Linshaw and Song developed important applications of vertex algebras in equivariant topology. Lian’s work in CY geometry and mirror symmetry began in early 90’s. Using a characteristic p version of higher order Schwarzian equations, Lian and Yau gave an elementary proof that the instanton formula of Candelas et al implies Clemens’s divisibility conjecture for the quintic threefold, for infinitely many degrees. In 1996, Lian (jointly with Hosono and Yau) answered the so-called Large Complex Structure Limit problem in the affirmative in many important cases. Around the same year, they announced their hyperplane conjecture, which gives a general formula for period integrals for a large class of CY manifolds, extending the formula of Candelas et al. Soon after, Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula. In 2003, inspired by mirror symmetry, Lian (jointly with Hosono, Oguiso and Yau) discovered an explicit counting formula for Fourier-Mukai partners, and settled an old problem of Shioda on abelian and K3 surfaces. Between 2009 and 2014, Lian (jointly with Bloch, Chen, Huang, Song, Srinivas, Yau, and Zhu) developed an entirely new approach to study the so-called Riemann-Hilbert problem for period integrals of CY manifolds, and extended it to general type manifolds. The approach leads to an explicit description of differential systems for period integrals with many applications. In particular, he answered an old question in physics on the completeness of Picard-Fuchs systems, and constructed new differential zeros of hypergeometric functions.


    Denis Auroux (Harvard University)

    AurouxDenis Auroux’s research concerns symplectic geometry and its applications to mirror symmetry. While his early work primarily concerned the topology of symplectic 4-manifolds, over the past decade Auroux has obtained pioneering results on homological mirror symmetry outside of the Calabi-Yau setting (for Fano varieties, open Riemann surfaces, etc.), and developed an extension of the SYZ approach to non-Calabi-Yau spaces.After obtaining his PhD in 1999 from Ecole Polytechnique (France), Auroux was employed as Chargé de Recherche at CNRS and CLE Moore Instructor at MIT, before joining the faculty at MIT in 2002 (as Assistant Professor from 2002 to 2004, and as Associate Professor from 2004 to 2009, with tenure starting in 2006). He then moved to UC Berkeley as a Full Professor in 2009.
    Auroux has published over 30 peer-reviewed articles, including several in top journals, and given 260 invited presentations about his work. He received an Alfred P. Sloan Research Fellowship in 2005, was an invited speaker at the 2010 International Congress of Mathematicians, and in 2014 he was one of the two inaugural recipients of the Poincaré Chair at IHP. He has supervised 10 PhD dissertations, won teaching awards at MIT and Berkeley, and participated in the organization of over 20 workshops and conferences in symplectic geometry and mirror symmetry.




    Senior Personnel:

    Artan Sheshmani (Harvard CMSA)

    unnamedArtan Sheshmani’s research is focused on enumerative algebraic geometry and mathematical aspects of string theory. He is interested in applying techniques in algebraic geometry, such as, intersection theory, derived category theory, and derived algebraic geometry to construct and compute the deformation invariants of algebraic varieties, in particular Gromov-Witten (GW) or Donaldson-Thomas (DT) invariants. In the past Professor Sheshmani has worked on proving modularity property of certain DT invariants of K3-fibered threefolds (as well as their closely related Pandharipande-Thomas (PT) invariants), local surface threefolds, and general complete intersection Calabi-Yau threefolds. The modularity of DT/PT invariants in this context is predicted in a famous conjecture of  string theory called S-duality modularity conjecture, and his joint work has provided the proof to some cases of it, using degenerations, virtual localizations, as well as wallcrossing techniques. Recently, Sheshmani has focused on proving a series of dualities relating the various enumerative invariants over threefolds, notably the GW invariants and invariants that arise in topological gauge theory. In particular in his joint work with Gholampour, Gukov, Liu, Yau he studied DT gauge theory and its reductions to D=4 and D=2 which are equivalent to local theory of surfaces in Calabi-Yau threefolds. Moreover, in a recent joint work with Yau and Diaconescu, he has studied the construction and computation of DT invariants of Calabi-Yau fourfolds via a suitable derived categorical reduction of the theory to the DT theory of threefolds. Currently Sheshmani is interested in a wide range of problems in enumerative geometry of CY varieties in dimensions 3,4,5.

    Artan has received his PhD and Master’s degrees in pure mathematics under Sheldon Katz and Thomas Nevins from the University of Illinois at Urbana Champaign (USA) in 2011 and 2008 respectively. He holds a Master’s degree in Solid Mechanics (2004) and two Bachelor’s degrees, in Mechanical Engineering and Civil Engineering from the Sharif University of Technology, Tehran, Iran.  Artan has been a tenured Associate Professor of Mathematics with joint affiliation at Harvard CMSA and center for Quantum Geometry of Moduli Spaces (QGM), since 2016. Before that he has held visiting Associate Professor and visiting Assistant Professor positions at MIT.

    An Huang (Brandeis University)

    unnamedThe research of An Huang since 2011 has been focused on the interplay between algebraic geometry, the theory of special functions and mirror symmetry. With S. Bloch, B. Lian, V. Srinivas, S.-T. Yau, X. Zhu, he has developed the theory of tautological systems, and has applied it to settle several important problems concerning period integrals in relation to mirror symmetry. With B. Lian and X. Zhu, he has given a precise geometric interpretation of all solutions to GKZ systems associated to Calabi-Yau hypersurfaces in smooth Fano toric varieties. With B. Lian, S.-T. Yau, and C.-L. Yu, he has proved a conjecture of Vlasenko concerning an explicit formula for unit roots of the zeta functions of hypersurfaces, and has further related these roots to p-adic interpolations of complex period integrals. Beginning in 2018, with B. Stoica and S.-T. Yau, he has initiated the study of p-adic strings in curved spacetime, and showed that general relativity is a consequence of the self-consistency of quantum p-adic strings. One of the goals of this study is to understand p-adic A and B models.

    An Huang received his PhD in Mathematics from the University of California at Berkeley in 2011. He was a postdoctoral fellow at the Harvard University Mathematics Department, and joined Brandeis University as an Assistant Professor in Mathematics in 2016.



    Siu Cheong Lau (Boston University)
    unnamed

    The research interest of Siu Cheong Lau lies in SYZ mirror symmetry, symplectic and algebraic geometry.  His thesis work has successfully constructed the SYZ mirrors for all toric Calabi-Yau manifolds based on quantum corrections by open Gromov-Witten invariants and their wall-crossing phenomenon.  In collaboration with N.C. Leung, H.H. Tseng and K. Chan, he derived explicit formulas for the open Gromov-Witten invariants for semi-Fano toric manifolds which have an obstructed moduli theory.  It has a beautiful relation with mirror maps and Seidel representations.   Recently he works on a local-to-global approach to SYZ mirror symmetry.  In joint works with C.H. Cho and H. Hong, he developed a noncommutative local mirror construction for immersed Lagrangians, and a natural gluing method to construct global mirrors.  The construction has been realized in various types of geometries including orbifolds, focus-focus singularities and pair-of-pants decompositions of Riemann surfaces.

    Siu-Cheong Lau has received the Doctoral Thesis Gold Award (2012) and the Best Paper Silver Award (2017) at the International Congress of Chinese Mathematicians.  He was awarded the Simons Collaboration Grant in 2018.  He received a Certificate of Teaching Excellence from Harvard University in 2014.


    Affiliates:

    • Netanel Rubin-Blaier (Cambridge)
    • Kwokwai Chan (Chinese University of Hong Kong)
    • Mandy Cheung (Harvard University, BP)
    • Chuck Doran (University of Alberta)
    • Honsol Hong (Yonsei University)
    • Shinobu Hosono (Gakushuin University, Japan)
    • Conan Leung (Chinese University of Hong Kong)
    • Yu-shen Lin (Boston University)
    • Hossein Movassati (IMPA Brazil)
    • Arnav Tripathhy (Harvard University, BP)

     

    Postdocs:

    • Dennis Borisov
    • Tsung-Ju Lee
    • Dingxin Zhang
    • Jingyu Zhao
    • Yang Zhou

    Jobs:

    Postdoctoral Fellowship in Algebraic Geometry

    Postdoctoral Fellowship in Mathematical Sciences

     

    To learn about previous programming as part of the Simons Collaboration, click here.

  • More events
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-16-2018 Mathematical Physics Seminar
      12:00 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      1/27/2020 Math Physics Seminar
      12:00 am-1:00 pm
      11/01/2019
    • CMSA EVENT: Quantum Matter Workshop
      All day
      11/01/2019
      Layer-2-600x338

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

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

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

       

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

      Speakers:

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-9-2018 Math Physics Seminar
      12:00 am
      11/01/2019
    • Colloquium
      5:00 am
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Workshop on Quantum Information
      8:00 am-6:07 pm
      11/01/2019-04/24/2017
      banner-image-1

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

      Register for the event here.

      The following speakers are confirmed:

    • CMSA EVENT: From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
      8:30 am-5:20 pm
      11/01/2019-08/20/2018
      Mumford-3

      David_Mumford-1

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

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

      Speakers:

      Organizers:

       

      Publication:

      Pure and Applied Mathematics Quarterly

      Special Issue: In Honor of David Mumford

      Guest Editors: Ching-Li Chai, Amnon Neeman

       

    • CMSA EVENT: Big Data Conference 2018
      8:30 am-2:50 pm
      11/01/2019-08/24/2018
      1 Oxford Street, Cambridge MA 02138
      Big-Data-2018-1

       

      shutterstock_547250785-e1527881194717

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

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

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

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

      Please register here. 

      Confirmed Speakers: 

      Organizers: 

      • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
      • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
      • Richard Freeman, Herbert Ascherman Professor of Economics, Harvard University
      • Jun Liu, Professor of Statistics, Harvard University
      • Horng-Tzer Yau, Professor of Mathematics, Harvard University
    • CMSA EVENT: F-Theory Conference
      8:30 am-3:00 pm
      11/01/2019-09/30/2018

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

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

      Click here for videos of the talks. 

      Organizers:

      Speakers:

    • CMSA EVENT: Workshop on Foundations of Computational Science
      8:30 am-2:45 pm
      11/01/2019-08/31/2019
      AI-Poster-3

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

      Please register here. 

      Speakers:

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

    • CMSA EVENT: Workshop on Aspects of General Relativity
      8:30 am-3:30 pm
      11/01/2019-05/26/2017

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

      Speakers:

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

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

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

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

      Schedule:

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

      Organizers: Piotr T. Chruściel and Shing-Tung Yau

    • CMSA EVENT: Workshop on Morphometrics, Morphogenesis and Mathematics
      8:30 am-2:00 pm
      11/01/2019-10/24/2018

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

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

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

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

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

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

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

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

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

      Videos of the talks

      Confirmed Speakers:

    • CMSA EVENT: Morphogenesis: Geometry and Physics
      8:30 am-2:30 pm
      11/01/2019-12/05/2018

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

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

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

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

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

      Videos

      Please Register Here

      PDF of the Schedule

      Speakers:

    • CMSA EVENT: Geometric Analysis Approach to AI Workshop
      8:30 am-5:30 pm
      11/01/2019-01/21/2019
      Geo-Analysis-Poster-final-e1547584167900

      Geo-Analysis-1-e1543848888343

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

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

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

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

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

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

      Please register here

      Speakers: 

    • CMSA EVENT: 2019 Big Data Conference
      8:30 am-4:40 pm
      11/01/2019-08/20/2019
      1 Oxford Street, Cambridge MA 02138
      Big-Data-2019-Poster-5-2

      shutterstock_547250785-e1527881194717

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

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

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

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

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

    • CMSA EVENT: 2015 Conference on Big Data
      8:45 am-4:00 pm
      11/01/2019-10/26/2015
      1 Oxford Street, Cambridge MA 02138

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

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

       

      Registration for the conference is now closed.

      Please click here for a downloadable version of this schedule.

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

      Monday, August 24

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

      Tuesday, August 25

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

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

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

       Wednesday, August 26 

      TimeSpeakerTitle
      8:45amMeet and Greet
      9:00amAnkur MoitraBeyond Matrix Completion
      9:45amFlorent KrzakalaOptimal compressed sensing with spatial coupling and message passing
      10:30amBreak
      10:45amPiotr IndykFast Algorithms for Structured Sparsity
      11:30amGuido ImbensExact p-values for network inference
      12:15pmBreak for lunch
      2:00pmEdo AiroldiSome fundamental ideas for causal inference on large networks
      2:45pmRonitt RubinfeldSomething for almost nothing: sublinear time approximation algorithms
      3:30pmBreak
      3:45pmLenka ZdeborovaClustering of sparse networks:  Phase transitions and optimal algorithms
      4:30pmJelani NelsonDimensionality reductions via sparse matrices
    • CMSA EVENT: Workshop on Probabilistic and Extremal Combinatorics
      9:00 am-1:30 pm
      11/01/2019-02/09/2018

      The workshop on Probabilistic and Extremal Combinatorics will take place February 5-9, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      Extremal and Probabilistic Combinatorics are two of the most central branches of modern combinatorial theory. Extremal Combinatorics deals with problems of determining or estimating the maximum or minimum possible cardinality of a collection of finite objects satisfying certain requirements. Such problems are often related to other areas including Computer Science, Information Theory, Number Theory and Geometry. This branch of Combinatorics has developed spectacularly over the last few decades. Probabilistic Combinatorics can be described informally as a (very successful) hybrid between Combinatorics and Probability, whose main object of study is probability distributions on discrete structures.

      There are many points of interaction between these fields. There are deep similarities in methodology. Both subjects are mostly asymptotic in nature. Quite a few important results from Extremal Combinatorics have been proven applying probabilistic methods, and vice versa. Such emerging subjects as Extremal Problems in Random Graphs or the theory of graph limits stand explicitly at the intersection of the two fields and indicate their natural symbiosis.

      The symposia will focus on the interactions between the above areas. These topics include Extremal Problems for Graphs and Set Systems, Ramsey Theory, Combinatorial Number Theory, Combinatorial Geometry, Random Graphs, Probabilistic Methods and Graph Limits.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Benny Sudakov and David Conlon.  More details about this event, including participants, will be updated soon.

    • CMSA EVENT: Simons Collaboration on Homological Mirror Symmetry
      9:00 am-5:00 pm
      11/01/2019-05/08/2016

      The Center of Mathematical Sciences and Applications will be hosting a 3-day workshop on Homological Mirror Symmetry and related areas on May 6 – May 8, 2016 at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

      Organizers:

      D. Auroux, S.C. Lau, N.C. Leung, Bong Lian, C.C. Liu, S.T. Yau

      Speakers:

      1. Netanel Blaier (MIT)
      2. Kwokwai Chan (CUHK)
      3. Bohan Fang (Peking University)
      4. Amanda Francis (BYU)
      5. Hansol Hong (CUHK)
      6. Heather Lee (Purdue University)
      7. Si Li (Tsinghua University)
      8. Yu-Shen Lin (Stanford University)
      9. Alex Perry (Harvard University)
      10. Hiro Tanaka (Harvard University)
      11. Sara Tukachinsky (HUJ)
      12. Michael Viscardi (MIT)
      13. Eric Zaslow (Northwestern University)
      14. Jingyu Zhao (Columbia University)

      Please click here for the conference Main Website.

      Please click Simons Workshop Schedule with Abstract for a downloadable schedule with talk abstracts.

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

      Schedule:

      May 6 – Day 1
      9:00amBreakfast
      9:35amOpening remarks
      9:45am – 10:45amSi Li, “Quantum master equation, chiral algebra, and integrability”
      10:45am – 11:15amBreak
      11:15am – 12:15pmSara Tukachinsky, “Point like bounding chains and open WDVV
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmBohan Fang, “Mirror B model for toric Calabi Yau 3 folds
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmHiro Tanaka, “Toward Fukaya categories over arbitrary coefficients
      4:00pm – 4:15pmBreak
      4:15pm – 5:15pmHansol Hong, “Noncommutative mirror functors
      May 7 – Day 2
      9:00amBreakfast
      9:45am – 10:45amEric Zaslow, “Lagrangian fillings what does the sheaf say?
      10:45am – 11:15amBreak
      11:15am – 12:15pmAlex Perry, “Derived categories of Gushel Mukai varieties
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmAmanda Francis, “A Landau Ginzburg mirror theorem inspired by Borcea Voisin symmetry
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmHeather Lee, “Homological mirror symmetry for open Riemann surfaces from pair of pants decompositions
      4:00pm – 4:15pmBreak
      4:15pm – 5:15pmYu-Shen Lin, “Counting Holomorphic Discs via Tropical Discs on K3 Surfaces
      May 8 – Day 3
      9:00amBreakfast
      9:45am – 10:45amKwokwai Chan, “HMS for local CY manifolds via SYZ
      10:45am – 11:15amBreak
      11:15am – 12:15pmNetanel Blaier, “The quantum Johnson homomorphism, formality and symplectic isotopy
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmJingyu Zhao, “Periodic symplectic cohomology and the Hodge filtration
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmMichael Viscardi, “Equivariant quantum cohomology and the geometric Satake equivalence
      * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Simons Collaboration on Homological Mirror symmetry“.

      This event is sponsored by the Simons Foundation and CMSA Harvard University.

    • CMSA EVENT: Workshop on Geometry, Imaging, and Computing
      9:00 am-6:15 pm
      11/01/2019-03/26/2018
      GIC-Poster-2-e1520002551865

      On March 24-26, The Center of Mathematical Sciences and Applications will be hosting a workshop on Geometry, Imaging, and Computing, based off  the journal of the same name. The workshop will take place in CMSA building, G10.

      The organizing committee consists of Yang Wang (HKUST), Ronald Lui (CUHK), David Gu (Stony Brook), and Shing-Tung Yau (Harvard).

      Please click here to register for the event.

      Confirmed Speakers:

    • CMSA EVENT: Workshop on Optimization in Image Processing
      9:00 am-12:30 pm
      11/01/2019-06/30/2016

      The Center of Mathematical Sciences and Applications will be hosting a workshop on Optimization in Image Processing on June 27 – 30, 2016. This 4-day workshop aims to bring together researchers to exchange and stimulate ideas in imaging sciences, with a special focus on new approaches based on optimization methods. This is a cutting-edge topic with crucial impact in various areas of imaging science including inverse problems, image processing and computer vision. 16 speakers will participate in this event, which we think will be a very stimulating and exciting workshop. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Titles, abstracts and schedule will be provided nearer to the event.

      Speakers:

      1. Antonin Chambolle, CMAP, Ecole Polytechnique
      2. Raymond Chan, The Chinese University of Hong Kong
      3. Ke Chen, University of Liverpool
      4. Patrick Louis Combettes, Université Pierre et Marie Curie
      5. Mario Figueiredo, Instituto Superior Técnico
      6. Alfred Hero, University of Michigan
      7. Ronald Lok Ming Lui, The Chinese University of Hong Kong
      8. Mila Nikolova, Ecole Normale Superieure Cachan
      9. Shoham Sabach, Israel Institute of Technology
      10. Martin Benning, University of Cambridge
      11. Jin Keun Seo, Yonsei University
      12. Fiorella Sgallari, University of Bologna
      13. Gabriele Steidl, Kaiserslautern University of Technology
      14. Joachim Weickert, Saarland University
      15. Isao Yamada, Tokyo Institute of Technology
      16. Wotao Yin, UCLA

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

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

      Please click here for registration – Registration Deadline: June 7, 2016; Registration is capped at 70 participants.

      Schedule:

      June 27 – Day 1
      9:00amBreakfast
      9:20amOpening remarks
      9:30am – 10:20amJoachim Weickert, “FSI Schemes: Fast Semi-Iterative Methods for Diffusive or Variational Image Analysis Problems”
      10:20am – 10:50amBreak
      10:50am – 11:40pmPatrick Louis Combettes“Block-Iterative Asynchronous Variational Image Recovery”
      11:40am – 12:30pmIsao Yamada“Spicing up Convex Optimization for Certain Inverse Problems”
      12:30pm – 2:00pmLunch
      2:30pm – 3:20pmFiorella Sgallari, “Majorization-Minimization for Nonconvex Optimization”
      3:20pm – 3:50pmBreak
      3:50pm – 4:40pmShoham Sabach“A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Problems”
      June 28 – Day 2
      9:00amBreakfast
      9:30am – 10:20amAntonin Chambolle“Acceleration of alternating minimisations”
      10:20am – 10:50amBreak
      10:50am – 11:40amMario Figueiredo“ADMM in Image Restoration and Related Problems: Some History and Recent Advances”
      11:40am – 12:30pmKe Chen“Image Restoration and Registration Based on Total Fractional-Order Variation Regularization”
      12:30pm – 2:30pmLunch
      2:30pm – 4:40pmDiscussions
      June 29 – Day 3
      9:00amBreakfast
      9:30am – 10:20amAlfred Hero“Continuum relaxations for discrete optimization”
      10:20am – 10:50amBreak
      10:50am – 11:40amWotao Yin“Coordinate Update Algorithms for Computational Imaging and Machine Learning”
      11:40am – 12:30pmMila Nikolova“Limits on noise removal using log-likelihood and regularization”
      12:30pm – 2:30pmLunch
      2:30pm – 3:20pmMartin Benning, “Nonlinear spectral decompositions and the inverse scale space method”
      3:20pm – 3:50pmBreak
      3:50pm – 4:40pmRonald Ming Lui“TEMPO: Feature-endowed Teichmuller extremal mappings of point cloud for shape classification”
      June 30 – Day 4
      9:00amBreakfast
      9:30am – 10:20amJin Keun Seo“Mathematical methods for biomedical impedance imaging”
      10:20am – 10:50amBreak
      10:50am – 11:40amGabriele Steidl, “Iterative Multiplicative Filters for Data Labeling”
      11:40am – 12:30pmRaymond Chan, “Point-spread function reconstruction in ground-based astronomy”
      * This event is sponsored by CMSA Harvard University.

      Organizers: Raymond Chan and Shing-Tung Yau

    • CMSA EVENT: Machine Learning for Multiscale Model Reduction Workshop
      9:00 am-11:55 am
      11/01/2019-03/29/2019
      Machine-Learning-Poster

      The Machine Learning for Multiscale Model Reduction Workshop will take place on March 27-29, 2019. This is the second of two workshops organized by Michael BrennerShmuel Rubinstein, and Tom Hou.  The first, Fluid turbulence and Singularities of the Euler/ Navier Stokes equations, will take place on March 13-15, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

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

      List of registrants

      Speakers:

    • CMSA EVENT: Simons Collaboration Workshop, Jan. 10-13, 2018
      9:00 am-12:00 pm
      11/01/2019-01/13/2017
      banner-image-1

      The CMSA will be hosting a four-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on January 10-13, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

      We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

       

      Confirmed Participants:

    • CMSA EVENT: Mini-school on Nonlinear Equations, December 3-4, 2016
      9:00 am-5:00 pm
      11/01/2019-12/04/2016

      The Center of Mathematical Sciences and Applications will be hosting a Mini-school on Nonlinear Equations on December 3-4, 2016. The conference will have speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138.

      The mini-school will consist of lectures by experts in geometry and analysis detailing important developments in the theory of nonlinear equations and their applications from the last 20-30 years.  The mini-school is aimed at graduate students and young researchers working in geometry, analysis, physics and related fields.

      Please click here to register for this event.

      Speakers:

      1. Cliff Taubes (Harvard University)
      2. Valentino Tosatti (Northwestern University)
      3. Pengfei Guan (McGill University)
      4. Jared Speck (MIT)

      Schedule:

      December 3rd – Day 1
      9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
      10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
      12:15pm – 1:45pmLUNCH
      1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
      3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”
      December 4th – Day 2
      9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
      10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
      12:15pm – 1:45pmLUNCH
      1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
      3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”

      Please click Mini-School Program for a downloadable schedule with talk abstracts.

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

      * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

    • CMSA EVENT: Workshop on Coding and Information Theory
      9:00 am-3:30 pm
      11/01/2019-04/13/2018

      The workshop on coding and information theory will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

      Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory.  One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program.  Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities.  Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics.  All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      Click here for a list of registrants. 

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

    • CMSA EVENT: Topology and Dynamics in Quantum Matter Workshop
      9:15 am-3:25 pm
      11/01/2019-09/11/2019
      Topology-Poster

      On September 10-11, 2019, the CMSA will be hosting a second workshop on Topological Aspects of Condensed Matter.

      New ideas rooted in topology have recently had a major impact on condensed matter physics, and have led to new connections with high energy physics, mathematics and quantum information theory.  The aim of this program will be to deepen these connections and spark new progress by fostering discussion and new collaborations within and across disciplines.

      Topics include i) the classification of topological states  ii) topological orders in two and three dimensions including quantum spin liquids, quantum Hall states and fracton phases and iii)  interplay of symmetry and topology in quantum many body systems, including symmetry protected topological phases, symmetry fractionalization and anomalies iv) topological phenomena in quantum systems  driven far from equlibrium v) quantum field theory approaches to topological matter.

      This workshop is part of the CMSA’s program on Program on Topological Aspects of Condensed Matterand is the second of two workshops, in addition to a visitor program and seminars.

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

      Click here for a list of restaurants in the area. 

      Organizers: Michael Hermele (CU Boulder) and Ashvin Vishwanath (Harvard)

      Partial list of speakers:

      Videos of the lectures can be found in the Youtube playlist below. Links to talks are also available on the schedule below.

    • CMSA EVENT: Workshop on Invariance and Geometry in Sensation, Action and Cognition
      9:15 am-10:00 am
      11/01/2019-04/17/2019

      As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

      Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, it has traditionally not been an important part of biology, except in the context of aspects of structural biology. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use.

      This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines? The aim is to revisit these old neuro-cognitive problems using a series of modern lenses experimentally, theoretically and computationally, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models.

      In addition to talks, there will be a set of tutorial talks on the mathematical description of invariance (P.J. Olver), the computer vision aspects of invariant algorithms (S. Soatto), and the neuroscientific and cognitive aspects of invariance (TBA). The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by L. Mahadevan (Harvard), Talia Konkle (Harvard), Samuel Gershman (Harvard), and Vivek Jayaraman (HHMI).

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

      List of registrants

      Videos

      Tentative Speaker List:

      Schedule:

      Monday, April 15

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:15amWelcome and Introduction
      9:15 – 10:00amVivek JayaramanTitle: Insect cognition: Small tales of geometry & invariance

      Abstract: Decades of field and laboratory experiments have allowed ethologists to discover the remarkable sophistication of insect behavior. Over the past couple of decades, physiologists have been able to peek under the hood to uncover sophistication in insect brain dynamics as well. In my talk, I will describe phenomena that relate to the workshop’s theme of geometry and invariance. I will outline how studying insects —and flies in particular— may enable an understanding of the neural mechanisms underlying these intriguing phenomena.

      10:00 – 10:45amElizabeth TorresTitle: Connecting Cognition and Biophysical Motions Through Geometric Invariants and Motion Variability

      Abstract: In the 1930s Nikolai Bernstein defined the degrees of freedom (DoF) problem. He asked how the brain could control abundant DoF and produce consistent solutions, when the internal space of bodily configurations had much higher dimensions than the space defining the purpose(s) of our actions. His question opened two fundamental problems in the field of motor control. One relates to the uniqueness or consistency of a solution to the DoF problem, while the other refers to the characterization of the diverse patterns of variability that such solution produces.

      In this talk I present a general geometric solution to Bernstein’s DoF problem and provide empirical evidence for symmetries and invariances that this solution provides during the coordination of complex naturalistic actions. I further introduce fundamentally different patterns of variability that emerge in deliberate vs. spontaneous movements discovered in my lab while studying athletes and dancers performing interactive actions. I here reformulate the DoF problem from the standpoint of the social brain and recast it considering graph theory and network connectivity analyses amenable to study one of the most poignant developmental disorders of our times: Autism Spectrum Disorders.

      I offer a new unifying framework to recast dynamic and complex cognitive and social behaviors of the full organism and to characterize biophysical motion patterns during migration of induced pluripotent stem cell colonies on their way to become neurons.

      10:45 – 11:15amCoffee Break
      11:15 – 12:00pmPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

      Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical prerequisites will be kept to a bare minimum.

      12:00 – 12:45pmStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

      Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

      While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

      12:45 – 2:00pmLunch
      2:00 – 2:45pmAnitha PasupathyTitle: Invariant and non-invariant representations in mid-level ventral visual cortex

      My laboratory investigates how visual form is encoded in area V4, a critical mid-level stage of form processing in the macaque monkey. Our goal is to reveal how V4 representations underlie our ability to segment visual scenes and recognize objects. In my talk I will present results from two experiments that highlight the different strategies used by the visual to achieve these goals. First, most V4 neurons exhibit form tuning that is exquisitely invariant to size and position, properties likely important to support invariant object recognition. On the other hand, form tuning in a majority of neurons is also highly dependent on the interior fill. Interestingly, unlike primate V4 neurons, units in a convolutional neural network trained to recognize objects (AlexNet) overwhelmingly exhibit fill-outline invariance. I will argue that this divergence between real and artificial circuits reflects the importance of local contrast in parsing visual scenes and overall scene understanding.

      2:45 – 3:30pmJacob FeldmanTitle: Bayesian skeleton estimation for shape representation and perceptual organization

      Abstract: In this talk I will briefly summarize a framework in which shape representation and perceptual organization are reframed as probabilistic estimation problems. The approach centers around the goal of identifying the skeletal model that best “explains” a given shape. A Bayesian solution to this problem requires identifying a prior over shape skeletons, which penalizes complexity, and a likelihood model, which quantifies how well any particular skeleton model fits the data observed in the image. The maximum-posterior skeletal model thus constitutes the most “rational” interpretation of the image data consistent with the given assumptions. This approach can easily be extended and generalized in a number of ways, allowing a number of traditional problems in perceptual organization to be “probabilized.” I will briefly illustrate several such extensions, including (1) figure/ground and grouping (3) 3D shape and (2) shape similarity.

      3:30 – 4:00pmTea Break
      4:00 – 4:45pmMoira DillonTitle: Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development

      Abstract: Formal geometry lies at the foundation of millennia of human achievement in domains such as mathematics, science, and art. While formal geometry’s propositions rely on abstract entities like dimensionless points and infinitely long lines, the points and lines of our everyday world all have dimension and are finite. How, then, do we get to abstract geometric thought? In this talk, I will provide evidence that evolutionarily ancient and developmentally precocious sensitivities to the geometry of our everyday world form the foundation of, but also limit, our mathematical reasoning. I will also suggest that successful geometric reasoning may emerge through development when children abandon incorrect, axiomatic-based strategies and come to rely on dynamic simulations of physical entities. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations.

      4:45 – 5:30pmMichael McCloskeyTitle: Axes and Coordinate Systems in Representing Object Shape and Orientation

      Abstract: I describe a theoretical perspective in which a) object shape is represented in an object-centered reference frame constructed around orthogonal axes; and b) object orientation is represented by mapping the object-centered frame onto an extrinsic (egocentric or environment-centered) frame.  I first show that this perspective is motivated by, and sheds light on, object orientation errors observed in neurotypical children and adults, and in a remarkable case of impaired orientation perception. I then suggest that orientation errors can be used to address questions concerning how object axes are defined on the basis of object geometry—for example, what aspects of object geometry (e.g., elongation, symmetry, structural centrality of parts) play a role in defining an object principal axis?

      5:30 – 6:30pmReception

       

      Tuesday, April 16

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:45amPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

      Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical pre

      9:45 – 10:30amStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

      Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

      While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

      10:30 – 11:00amCoffee Break
      11:00 – 11:45amJeannette BohgTitle: On perceptual representations and how they interact with actions and physical representations

      Abstract: I will discuss the hypothesis that perception is active and shaped by our task and our expectations on how the world behaves upon physical interaction. Recent approaches in robotics follow this insight that perception is facilitated by physical interaction with the environment. First, interaction creates a rich sensory signal that would otherwise not be present. And second, knowledge of the regularity in the combined space of sensory data and action parameters facilitate the prediction and interpretation of the signal. In this talk, I will present two examples from our previous work where a predictive task facilitates autonomous robot manipulation by biasing the representation of the raw sensory data. I will present results on visual but also haptic data.

      11:45 – 12:30pmDagmar SternadTitle: Exploiting the Geometry of the Solution Space to Reduce Sensitivity to Neuromotor Noise

      Abstract: Control and coordination of skilled action is frequently examined in isolation as a neuromuscular problem. However, goal-directed actions are guided by information that creates solutions that are defined as a relation between the actor and the environment. We have developed a task-dynamic approach that starts with a physical model of the task and mathematical analysis of the solution spaces for the task. Based on this analysis we can trace how humans develop strategies that meet complex demands by exploiting the geometry of the solution space. Using three interactive tasks – throwing or bouncing a ball and transporting a “cup of coffee” – we show that humans develop skill by: 1) finding noise-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, and 3) optimizing predictability of the object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, attractors with few invariant types that overcome substantial delays and noise in the neuro-mechanical system.

      12:30 – 2:00pmLunch
      2:00 – 2:45pmSam OckoTitle: Emergent Elasticity in the Neural Code for Space

      Abstract: To navigate a novel environment, animals must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such internal maps, and how are these maps used to maintain representations of an animal’s position within an environment. We demonstrate analytically how a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent internal map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network during exploration. Moreover, we verify several experimentally testable predictions of our model, including: (1) systematic deformations of grid cells in irregular environments, (2) path-dependent shifts in grid cells towards the most recently encountered landmark, (3) a dynamical phase transition in which grid cells can break free of landmarks in altered virtual reality environments and (4) the creation of topological defects in grid cells. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

      2:45 – 3:30pmTatyana SharpeeTitle: Hyperbolic geometry of the olfactory space

      Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the production of a specific poison by a plant or bacteria will be accompanied by the emission of certain sets of volatile compounds. An animal can therefore judge the presence of poisons in the food by how the food smells. This perspective suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendrograms, and more generally between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

      3:30 – 4:00pmTea Break
      4:00 – 4:45pmEd ConnorTitle: Representation of solid geometry in object vision cortex

      Abstract: There is a fundamental tension in object vision between the 2D nature of retinal images and the 3D nature of physical reality. Studies of object processing in the ventral pathway of primate visual cortex have focused mainly on 2D image information. Our latest results, however, show that representations of 3D geometry predominate even in V4, the first object-specific stage in the ventral pathway. The majority of V4 neurons exhibit strong responses and clear selectivity for solid, 3D shape fragments. These responses are remarkably invariant across radically different image cues for 3D shape: shading, specularity, reflection, refraction, and binocular disparity (stereopsis). In V4 and in subsequent stages of the ventral pathway, solid shape geometry is represented in terms of surface fragments and medial axis fragments. Whole objects are represented by ensembles of neurons signaling the shapes and relative positions of their constituent parts. The neural tuning dimensionality of these representations includes principal surface curvatures and their orientations, surface normal orientation, medial axis orientation, axial curvature, axial topology, and position relative to object center of mass. Thus, the ventral pathway implements a rapid transformation of 2D image data into explicit representations 3D geometry, providing cognitive access to the detailed structure of physical reality.

      4:45 – 5:30pmL. MahadevanTitle: Simple aspects of geometry and probability in perception

      Abstract: Inspired by problems associated with noisy perception, I will discuss two questions: (i) how might we test people’s perception of probability in a geometric context ? (ii) can one construct invariant descriptions of 2D images using simple notions of probabilistic geometry? Along the way, I will highlight other questions that the intertwining of geometry and probability raises in a broader perceptual context.


      Wednesday, April 17

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:45amGily GinosarTitle: The 3D geometry of grid cells in flying bats

      Abstract: The medial entorhinal cortex (MEC) contains a variety of spatial cells, including grid cells and border cells. In 2D, grid cells fire when the animal passes near the vertices of a 2D spatial lattice (or grid), which is characterized by circular firing-fields separated by fixed distances, and 60 local angles – resulting in a hexagonal structure. Although many animals navigate in 3D space, no studies have examined the 3D volumetric firing of MEC neurons. Here we addressed this by training Egyptian fruit bats to fly in a large room (5.84.62.7m), while we wirelessly recorded single neurons in MEC. We found 3D border cells and 3D head-direction cells, as well as many neurons with multiple spherical firing-fields. 20% of the multi-field neurons were 3D grid cells, exhibiting a narrow distribution of characteristic distances between neighboring fields – but not a perfect 3D global lattice. The 3D grid cells formed a functional continuum with less structured multi-field neurons. Both 3D grid cells and multi-field cells exhibited an anatomical gradient of spatial scale along the dorso-ventral axis of MEC, with inter-field spacing increasing ventrally – similar to 2D grid cells in rodents. We modeled 3D grid cells and multi-field cells as emerging from pairwise-interactions between fields, using an energy potential that induces repulsion at short distances and attraction at long distances. Our analysis shows that the model explains the data significantly better than a random arrangement of fields. Interestingly, simulating the exact same model in 2D yielded a hexagonal-like structure, akin to grid cells in rodents. Together, the experimental data and preliminary modeling suggest that the global property of grid cells is multiple fields that repel each other with a characteristic distance-scale between adjacent fields – which in 2D yields a global hexagonal lattice while in 3D yields only local structure but no global lattice.

      Gily Ginosar 1 , Johnatan Aljadeff 2 , Yoram Burak 3 , Haim Sompolinsky 3 , Liora Las 1 , Nachum Ulanovsky 1

      (1) Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel

      (2) Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK

      (3) The Edmond and Lily Safra Center for Brain Sciences, and Racah Institute of Physics, The Hebrew

      University of Jerusalem, Jerusalem, 91904, Israel

      9:45 – 10:30amSandro RomaniTitle: Neural networks for 3D rotations

      Abstract: Studies in rodents, bats, and humans have uncovered the existence of neurons that encode the orientation of the head in 3D. Classical theories of the head-direction (HD) system in 2D rely on continuous attractor neural networks, where neurons with similar heading preference excite each other, while inhibiting other HD neurons. Local excitation and long-range inhibition promote the formation of a stable “bump” of activity that maintains a representation of heading. The extension of HD models to 3D is hindered by complications (i) 3D rotations are non-commutative (ii) the space described by all possible rotations of an object has a non-trivial topology. This topology is not captured by standard parametrizations such as Euler angles (e.g. yaw, pitch, roll). For instance, with these parametrizations, a small change of the orientation of the head could result in a dramatic change of neural representation. We used methods from the representation theory of groups to develop neural network models that exhibit patterns of persistent activity of neurons mapped continuously to the group of 3D rotations. I will further discuss how these networks can (i) integrate vestibular inputs to update the representation of heading, and (ii) be used to interpret “mental rotation” experiments in humans.

      This is joint work with Hervé Rouault (CENTURI) and Alon Rubin (Weizmann Institute of Science).

      10:30 – 11:00amCoffee Break
      11:00 – 11:45amSam GershmanTitle: The hippocampus as a predictive map

      Abstract: A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. I approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? I show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, I argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning.

      11:45 – 12:30pmLucia JacobsTitle: The adaptive geometry of a chemosensor: the origin and function of the vertebrate nose

      Abstract: A defining feature of a living organism, from prokaryotes to plants and animals, is the ability to orient to chemicals. The distribution of chemicals, whether in water, air or on land, is used by organisms to locate and exploit spatially distributed resources, such as nutrients and reproductive partners. In animals, the evolution of a nervous system coincided with the evolution of paired chemosensors. In contemporary insects, crustaceans, mollusks and vertebrates, including humans, paired chemosensors confer a stereo olfaction advantage on the animal’s ability to orient in space. Among vertebrates, however, this function faced a new challenge with the invasion of land. Locomotion on land created a new conflict between respiration and spatial olfaction in vertebrates. The need to resolve this conflict could explain the current diversity of vertebrate nose geometries, which could have arisen due to species differences in the demand for stereo olfaction. I will examine this idea in more detail in the order Primates, focusing on Old World primates, in particular, the evolution of an external nose in the genus Homo.

      12:30 – 1:30pmLunch
      1:30 – 2:15pmTalia KonkleTitle: The shape of things and the organization of object-selective cortex

      Abstract: When we look at the world, we effortlessly recognize the objects around us and can bring to mind a wealth of knowledge about their properties. In part 1, I’ll present evidence that neural responses to objects are organized by high-level dimensions of animacy and size, but with underlying neural tuning to mid-level shape features. In part 2, I’ll present evidence that representational structure across much of the visual system has the requisite structure to predict visual behavior. Together, these projects suggest that there is a ubiquitous “shape space” mapped across all of occipitotemporal cortex that underlies our visual object processing capacities. Based on these findings, I’ll speculate that the large-scale spatial topography of these neural responses is critical for pulling explicit content out of a representational geometry.

      2:15 – 3:00pmVijay BalasubramanianTitle: Becoming what you smell: adaptive sensing in the olfactory system

      Abstract: I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors.  In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors.  The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules.  I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors.  The resulting algorithm for “estimation by elimination” can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain.  The theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans.   It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb.

      3:00 – 3:45pmIla FeiteTitle: Invariance, stability, geometry, and flexibility in spatial navigation circuits

      Abstract: I will describe how the geometric invariances or symmetries of the external world are reflected in the symmetries of neural circuits that represent it, using the example of the brain’s networks for spatial navigation. I will discuss how these symmetries enable spatial memory, evidence integration, and robust representation. At the same time, I will discuss how these seemingly rigid circuits with their inscribed symmetries can be harnessed to represent a range of spatial and non-spatial cognitive variables with high flexibility.

      3:45 – 4:00pmL Mahadevan – summary
    • CMSA EVENT: The 2017 Charles River Lectures
      9:15 am-5:30 pm
      11/01/2019

      The 2017 Charles River Lectures

      Charles River with Bench at Sunset

      Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community.

      The 2017 lectures will take place 9:15am – 5:30pm on Monday, October 2 at Harvard University  in the Harvard Science Center.


      ***************************************************

      UPDATED LOCATION

      Harvard University

      Harvard Science Center (Halls C & E)

      1 Oxford Street, Cambridge, MA 02138 (Map)

      Monday, October 2, 2017

      9:15 AM – 5:30 PM

      **************************************************

      Please note that registration has closed.

      Speakers:

      Agenda:

      In Harvard Science Center Hall C:

      8:45 am – 9:15 amCoffee/light breakfast

      9:15 am – 10:15 am: Ofer Zeitouni

      Title: Noise stability of the spectrum of large matrices

      Abstract: The spectrum of large non-normal matrices is notoriously sensitive to perturbations, as the example of nilpotent matrices shows. Remarkably, the spectrum of these matrices perturbed by polynomially (in the dimension) vanishing additive noise is remarkably stable. I will describe some results and the beginning of a theory.

      The talk is based on joint work with Anirban Basak and Elliot Paquette, and earlier works with Feldheim, Guionnet, Paquette and Wood.

      10:20 am – 11:20 am: Andrea Montanari

      Title: Algorithms for estimating low-rank matrices 

      Abstract: Many interesting problems in statistics can be formulated as follows. The signal of interest is a large low-rank matrix with additional structure, and we are given a single noisy view of this matrix. We would like to estimate the low rank signal by taking into account optimally the signal structure. I will discuss two types of efficient estimation procedures based on message-passing algorithms and semidefinite programming relaxations, with an emphasis on asymptotically exact results.

      11:20 am – 11:45 amBreak

      11:45 am – 12:45 pm: Paul Bourgade

      Title: Random matrices, the Riemann zeta function and trees

      Abstract: Fyodorov, Hiary & Keating have conjectured that the maximum of the characteristic polynomial of random unitary matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the typical size of local maxima of the Riemann zeta function along the critical axis. I will first explain the origins of this conjecture, and then outline the proof for the leading order of the maximum, for unitary matrices and the zeta function. This talk is based on joint works with Arguin, Belius, Radziwill and Soundararajan.

      1:00 pm – 2:30 pm: Lunch

      In Harvard Science Center Hall E:

      2:45 pm – 3:45 pm: Roman Vershynin

      Title: Deviations of random matrices and applications

      Abstract: Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This lecture will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science.

      3:45 pm – 4:15 pm: Break

      4:15 pm – 5:15 pm: Massimiliano Gubinelli

      Title: Weak universality and Singular SPDEs

      Abstract: Mesoscopic fluctuations of microscopic (discrete or continuous) dynamics can be described in terms of nonlinear stochastic partial differential equations which are universal: they depend on very few details of the microscopic model. This universality comes at a price: due to the extreme irregular nature of the random field sample paths, these equations turn out to not be well-posed in any classical analytic sense. I will review recent progress in the mathematical understanding of such singular equations and of their (weak) universality and their relation with the Wilsonian renormalisation group framework of theoretical physics.

      Poster:

      2017 Charles River Lectures Poster

      Organizers:

       Alexei BorodinHenry CohnVadim GorinElchanan MosselPhilippe RigolletScott Sheffield, and H.T. Yau

    • CMSA EVENT: Kickoff Workshop on Topology and Quantum Phases of Matter
      9:20 am-3:15 pm
      11/01/2019-08/28/2018
      Topological-1

      Screen-Shot-2018-08-13-at-2.28.22-PM

      On August 27-28, 2018, the CMSA will be hosting a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines.

      This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter,  and will be the first of two workshops, in addition to a visitor program and seminars.

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

      Please register here

      Speakers: 

    • Special Seminar
      Special Seminar
      3/30/2018 Special Seminar
      9:30 am-11:00 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/18/2019 General Relativity Seminar
      9:30 am-10:30 am
      11/01/2019
    • CMSA EVENT: Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
      9:30 am-5:00 pm
      11/01/2019-03/01/2019

      From February 25 to March 1, the CMSA will be hosting a workshop on Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations. 

      Key participants of this workshop include David Jerison (MIT), Alexander Logunov (IAS), and Eugenia Malinnikova (IAS).  This workshop will have morning sessions on Monday-Friday of this week from 9:30-11:30am, and afternoon sessions on Monday, Tuesday, and Thursday from 3:00-5:00pm.
      The sessions will be held in  \(G02\) (downstairs) at 20 Garden, except for Tuesday afternoon, when the talk will be in \(G10\).

    • Special Seminar
      9:30 am
      11/01/2019
    • Seminars
      9:50 am-10:50 am
      11/01/2019

      The seminar for evolution equations, hyperbolic equations, and fluid dynamics will be held on Thursdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule of speakers is below. Titles for the talks will be added as they are received.

      DateNameTitle
      09-03-2015Long JinScattering Resonances for Convex Obstacles
      09-10-2015Chunjing XieWell/ill-posedness for the rotating shallow water system
      09-17-2015Xiangdi HuangGlobal classical and weak Solutions to the 3D fully compressible Navier-Stokes-Fourier system
      09-24-2015Felix FinsterCausal fermion systems and the causal action principle
      10-01-2015Pin YuConstruction of Cauchy data of vacuum Einstein field equations evolving to black holes
      10-08-2015Chunjing XieSteady Euler flows past a wall or through a nozzle
      10-15-2015Zhou Ping XinOn Global Well-Posedness of The Compressible Navier-Stokes Systems with Large Oscillations
      10-22-2015Xiangdi HuangOn Nash’s problem for compressible flows
      10-29-2015Pin YuShock formations for 3 dimensional wave equations
      11-05-2015No talk 
      11-12-2015Zhou Ping Xin (9:30am-10:30am) Nicolai Krylov (10:30am-11:30am)Nonlinear Asymptotic Stability of Lane-Emden Solutions for The Viscous Gaseous Star ProblemOn the existence of $\bf W^{2}_{p}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions
      11-19-2015Nicolai KrylovTo the theory of viscosity solutions for uniformly parabolic Isaacs equations
      11-26-2015ThanksgivingNo seminar
      12-4-2015John Loftin (@11:00am)Moduli of Equivariant Minimal Surfaces in CH^2$
      01-28-2016Xiaoli HanThe symplecitic and Lagrangian mean curvature flow 
      02-04-2016Pranav PanditCategorical Kähler Geometry
      02-11-2016Lydia BieriEinstein’s Equations, Energy and Gravitational Radiation
      02-18-2016Zuoqiang ShiLow dimensional manifold model for image processing
      02-25-2016Chun Peng WangSmooth Transonic Flows of Meyer Type in De Laval Nozzles
      03-03-2016Piotr ChruscielSingularities in general relativity
      03-10-2016Feimin HuangIsometric immersion of complete surface with slowly decaying negative Gauss curvature
      03-17-2016Spring BreakNo Talk
      03-24-2016Michael EichmairMinimal surfaces, isoperimetry, and non-negative scalar curvature in asymptotically flat manifolds
      03-31-2016Felix FinsterLorentzian spectral geometry and the fermionic signature operator
      04-07-2016(Room 232, Science Center)Stefano Bianchini, SISSAConcentration of entropy dissipation for scalar conservation laws
      04-14-2016Tai-peng TsaiStability of periodic waves of the 1D nonlinear Schr\”odinger equations
      04-21-2016Stefano Bianchini, SISSAQuadratic interaction functional for system of conservation laws
      04-28-2016Mihalis Dafermos, PrincetonThe linear stability of the Schwarzschild solution to gravitational perturbations
      05-05-2016Xu-Jia WangMonge-Ampere equations arising in geometric optics
      05-12-2016Stefano Bianchini
    • Special Seminar
      9:50 am-10:50 am
      11/01/2019-04/26/2016

      The seminar on geometric analysis will be held on Tuesdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule can be found below. Titles will be added as they are provided.

      DayNameTitle
      09-08-2015Binglong ChenOn the geometry of complete positively curved Kahler manifolds
      09-15-2015Hongwei XuMean Curvature Flow and Sphere Theorem
      09-22-2015Teng FeiSome new solutions to the Strominger system
      09-29-2015Xuqian FanThe Steklov eigenvalues on annuli
      10-06-2015Binglong ChenRicci flow and the moduli spaces of positive isotropic curvature metrics on four-manifolds
      10-13-2015Pengfei GuanIsometric embeddings of $(S^2,g)$ to general warped product space $(N^3,\bar g)$.
      10-20-2015Ovidiu SavinSmoothness of the eigenfunction for the Monge-Ampere equation
      10-27-2015Tom IlmanenFlow of curves by curvature in R^n
      11-03-2015Tom Hou (Caltech)Existence and stability of self-similar singularities for a 1D model of the 3D axisymmetric Euler equations
      11-10-2015Jerome Darbon (9:30am-10:30am) Adam Jacob (10:30am-11:30am)On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton-Jacobi Equations(1,1) forms with specified Lagrangian phase
      11-17-2015Ovidiu SavinExamples of singular minimizers in the calculus of variations
      11-24-2015Hongwei XuMean curvature flow meets Ricci flow:  Convergence and sphere theorems of sub manifolds arising from Yau rigidity theory
      12-01-2015Tom Ilmanen
      01-26-2016Mao ShengUniformization of p-adic curves
      02-02-2016Yi ZhangHodge Bundles on Smooth Compactifications of Siegel Varieties
      02-09-2016Valentino TosattiNon-Kahler Calabi-Yau manifolds
      02-16-2016Camillo De LellisApproaching Plateau’s problem with minimizing sequences of sets
      02-23-2016Junbin LiConstruction of black hole formation spacetimes
      03-01-2016Ben WeinkoveMonge-Ampere equations and metrics on complex manifolds
      03-08-2016Albert ChauSurvey on Kahler Ricci flow on non-negatively curved non-compact manifolds
      03-15-2016Spring Break 
      03-22-2016Richard Schoen (Standford)The geometry of eigenvalue extremal problems
      03-29-2016Piotr ChruscielMass of characteristic surfaces
      04-05-2016 (Room 232, Science Center)Niky Kamran, McGill UniversityNon-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets
      04-12-2016Connor Mooney, UT AustinFinite time blowup for parabolic systems in the plane
      04-19-2016 (Room 232, Science Center)Xu-Jia WangBoundary behaviour of solutions to singular elliptic equations
      04-26-2016Andre NevesA path to Yau’s conjecture
    • Seminars
      Seminars Colloquia & Seminar
      13/3/2018 Topology Seminar
      10:00 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/22/2018 Topology Seminar
      10:00 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/18/2019 General Relativity
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/24/2019 General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/10/18 Topology Seminar
      10:30 am-12:00 am
      11/01/2019-09/11/2018
    • Seminars
      10:30 am-11:42 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/26/2019 Topology
      10:30 am-12:40 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/16/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/11/2019 General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/13/2019 General Relativity
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/25/2019 General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/18/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/20/2019 General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      10:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/9/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      11/1/2019 General Relativity Seminar
      10:30 am-11:30 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/30/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/2/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/1/2020 Quantum Matter seminar
      10:30 am-12:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-02-2016 Random Matrix & Probability Theory Seminar
      10:32 am
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      10:36 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-07-16 Mathematical Physics Seminar
      10:38 am
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      Special Seminar
      11-04-16 Special Seminar
      10:42 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      10:43 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-09-2016 Random Matrix & Probability Theory Seminar
      10:44 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9-29-2016 Homological Mirror Symmetry Seminar
      10:46 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-08-2016 Social Sciences Applications Forum
      10:56 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-15-2016 Social Sciences Applications Forum
      10:57 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-14-16 Mathematical Physics Seminar
      10:58 am
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
    • General Relativity Seminar
    • Seminars
      Seminars Colloquia & Seminar
      02-09-2018 Mirror Symmetry Seminar
      11:00 am
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-16-2016 Random Matrix & Probability Theory Seminar
      11:00 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/19/2018 Mirror Symmetry Seminar
      11:00 am-11:00 pm
      11/01/2019
    • General Relativity Seminar
    • General Relativity Seminar
    • Seminars
      Seminars Colloquia & Seminar
      2-16-2018 Mirror Symmetry Seminar
      11:00 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2-23-2018 Mirror Symmetry Seminar
      11:00 am
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3-2-2018 Mirror Symmetry Seminar
      11:00 am-12:00 am
      11/01/2019-03/03/2018
    • General Relativity Seminar
    • Seminars
      Seminars Colloquia & Seminar
      4-13-2018 Mirror Symmetry Seminar
      11:00 am-12:00 am
      11/01/2019-04/14/2018
    • Member Seminar
      11:01 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-21-16 Mathematical Physics Seminar
      11:02 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:03 am-11:04 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      11:03 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:04 am
      11/01/2019

      The  CMSA Colloquium will take place every Wednesday from 4:30-5:30pm in CMSA Building, 20 Garden Street, G10.

      Spring 2020

      DateSpeakerTitle/Abstract
      1/29/2020David Yang (Harvard)

      Abstract: Data-intensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in data-intensive economies: first, states are key collectors and repositories of data; second, data is a non-rival input in innovation. We document the importance of state-collected data for innovation using comprehensive data on Chinese facial recognition AI firms and government contracts. Firms produce more commercial software and patents, particularly data-intensive ones, after receiving government public security contracts. Moreover, effects are largest when contracts provide more data. We then build a directed technical change model to study the state’s role in three applications: autocracies demanding AI for surveillance purposes, data-driven industrial policy, and data regulation due to privacy concerns. When the degree of non-rivalry is as strong as our empirical evidence suggests, the state’s collection and processing of data can shape the direction of innovation and growth of data-intensive economies.

      2/5/2020Scott Aaronson (UT Austin)

      Video

      Title: Gentle Measurement of Quantum States and Differential Privacy

      Abstract: I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography”
      of quantum states (that is, answering a large number of questions about a quantum state given few copies of it).

      Based on joint work with Guy Rothblum (arXiv:1904.08747)

      2/12/2020Scott Kominers (Harvard)Title: A Compact, Logical Approach to Large-Market Analysis

      Abstract: In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

      2/19/2020Peter Shor (MIT)Title: Quantum Money from Lattices

      Abstract: Quantum money is  a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.

      2/26/2020Daneil Wise (McGill)Title: The Cubical Route to Understanding Groups

      Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds and simultaneously dramatically extended our understanding of many infinite groups.
      3/4/2020

      4:45 – 5:45pm

      Salil Vadhan (Harvard)Title: Derandomizing Algorithms via Spectral Graph Theory

      Abstract: Randomization is a powerful tool for algorithms; it is often easier to design efficient algorithms if we allow the algorithms to “toss coins” and output a correct answer with high probability. However, a longstanding conjecture in theoretical computer science is that every randomized algorithm can be efficiently “derandomized” — converted into a deterministic algorithm (which always outputs the correct answer) with only a polynomial increase in running time and only a constant-factor increase in space (i.e. memory usage).

      In this talk, I will describe an approach to proving the space (as opposed to time) version of this conjecture via spectral graph theory. Specifically, I will explain how randomized space-bounded algorithms are described by random walks on directed graphs, and techniques in algorithmic spectral graph theory (e.g. solving Laplacian systems) have yielded deterministic space-efficient algorithms for approximating the behavior of such random walks on undirected graphs and Eulerian directed graphs (where every vertex has the same in-degree as out-degree). If these algorithms can be extended to general directed graphs, then the aforementioned conjecture about derandomizing space-efficient algorithms will be resolved.

      3/11/2020

      Postponed

      Jose Scheinkman

      (Columbia)

      This colloquium will be rescheduled at a later date. 

      Title: Menu Costs and the Volatility of Inflation

      Abstract: We present a state-dependent equilibrium pricing model that generates inflation rate fluctuations from idiosyncratic shocks to the cost of price changes of individual firms.  A firm’s nominal price increase lowers other firms’ relative prices, thereby inducing further nominal price increases. We first study a mean-field limit where the equilibrium is characterized by a variational inequality and exhibits a constant rate of inflation. We use the limit model to show that in the presence of a large but finite number n of firms the snowball effect of repricing causes fluctuations to the aggregate price level  and these fluctuations converge to zero slowly as n grows. The fluctuations caused by this mechanism are larger when the density of firms at the repricing threshold is high, and the density at the threshold is high when the trend inflation level is high. However a calibration to US data shows that this mechanism is quantitatively important even at modest levels of trend inflation and  can account for the positive relationship between inflation level and volatility that has been observed empirically.

      3/12/2020

      4:00 – 5:00pm

      Daniel Forger (University of Michigan)This meeting will be taking place virtually on Zoom.

      Title: Math, Music and the Mind; Mathematical analysis of the performed Trio Sonatas of J. S. Bach

      Abstract: I will describe a collaborative project with the University of Michigan Organ Department to perfectly digitize many performances of difficult organ works (the Trio Sonatas by J.S. Bach) by students and faculty at many skill levels. We use these digitizations, and direct representations of the score to ask how music should encoded in the mind. Our results challenge the modern mathematical theory of music encoding, e.g., based on orbifolds, and reveal surprising new mathematical patterns in Bach’s music. We also discover ways in which biophysical limits of neuronal computation may limit performance.

      Daniel Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan. He is also a visiting scholar at Harvard’s NSF-Simons Center and an Associate of the American Guild of Organists.

      3/25/2020Cancelled
      4/1/2020Mauricio Santillana (Harvard)This meeting will be taking place virtually on Zoom.

      Title: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring

      Abstract: I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.

      4/8/2020Juven Wang (CMSA)This meeting will be taking place virtually on Zoom.

      Title: Quantum Matter Adventure to Fundamental Physics and Mathematics (Continued)

      Abstract: In 1956, Parity violation in Weak Interactions is confirmed in particle physics. The maximal parity violation now is a Standard Model physics textbook statement, but it goes without any down-to-earth explanation for long. Why? We will see how the recent physics development in Quantum Matter may guide us to give an adventurous story and possibly a new elementary
      explanation.  We will see how the topology and cobordism in mathematics may come into play of anomalies and non-perturbative interactions in
      fundamental physics. Perhaps some of you (geometers,  string theorists, etc.) can team up with me to understand the “boundary conditions” of the Standard Model and Beyond

      4/15/2020
      Lars Andersson (Max-Planck Institute for Gravitational Physics)
      This meeting will be taking place virtually on Zoom.

      Title: Stability of spacetimes with supersymmetric compactifications

      Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and Shing-Tung Yau.

      4/22/2020William Minicozzi (MIT)This meeting will be taking place virtually on Zoom.

      Title: Mean curvature flow in high codimension

      Abstract: I will talk about joint work with Toby Colding on higher codimension mean curvature flow.  Some of the ideas come from function theory on manifolds with Ricci curvature bounds.

      4/29/2020Gerhard Huisken (Tübingen University / MFO)This meeting will be taking place virtually on Zoom.

      Title: Mean curvature flow of mean-convex embedded 2-surfaces in 3-manifolds

      Abstract: The lecture describes joint work with Simon Brendle on the deformation of embedded surfaces with positive mean curvature in Riemannian 3-manifolds in direction of their mean curvature vector. It is described how to find long-time solutions of this flow, possibly including singularities that are overcome by surgery, leading to a comprehensive description of embedded mean-convex surfaces and the regions they bound in a 3-manifold. The flow can be used to sweep out the region between space-like infinity and the outermost horizon in asymptotically flat 3-manifolds arising in General Relativity. (Joint with Simon Brendle.)

      5/6/2020Lydia Bieri (UMich)This meeting will be taking place virtually on Zoom.

      Title: Energy, Mass and Radiation in General Spacetimes

      Abstract: In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. Isolated gravitating systems such as binary stars, black holes or galaxies can be described in GR by asymptotically flat (AF) solutions of these equations. These are solutions that look like flat Minkowski space outside of spatially compact regions. There are well-defined notions for energy and mass for such systems. The energy-matter content as well as the dynamics of such a system dictate the decay rates at which the solution tends to the flat one at infinity. Interesting questions occur for very general AF systems of slow decay. We are also interested in spacetimes with pure radiation. In this talk, I will review what is known for these systems. Then we will concentrate on spacetimes with pure radiation. In particular, we will compare the situations of incoming radiation and outgoing radiation under various circumstances and what we can read off from future null infinity.

      5/13/2020Mikhail Lukin (Harvard)

      Video

      This meeting will be taking place virtually on Zoom.

      Title: Exploring New Frontiers of Quantum Science with Programmable Atom Arrays

      Abstract: We will discuss recent work at a new scientific interface between  many-body physics and quantum information science. Specifically, we will  describe the advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Within this system we performed quantum simulations of one dimensional spin models, discovered a new type of non-equilibrium quantum dynamics associated with the so-called many body scars and created large-scale entangled states. We will also describe the most recent developments that now allow the control over 200 atoms in two-dimensional arrays.   Ongoing efforts  to study exotic many-body phenomena and to realize and test quantum optimization algorithms within such systems will be discussed.

      5/20/2020This meeting will be taking place virtually on Zoom.

      Fall 2019

      DateSpeakerTitle/Abstract
      9/18/2019Bill Helton (UC San Diego)Title:  A taste of noncommutative convex algebraic geometry

      Abstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example,

      ◦ A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials.

      ◦ A convex NC semialgebraic set has a linear matrix inequality representation.

      ◦ The natural Nullstellensatz are falling into place.

      The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019.

      9/25/2019Pavel Etingof (MIT)

       

      Title: Double affine Hecke algebras

      Abstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications.

      10/2/2019Spiro Karigiannis (University of Waterloo)Title: Cohomologies on almost complex manifolds and their applications

      Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.

      10/9/2019Hans Lindblad (Johns Hopkins University)Title:  Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition

       

      Abstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition  satisfy the preserved wave coordinate condition.

       

      Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times.

      John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas  lainerman came up with the ‘null condition’, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition.

      Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition.

      Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to afraction and has now been used to prove global existence also with matter fields.

      Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equationsbackwards to obtain global solutions with given data at infinity.

      10/16/2019Aram Harrow (MIT)

      Video

      Title: Monogamy of entanglement and convex geometry

      Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems.

      10/23/2019No talk
      10/30/2019Nima Arkani-Hamed (IAS)

      Video

      Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity
      11/6/2019Kevin Costello (Perimeter Institute)

      Video

      Title: A unified perspective on integrability

       

      Abstract: Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics.   I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu.

      11/13/2019Heather  Harrington (University of Oxford)Title:  Algebra, Geometry and Topology of ERK Enzyme Kinetics

      Abstract: In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

      11/20/2019Xi Yin (Harvard)

      Video

      Title: An Introduction to the Non-Perturbative Bootstrap

      Abstract: I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap

      11/25/2019

      Monday

      Madhu Sudan (Harvard)
      Abstract: The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits.

      In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction.

      Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard).

      12/4/2019Xiao-Gang Wen (MIT)
      Video
      Title: Emergence of graviton-like excitations from a lattice model

      Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases.

      2018-2019

      DateSpeakerTitle/Abstract
      9/26/2018Xiao-Gang Wen (MIT)Title: A classification of low dimensional topological orders and fully extended TQFTs

      Abstract: In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1-dimension, there is no non-trivial topological orders. In 2-dimensions, the topological orders are classified by modular tensor category theory. In 3-dimensions, the topological orders are classified by a simple class of braided fusion 2-categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs.

      10/03/2018Richard Schoen (Stanford)Title: Perspectives on the scalar curvature

      Abstract: This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied.

      10/10/2018Justin Solomon (MIT)Title: Correspondence and Optimal Transport for Geometric Data Processing

      Abstract: Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make large-scale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometrically-structured data.

      10/17/2018Jeremy England (MIT)Title: Wisdom of the Jumble

      Abstract: There are certain, specific behaviors that are particularly distinctive of life. For example, living things self-replicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of life-like phenomena in a wide range of messy systems made of many interacting components.

      In this talk I will discuss some of the recent insights we have gleaned from studying emergent fine-tuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more life-like ways of computing that have the potential to either be cheaper or more powerful than existing means.

      10/31/2018Moon Duchin (Tufts)Title: Exploring the (massive) space of graph partitions

      Abstract: The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts).  I’ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics.

      11/14/2018Dusa McDuff (Columbia)Title: The virtual fundamental class in symplectic geometry

      Abstract: Essential to many constructions and applications of symplectic  geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well  understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so  that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there  are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a  construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim.

      11/19/2018Xiaoqin Wang (Johns Hopkins)Title: Computational Principles of Auditory Cortex

      Abstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication.

      11/28/2018Robert Haslhofer (University of Toronto)Title: Recent progress on mean curvature flow

      Abstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanen’s multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits.

      12/5/2018Robert McCann (University of Toronto)Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity

      Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of  probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics.

      Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf

      12/12/2018Zhiwei Yun (MIT)Title: Shtukas: what and why

      Abstract: This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them.

      1/30/2019Richard Freeman (Harvard)Title:  Innovation in Cell Phones in the US and China: Who Improves Technology Faster?

      Abstract:  Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps.  Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones.  Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality.  The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being.

      2/7/2019

      *Thursday*

      Ulrich Mueller (Princeton)Title: Inference for the Mean

      Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.

      2/13/2019Christian Santangelo (UMass Amherst)Title: 4D printing with folding forms

      Abstract: 4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target three-dimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our group’s efforts to understand and design structures that can fold from an initially flat sheet to target three-dimensional shapes. After reviewing the state-of-the-art in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome.

      2/20/2019Michael Woodford (Columbia)Title: Optimally Imprecise Memory and Biased Forecasts

      Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings.

      [authors: Rava Azeredo da Silveira (ENS) and Michael Woodford (Columbia)]

      2/27/2019

      2:30pm

      Ian Martin (LSE)Title: Sentiment and Speculation in a Market with Heterogeneous Beliefs

      Abstract: We present a dynamic model featuring risk-averse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so “the market” is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou]

      3/6/2019

      2:30pm

      Philippe Sosoe (Cornell)Title:  A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation

      Abstract:  In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS’s result, and discuss a sharp transition in the construction of the Gibbs-type invariant measures considered by these authors.  (Joint work with Tadahiro Oh and Leonardo Tolomeo)

      3/13/2019

      5:15pm

      Greg Galloway (University of Miami)Title:  On the geometry and topology of initial data sets in General Relativity

      Abstract:  A theme of long standing interest (to the speaker!)  concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness).  Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple.  The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces,  which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack.

      3/20/2019Sonia Jaffe (Microsoft)Title:  Quality Externalities on Platforms:  The Case of Airbnb

      Abstract:  We explore quality externalities on platforms:  when buyers have limited information, a seller’s quality affects whether her buyers return to the platform, thereby impacting other sellers’ future business.  We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller’s customers to return to the platform.  We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higher-GRP sellers, platforms may be able to increase overall seller surplus.  (Joint work with Peter Coles, Steven Levitt, and Igor Popov.)

      3/27/2019

      5:15pm

      Tatyana Sharpee (Salk Institute for Biological Studies)Title: Hyperbolic geometry of the olfactory space.

      Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their co-occurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical tree-like networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

      4/3/2019

      2:30pm

      Sarah Moshary (Chicago Booth)Title:  Deregulation through Direct Democracy:  Lessons from Liquor

      Abstract:  This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool.

      4/10/2019

      2:30pm

      Pietro Veronesi (Chicago Booth)Title: Inequality Aversion, Populism, and the Backlash Against Globalization

      Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model.

      Paper

      Online Appendix

      4/17/2019Yi-Zhuang You (UCSD)Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

      Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

      .

      [1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103

      [2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804

      [3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223

      4/24/2019Shengwu Li (Harvard)
      Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.
      Date…………SpeakerTitle
      02-09-2018 *Friday       Fan Chung

      (UCSD)

      Sequences: random, structured or something in between

      There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns;

      testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems.

      02-14-2018Zhengwei Liu

      (Harvard Physics)

      A new program on quantum subgroups

      Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing.

      02-21-2018Don Rubin

      (Harvard)

      Essential concepts of causal inference — a remarkable history

      Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis.

      02-26-2018 *MondayTom Hou

      (Caltech)

      Computer-assisted analysis of singularity formation of a regularized 3D Euler equation

      Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate self-similar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate self-similar solution, which implies the existence of the finite time blow-up of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu.

      03-07-2018Richard Kenyon

      (Brown)

      Harmonic functions and the chromatic polynomial

      Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam.

      03-14-2018
      03-21-2018
      03-28-2018Andrea Montanari (Stanford)A Mean Field View of the Landscape of Two-Layers Neural Networks

      Abstract: Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD).  Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties?

      We consider a simple case, namely two-layers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to `average-out’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well.
      [Based on joint work with Song Mei and Phan-Minh Nguyen]

      03-30-2018
      04-04-2018Ramesh Narayan 

      (Harvard)

      Black Holes and Naked Singularities

      Abstract: Black Hole solutions in General Relativity contain Event Horizons and
      Singularities. Astrophysicists have discovered two populations of
      black hole candidates in the Universe: stellar-mass objects with
      masses in the range 5 to 30 solar masses, and supermassive objects
      with masses in the range million to several billion solar
      masses. There is considerable evidence that these objects have Event
      Horizons. It thus appears that astronomical black hole candidates are
      true Black Holes. Direct evidence for Singularities is much harder to
      obtain since, at least in the case of Black Holes, the Singularities
      are hidden inside the Event Horizon. However, General Relativity also
      permits Naked Singularities which are visible to external
      observers. Toy Naked Singularity models have been constructed, and
      some observational features of accretion flows in these spacetimes
      have been worked out.

      04-11-2018Pablo Parrilo

      (MIT)

      Graph Structure in Polynomial Systems: Chordal Networks

      Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).

      04-18-2018Washington Taylor

      (MIT)

      On the fibration structure of known Calabi-Yau threefolds

      Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds.

      04-25-2018 Xi Yin

      (Harvard)

      How we can learn what we need to know about M-theory

      Abstract: M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory.

      05-02-2018
      05-09-2018

      2016-2017

      DateNameTitle/Abstract
      01-25-17Sam Gershman, Harvard Center for Brain Science, Department of Psychology

      Title: Spectral graph theory of cognitive maps

      Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory.

      02-01-17Sean Eddy, Harvard Department of Molecular and Cellular Biology

      Sean_Eddy

      Title: Biological sequence homology searches: the future of deciphering the past 

      Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK.

      02-08-17Matthew Headrick, Brandeis University

      matthew_headrick

      Title: Quantum entanglement, classical gravity, and convex programming: New connections

      Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differential-geometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way.

      02-15-17Masahito Yamazaki, IMPU

      Masahito Yamazaki

       Title: Geometry of 3-manifolds and Complex Chern-Simons Theory

      Abstract: The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras.

      Video

      02-22-17Steven Rayan, University of Saskatchewan

      Title: Higgs bundles and the Hitchin system

      Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics.  As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence.  From this point of view, the Hitchin map and spectral curves emerge.  We’ll use these to form an impression of what the moduli space “looks like”.  I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry.

      Video

      03-01-17Jun Liu, Harvard University

      Jun liu

      Title: Expansion of biological pathways by integrative Genomics

      Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays.

      Based on the joint work with Yang Li and the Vamsi Mootha lab.

      Video

      03-08-17Gabor Lippner, Northeastern University

      ---

      Title: Evolution of cooperation in structured populations

      Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics.  Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies.  It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution.

      In this talk I will present new results about the model where the population is represented by an interaction network.  We study the likelihood of a random mutation spreading through the entire population.  The main question is to understand how the network influences this likelihood.  After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks.
      03-15-17 Spring Break: No session
      03-22-17Gunther Uhlmann, University of Washington

      guntherUhlman

      Abstract We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of
      waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others.
      The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.
      We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.
      03-29-17Leslie Greengard, Courant InstituteLeslie_GreengardTitle: Inverse problems in acoustic scattering and cryo-electron microscopy

      Abstract: A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy.

      NOTE: This talk will begin at 4:00pm

      04-05-17Gongjie Li, Harvard University

      GongjieLi

      Title: Unveiling the Origin of Planetary Systems by Dynamical and Statistical Approaches

      Abstract: The unexpected diversity of observed extrasolar planetary systems has posed new challenges to our classical understanding of planetary formation. A lot of these challenges can be addressed by a deeper understanding of the dynamics in planetary systems, which will also allow us to construct more accurate planetary formation theories consistent with observations. In this talk, I will first explain the origin of counter orbiting planets using a new dynamical mechanism I discovered, which also has wide implications in other astrophysical systems, such as the enhancement of tidal disruption rates near supermassive black hole binaries. In addition, I will discuss the architectural properties of circumbinary planetary systems from selection biases using statistical methods, and infer the origin of such systems.

      Video

      04-12-17Shlomo Razamat, Israel Institute of Technology

      ShlomoRazamat

      Title: Complicated four-dimensional physics and simple mathematics

      Abstract: We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index,  of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of Ruijsenaars-Schneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven.

      Video

      04-19-17Cumrun Vafa, Harvard University

      CumrunVafa

      Title: String Swampland

      Abstract: In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a no-go theorem for non-supersymmetric AdS/CFT holography.

      04-27-17Mehran Kardar, MIT

      MehranKardar

      Title: Levitation by Casimir forces in and out of equilibrium

      Abstract: Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw’s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint.

      Note: This talk will begin at 3:00pm

      05-02-17Simona Cocco, Laboratoire de Physique Statistique de l’ENSTitle: Reverse modeling of protein sequence data: from graphical models to structural and functional predictions

      Body: A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing
      similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models
      have led to substantial progress in protein structural and functional
      predictions.

      Note:  This talk will begin at 4:00pm

      05-03-17Xue-Mei Li, University of WarwickTitle: Perturbation to conservation law and stochastic averaging

      Abstract: A deterministic or random system with a conservation law is often used to
      approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces.

      Note: This talk will be held in the Science Center, Room 507

      05-10-17
      05-17-17Kwok Wai Chan, Chinese University of Hong KongTitle: Scattering diagrams from asymptotic analysis on Maurer-Cartan equations

      Abstract:  In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on Maurer-Cartan equations. In this talk, I will explain some results which implement part of Fukaya’s program. More precisely, I will show how semi-classical limits of Maurer-Cartan solutions give rise naturally to consistent scattering diagrams, which are known to encode Gromov-Witten data on the mirror side and have played an important role in the works of Kontsevich-Soibelman and Gross-Siebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015).

      05-24-17 NO COLLOQUIUM
      05-31-17Peter Michor, University of Vienna

       Title: Geometry of shape spaces and diffeomorphism groups and some of their uses

      Abstract: This talk is devoted to shape spaces, Riemannian metrics on them, their geodesics and distance functions, and some of their uses, mainly in computational anatomy. The simplest Riemannian metrics have vanishing geodesic distance, so one has to use, for example, higher order Sobolev metrics on shape spaces. These have curvature, which complicates statistics on these spaces.

      DateNameTitle
      09-09-16

      Bong Lian, Brandeis

      portrait

      Title: Riemann-Hilbert Problem and Period Integrals

      Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems.

      09-14-16Sze-Man Ngai, Georgia Southern UniversityngaiTitle: The multifractal formalism and spectral asymptotics of self-similar measures with overlaps

      Abstract: Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum.  The asymptotic behavior of the eigenvalue counting function for the associated  Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results.

      09-21-16Prof. L. Mahadevan, Harvard SEAS

      Mahadevan_200x300

      Title: “Morphogenesis: Biology, Physics and Mathematics”

      Abstract:  A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology.  Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains.  I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology.

      09-28-16Hong Liu, MIT

      liu_hong

      Title: A new theory of fluctuating hydrodynamics

      Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate  for capturing  fluctuations.  In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure.

      We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular,  the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations.

      Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anti-commuting variables and the theory exhibits an emergent supersymmetry.

      10-05-16

      Alexander LogunovTel-Aviv University

      alex

      Title: Zeroes of harmonic functions and Laplace eigenfunctions

       Abs: Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete.

      10-12-16 Conan Nai Chung Leung, CUHK

      conan_profile

      Title:  Coisotropic A-branes and their SYZ transform

      Abstract: “Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit.”

      10-19-16Vaughan Jones, UC Berkeley

      vj6

      Title: Are the Thompson groups any good as a model for Diff(S^1)?

      Abstract. The Thompson groups are by definition groups of piecewise linear
      diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can
      be conjugated to a group of smooth diffeomorphisms. That’s the good news.
      The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any
      procedure analogous to the constructions of the central extension of Diff(S^1)?
      I will define all the players in this game, explain this question in detail,and present some failed attempts to answer it.

       10-26-16

      Henry Cohn, Microsoft

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      Sums of squares, correlation functions, and exceptional geometric structures

      Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding.  How can we understand and prove their optimality?  In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems.

      11-02-16

      Christian Borgs, Microsoft

      Borgs

      Title:  Graphon processes and limits of   sparse graph sequences

      Abstract:  The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for so-called exchangeable random graphs.   Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection.  While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model.  

      In this talk I describe a new model, where the underlying probability space is replaced by a sigma-finite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits.  The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life.

      11-09-16

      TIME CHANGE: 4PM

      Norden E. HuangNational Central University, (Taiwan)

      member1_clip_image003

      Title: On Holo-Hilbert Spectral Analysis

      Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation.

      11-16-16Tristan Collins, Harvard University

      image

      TIME CHANGE: 3:30PM

      Title: Restricted volumes and finite time singularities of the Kahler-Ricci flow

      Abstract:  I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow.  This is joint work with Valentino Tosatti.

      11-22-16 TUESDAY

      TIME CHANGE: 4-5PM

      Xiangfeng Gu, Stonybrook

      Title: Differential Geometric Methods for Engineering Applications

      Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation.

      11-30-16

      TIME CHANGE: 4:20PM

      Sharad Ramanathan, Harvard MCB & SEAS

      Ramanathan.Sharad_200x300

      Title: Finding co-ordinate systems to monitor the development of mammalian embryos
       12-07-16

      Valentino Tosatti, Northwestern

      Title: Metric limits of hyperkahler manifolds

      Abstract: I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang.

       12-14-16

      2015-2016

      DateNameTitle
      09-02-2015Madhu SudanRobust low-degree testing
      09-09-2015Mithat Unsal
      What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
      09-16-2015Subir SachdevBekenstein-Hawking entropy and strange metals
      09-23-2015Felix FinsterLinear hyperbolic equations in a rotating black hole geometry
      09-30-2015Leslie ValiantHolographic Algorithms
      10-07-2015Christopher RoganExploring the Frontier of Size and Energy with the Large Hadron Collider: sub-atomic particles, the Higgs Boson and beyond
      10-14-2015Boaz Barak, Harvard SEASConvexity, Bayesianism, and the quest towards Optimal Algorithms
      10-21-2015Zhouping XinEntropy and Uniqueness of Weak Solutions to The Multi-Dimensional Compressible Euler Systems
      10-28-2015Cristopher MooreStatistical inference, statistical physics, and the community detection problem
      11-04-2015Tom HouBlowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations
      11-11-2015Stan Osher, UCLAOvercoming the curse of dimensionality for certain Hamilton-Jacobi (HJ) equations arising in control theory and elsewhere
      11-18-2015Xiaole Shirley LiuInference of transcriptional regulation in cancers
      11-25-2015ThanksgivingNo seminar
      12-02-2015Scott KominersGeneralized Matching Market Design: Theory and Practice
      12-09-2015Matthew HolmanDynamical Chaos in Kepler Planetary Systems
      01-27-2016Conan LeungSome modern aspects of Morse theory 
      02-03-2016Camillo De LellisFrom Nash to Onsager, funny coincidences across differential geometry and the theory of turbulence
      02-10-2016Chun Peng Wang
      02-17-2016Samuel Kou, Harvard StatisticsBig data, Google and disease detection: the statistical story
      02-24-2016Dan Xie, Harvard CMSASingularity theory and supersymmetric field theory
      03-02-2016Lydia BieriMathematical General Relativity
      03-09-2016Piotr ChruscielThe mathematics of gravitation
      03-16-2016Spring BreakNo Talk
      03-23-2016Richard Freeman, Harvard EconomicsPulling Apart of Wages and Productivity: why “identical” workers have increasingly different pay and productivity.
      03-30-2016David Garfinkel, Oakland UniversityGravitational Wave Memory
      04-04-2016 (Hall A, Science Center)Xianfeng David Gu, Stony Brook UniversityA Discrete Variational Approach for Solving Monge-Ampere Equation
      04-06-2016Lars Hernquist, HarvardNext Generation Cosmological Simulations: Galaxy Assembly and Evolution
      04-13-2016Jun Zhang, Univ. of Michigan-Ann ArborKahler and Para-Kahler Structure in Information Geometry
      04-20-2016Sijue Wu, Univ. of MichiganOn two dimensional gravity water waves with angled crests
      04-27-2016Paul Seidel, MITTopological quantum field theory and the Gauss-Manin connection
      05-04-2016Hirosi Ooguri, CaltechString Theory And Its Applications in Mathematics and Physics
      05-11-2016      (4pm – 5pm)Juerg Froehlich, ETH and IASImplications of the Chiral Anomaly – From the Quantum Hall Effect to Topological Insulators and Out to Space
    • Colloquium
      11:05 am-11:06 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:07 am-11:08 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:08 am-11:09 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-22-2016 Random Matrix & Probability Theory Seminar
      11:12 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-07-2016 Random Matrix & Probability Theory Seminar
      11:16 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12-05-16 Mathematical Physics Seminar
      11:17 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:21 am-11:22 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      11:21 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-14-2016 Random Matrix & Probability Theory Seminar
      11:22 am
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      11:24 am
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      11:25 am
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Learning from health data in the million genome era
      11:26 am
      11/01/2019

      On November 12019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system.

      Speakers: 

      • Heidi Rehm, Ph.D.
        Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform.
      • Saiju Pyarajan, Ph.D.
        Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS
      • Tianxi Cai, Sci.D
        John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health
      • Susan Redline, M.D., M.P.H
        Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center
      • Avinash Sahu, Ph.D.
        Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health
      • Peter J. Park, Ph.D.
        Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School
      • David Roberson
        Community Engagement Manager, Seven Bridges

      Registration & Schedule

    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 Quantum Field Theory Seminar
      11:30 am-12:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      01-30-2017 Mathematical Physics Seminar
      11:30 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-07-2017 Social Sciences Applications Forum
      11:32 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      02-06-2017 Mathematical Physics Seminar
      11:33 am
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      02-13-2017, Mathematical Physics Seminar
      11:34 am
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      11:35 am
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Spacetime and Quantum Mechanics Master Class Workshop
      11:36 am
      11/01/2019-10/30/2019
      Space-Time-poster-5

      As part of the program on Spacetime and Quantum Mechanics, Total Positivity and Motives, the CMSA will host a “Master Class Workshop”  on October 28-30, 2019. Each day of the workshop will feature an intensive full day of pedagogical lectures, with the aim of bringing actively interested but non-expert physicists and mathematicians up to speed on the featured topics.

      Everyone is welcome to attend the lectures.

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

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

      Photos of the event

      Organizers:

    • Member Seminar
      11:37 am
      11/01/2019

      Hansol Hong, Harvard

      Title: Homological Mirror Functors

      Abstract: I will first give a brief introduction to mirror symmetry, which intertwines symplectic geometry and complex geometry of a pair of Kahler manifolds, and explain mirror construction using formal deformation of a Lagrangian submanifold.  We will see that counting of holomorphic discs bounding Lagrangian naturally gives rise to a mirror space (Landau-Ginzburg model) and  a functor from Fukaya category to its mirror matrix factorization category. I will mainly focus on one specific example to give a concrete description of the construction.

    • Colloquium
      11:39 am-11:40 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:40 am-11:41 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-14-2017 Social Science Applications Forum
      11:42 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:43 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:45 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/24/2019 Quantum Matter Seminar
      11:50 am-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/31/2019 Condensed Matter Seminar
      11:50 am-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/10/2019 Condensed Matter Seminar
      11:50 am-1:00 pm
      11/01/2019
    • CMSA EVENT: Quantum Information Workshop
      11:52 am-11:53 am
      11/01/2019
      Asset-6-600x338

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

      The CMSA will host a workshop on Quantum Information. This workshop will be held virtually using Zoom.

      The workshop on Quantum information is organized by Mikhail LukinHorng-Tzer Yau, and Norman Yao.

      More information to follow.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-12-2017 Random Matrix & Probability Theory Seminar
      11:56 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:56 am
      11/01/2019

      No additional detail for this event.

    • Colloquium
      11:58 am
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-22-2017 Random Matrix & Probability Theory Seminar
      11:58 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-21-2017 Social Science Applications Forum
      11:59 am
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      5/6/2019 Math Physics
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4-17-2018 Special Algebraic Geometry Seminar
      12:00 pm-1:30 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/19/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12/3/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/8/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/29/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/26/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/25/2019 Fluid Dynamics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/3/2019 Condensed Matter Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/5/2018 Math Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/7/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/22/2019 Math Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/29/2018 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/15/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/9/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      1/28/2018 Mathematical Physics Seminar
      12:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/4/2019 Math Physics Seminar
      12:00 pm-2:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/25/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • General Relativity Seminar
      12:00 pm-1:00 pm
      11/01/2019

      The Seminar on General Relativity will take place every Wednesday from 12pm – 1pm in CMSA Building, 20 Garden Street, G10.

      The list of speakers is below and will be updated as details are confirmed.

      DateNameTitle
      04-06-2016Mihalis Dafermos (Princeton)The black hole stability problem: the inside story
      04-13-2016Felix Finster, University of RegensburgLinear stability of Kerr black holes
      04-20-2016Paul Chesler, Harvard PhysicsNumerical relativity in asymptotically anti-de Sitter spacetime
      04-27-2016Andy Strominger (Harvard Physics) & Mihalis Dafermos (Princeton University)The Scattering Problem in General Relativity
      05-04-2016Robert Penna, MITBMS invariance and the membrane paradigm
      05-11-2016Piotr T. Chruściel, University of ViennaGluing things in general relativity
      05-18-2016Achilleas Porfyriadis, Harvard PhysicsGravitational waves from the Kerr/CFT correspondence
      05-25-2016Scott Hughes, MITThe gravitational-wave event GW150914: What we learned, and how we learned it
    • Seminars
      Seminars Colloquia & Seminar
      3/4/2019 Mathematical Physics Seminar
      12:00 pm-2:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      1-5-2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Quantum Matter Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/28/2019 Math Physics
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/16/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-2-2018 Mathematical Physics Seminar
      12:00 pm-1:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/25/2019 Math Physics Seminar
      12:00 pm-2:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/1/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/11/2019 Mathematical Physics Seminar
      12:00 pm-2:00 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3/19/2018 Mathematical Physics Seminar
      12:00 pm-1:30 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-26-2018 Math Physics Seminar
      12:00 pm-1:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Condensed Matter Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/30/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-22-2017 Random Matrix & Probability Theory Seminar
      12:01 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:03 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Cosmic Road to New Physics
      12:04 pm
      11/01/2019
      The colourful star cluster NGC 3532

      The CMSA will host a 3-day workshop on cosmological signatures of fundamental physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

      The next decade will see a wealth of new cosmological data, which can lead to new insights for fundamental physics. This upcoming data will span the entire history of the cosmos, from the era prior to big-bang nucleosynthesis to the inner Galactic structure today, including the intervening eras of recombination and cosmic dawn. Often, beyond-standard-model (BSM) physics will leave imprints in more than one of these eras. Thus, it is timely to gather experts in BSM physics across the entire cosmic history to exchange ideas and develop joint and powerful probes of new physics. For this program, it will be crucial to have an overlap of particle physicists, astrophysicists and cosmologists. There are a number of tools and techniques being actively developed across these disciplines. The workshop aims to provide a platform for efficient exchange of these new ideas.

      The first day we will discuss sub-Galactic probes, including Gaia data and gravitational waves. The second day we will cover cosmological probes, such as the cosmic microwave background and the 21-cm line. The third day we will discuss early Universe probes, such as inflation and phase transitions. Every day the meeting will begin with a pedagogical blackboard talk plus an overview talk, followed by about 4 talks on more specific topics.

      Organizers:

      Scientific Advisory:

      Speakers: 

      CosmicRoad_Poster

    • Colloquium
      12:05 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:06 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:08 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:09 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      12:10 pm-1:10 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

       

      Speaker: Man-Wai Cheung

      Title: Compactification for cluster varieties without frozen variables of finite type

      Abstract: Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev–Borisov construction.

    • CMSA EVENT: 2019 Ding Shum Lecture
      12:11 pm
      11/01/2019
      DingShum-2019

      DSC_0468-e1568985499370

      On October 22, 2019, the CMSA will be hosting our third annual Ding Shum lecture. This year’s lecture will be a talk on “Election Security” by Ronald L. Rivest (MIT). The lecture will take place from 4:30-5:30pm in Science Center, Hall A.

      Ronald L. Rivest is an Institute Professor at the Massachusetts Institute of Technology. He is a member of the Electrical Engineering and Computer Science Department and the Computer Science and Artificial Intelligence Laboratory (CSAIL) and a founder of the Cryptography and Information Security research group within CSAIL. His research has been in the areas of algorithms, machine learning, cryptography, and election security, for which he has received multiple awards, including: the ACM Turing Award (with Adleman and Shamir), the BBVA Frontiers of Knowledge Award, National Inventor’s Hall of Fame membership, and the Marconi Prize.

      Prof. Rivest is also well-known as a co-author of the textbook “Introduction to Algorithms” (with Cormen, Leiserson, and Stein), and as a co-inventor of the RSA public-key cryptosystem (with Adleman and Shamir). He is a co-founder of RSA and of Verisign.He has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), in charge of the Security subcommittee. He is a member of the CalTech/MIT Voting Technology Project, on the Board of Verified Voting, and an advisor to the Electronic Privacy Information Center. Additionally, he has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), as a member of the CalTech/MIT Voting Technology Project, and as an advisor to the Electronic Privacy Information Center.

      Last year featured Eric Maskin, who spoke on “How to Improve Presidential Elections: the Mathematics of Voting.” The first Ding Shum lecture took place on October 10, 2017, featuring Leslie Valiant on “Learning as a Theory of Everything.”

      This event is made possible by the generous funding of Ding Lei and Harry Shum.

      DingShum-2019

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-1-2017 Random Matrix & Probability Seminar
      12:11 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Special Lecture Series on Donaldson-Thomas and Gromov-Witten Theories
      12:11 pm
      11/01/2019-04/19/2017

      From March 8 to April 19, the Center of Mathematical Sciences and Applications will be hosting a special lecture series on Donaldson-Thomas and Gromov-Witten Theories. Artan Sheshmani (QGM Aarhus and CMSA Harvard) will give eight talks on the topic on Wednesdays and Fridays from 9:00-10:30 am, which will be recorded and promptly available on CMSA’s Youtube Channel.

    • Colloquium
      12:12 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:13 pm-12:14 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2-27-2017 Mathematical Physics Seminar
      12:14 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-7-2017 Social Science Applications Forum
      12:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/13/2019 Special Seminar
      12:15 pm-1:05 pm
      11/01/2019
    • Colloquium
      12:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-8-2017 CMSA Special Lecture Series
      12:16 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Noncommutative Analysis, Computational Complexity, and Quantum Information
      12:19 pm
      11/01/2019-10/18/2019
      Noncommutative-Analysis-Poster-3

      On October 16-18, 2019 the CMSA will be hosting a workshop on Noncommutative Analysis, Computational Complexity, and Quantum Information.

      This workshop will focus on  linking three different rapidly developing areas: noncommutative real algebraic geometry (RAG), theory of computation and quantum information theory. This mix of overlapping but independently developing topics should lead to a stimulating flow of tools and important problems into several disciplines.  Given the different communities there will be an emphasis on tutorials and making the lectures broadly understandable.

      The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by Boaz Barak, Bill Helton, Pablo Parrilo, Tselil Schramm.

      Please register here

      Speakers:

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

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-8-2017 Random Matrix & Probability Theory Seminar
      12:21 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-6-2017 Mathematical Physics Seminar
      12:24 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      12:25 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-10-2017 Special Lecture Series
      12:27 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
      12:28 pm
      11/01/2019-05/05/2019
      1 Oxford Street, Cambridge MA 02138
      Differential Geometry, Calabi-Yau theory and General Relativity

      Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau

      On May 2-5, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the  Science Center, Lecture Hall C. 

      Organizers:

      • Horng-Tzer Yau (Harvard)
      • Wilfried Schmid (Harvard)
      • Clifford Taubes (Harvard)
      • Cumrun Vafa (Harvard)

      Speakers:

      • Lydia Bieri, University of Michigan
      • Tristan Collins, MIT
      • Simon Donaldson, Imperial College
      • Fan Chung Graham, UC San Diego
      • Nigel Hitchin, Oxford University
      • Jun Li, Stanford University
      • Kefeng Liu, UCLA
      • Chiu-Chu Melissa Liu, Columbia University
      • Alina Marian, Northeastern University
      • Xenia de la Ossa, Oxford University
      • Duong H. Phong, Columbia University
      • Richard Schoen, UC Irvine
      • Andrew Strominger, Harvard University
      • Nike Sun, MIT
      • Clifford Taubes, Harvard University
      • Chuu-Lian Terng, UC Irvine
      • Valentino Tosatti, Northwestern University
      • Karen Uhlenbeck, University of Texas
      • Cumrun Vafa, Harvard University
      • Mu Tao Wang, Columbia University
      • Edward Witten, IAS
      • Stephen Yau, Tsinghua University, P.R. China
    • Seminars
      Seminars Colloquia & Seminar
      3-21-2017 Social Science Applications Forum
      12:28 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:30 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-20-2017 Mathematical Physics Seminar
      12:30 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-5-2017 Random Matrix & Probability Theory Seminar
      12:31 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:32 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Conference on Algebraic Geometry, Representation theory and Mathematical Physics
      12:33 pm
      11/01/2019-05/01/2019

      From April 29 to May 1, 2019 the CMSA will be hosting a Conference on Algebraic Geometry, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.  

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

      List of registrants

      Videos

      Speakers: 

       

      Monday, April 29

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amWei Zhang, MITTitle: The arithmetic fundamental lemma for diagonal cycles

      Abstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization, the arithmetic Gan-Gross-Prasad conjecture, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions.  The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.

      10:00 – 10:30amBreak
      10:30 – 11:30amYuri Tschinkel, NYUTitle: Equivariant birational geometry and modular symbols

      Abstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).

      11:30 – 1:30pmLunch
      1:30 – 2:30pmAlexander Efimov, MoscowTitle: Torsionness for regulators of canonical extensions

      Abstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.

      2:30 – 3:00pmBreak
      3:00 – 4:00pmAmin Gholampour, MarylandTitle: Euler Characteristics of punctual quot schemes on threefolds

      Abstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F, n) and Quot(G,n), where Quot(-,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.

      4:00 – 4:30pmBreak
      4:30 – 5:30pmMaksym Fedorchuck, BCTitle:  Stability of one-parameter families of weighted hypersurfaces

      Abstract:  We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space.  The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions, and, if time permits, examples where this machinery can be used to produce birational models with good properties.  Joint work with Hamid Ahmadinezhad and Igor Krylov.

       

      Tuesday, April 30

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amBrendan Hassett, BrownTitle: Rationality for geometrically rational threefolds

      Abstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure, like smooth complete intersections of two quadrics.  (joint with Tschinkel)

      10:00 – 10:30amBreak
      10:30 – 11:30amDennis Gaitsgory, HarvardTitle: The Fundamental Local Equivalence in quantum geometric Langlands

      Abstract: The Fundamental Local Equivalence is statement that relates the q-twisted  Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its  dual is combinatorial, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra, which in itself is a geometric device that concisely encodes the root data.

      11:30 – 1:00pmLunch
      1:00- 2:00pmAndrei Negut, MITTitle: AGT relations in geometric representation theory

      Abstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces, and the goal is to connect them with the W-algebra of type gl_n.

      2:00 – 2:15pmBreak
      2:15 – 3:15pmDan Abramovich, BrownTitle: Resolution in characteristic 0 using weighted blowing up

      Abstract: Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved.

      Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop.

      We show that there is a functorial way to resolve varieties using \emph{weighted} blowings up, in the stack-theoretic sense. To an embedded variety $X \subset Y$ one functorially assigns an invariant $(a_1,\ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , \ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.

      This is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.

      3:15 – 3:30pmBreak
      3:30 – 4:30pmFedor Bogomolov, NYUTitle: On the base of a Lagrangian fibration for a compact hyperkahler manifold.

      Abstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of  Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.

      4:30 – 4:45pmBreak
      4:45 – 5:45pmDawei Chen, BCTitle: Volumes and intersection theory on moduli spaces of Abelian differentials

      Abstract: Computing volumes of moduli spaces has significance in many fields. For instance, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

       

      Wednesday, May 1

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amPavel Etingof, MITTitle: Short star-products for filtered quantizations

      Abstract: PDF

      This is joint work with Eric Rains and Douglas Stryker.

      10:00 – 10:30amBreak
      10:30 – 11:30amRoman Bezrukavnikov, MITTitle: Stability conditions and representation theory

      Abstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)
      and its relation to modular Lie algebra representations. I will also address a potential generalization of that picture
      to modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.

      11:30 – 11:45amBreak
      11:45 – 12:45pmQile Chen, BCTitle: Counting curves in critical locus via logarithmic compactification

      Abstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles, the non-compactness of the R-maps moduli makes such powerful torus action useless.

      In this talk, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action.

      This is a joint work with Felix Janda and Yongbin Ruan.

      12:45 – 2:30pmLunch
      2:30 – 3:30pmSi Li, TsinghuaTitle: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry

      Abstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.

      3:30 – 4:00pmBreak
      4:00 – 5:00pmLudmil Katzarkov, MoscowTitle: PDE’s non commutative  motives and HMS.

      Abstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir.  Geometry will be discussed.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-29-2017 Random Matrix & Probability Theory Seminar
      12:35 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-24-2017 Random Matrix & Probability Theory Seminar
      12:37 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-30-2017 CMSA Special Seminar
      12:38 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      03-27-2017 Mathematical Physics Seminar
      12:40 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:41 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-5-2017 Special Lecture Series
      12:42 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-7-2017 Special Lecture Series
      12:43 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:43 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-12-2017 Special Lecture Series
      12:44 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:45 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-14-2017 Special Lecture Series
      12:46 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-3-2017 Mathematical Physics Seminar
      12:50 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      12:51 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-12-2017 Social Science Applications Forum
      12:53 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Workshop on Mirror Symmetry and Stability
      12:55 pm
      11/01/2019-03/20/2019
      HMS-2019-1

      This three-day workshop will take place at Harvard University on March 18-20, 2019 in Science Center room 507. The main topic will be stability conditions in homological mirror symmetry. This workshop is funded by the Simons Collaboration in Homological Mirror Symmetry.

      Organizers: Denis Auroux, Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau, Bong Lian, Shing-Tung Yau, Jingyu Zhao

      Speakers:

      Dylan Allegretti (Sheffield)
      Tristan Collins (MIT)
      Naoki Koseki (Tokyo)
      Chunyi Li (Warwick)
      Jason Lo (CSU Northridge)
      Emanuele Macrì (NEU & IHES)
      Genki Ouchi (Riken iTHEMS)
      Pranav Pandit (ICTS)
      Laura Pertusi (Edinburgh)
      Jacopo Stoppa (SISSA)
      Alex Takeda (UC Berkeley)
      Xiaolei Zhao (UC Santa Barbara)

      More details will be added later.

      Visit the event page for more information. 

       

      HMS-2019-1

    • Colloquium
      12:55 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      12:57 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Simons Collaboration Workshop, April 5-7, 2018
      1:00 pm-6:00 pm
      11/01/2019-04/07/2018
      banner-image-1

      The CMSA will be hosting a three-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 5-7, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

      We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

      Confirmed Speakers:

    • Seminars
      Seminars Colloquia & Seminar
      4-11-2017 Social Science Applications Forum
      1:00 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      Combinatorics & Complexity Seminar, Fridays
      1:00 pm-4:00 pm
      11/01/2019

      The seminar on Combinatorics and Complexity will be held every Friday from 1:00-4:00pm in CMSA Building, 20 Garden Street, Room G10.

      The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

      Additional information on CMSA’s Combinatorics and Complexity program can be found here.

       

      DateNameTitle/Abstract
      09-08-17TBA
      09-15-2017TBA
      09-22-17TBA
      09-29-17TBA
      10-06-17 TBA
      10-13-2017TBA
      10-20-2017TBA
      10-27-2017TBA
      11-03-2017TBA
      11-10-2017TBA
      11-17-2017TBA
      11-24-2017TBA
      12-01-2017TBA
      12-08-2017 TBA
    • CMSA EVENT: Second Annual STAR Lab Conference
      1:01 pm-1:02 pm
      11/01/2019

      The second annual STAR Lab conference is running 10/29/-10/30/2015 at the Harvard Business School.  This event is co-sponsored by the Center of Mathematical Sciences and Applications.

      For more information, please consult the event’s website.

    • Colloquium
      1:02 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:07 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-10-2017 Mathematical Physics Seminar
      1:07 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-21-2015 Mathematical Physics Seminar
      1:09 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      1:10 pm-3:00 pm
      11/01/2019
    • Colloquium
      1:10 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      08-31-2015 Mathematical Physics Seminar
      1:10 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:11 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-01-2015 Differential Geometry Seminar
      1:12 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-12-2017 Random Matrix & Probability Theory Seminar
      1:12 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:13 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-01-2015 Evolution Equation Seminar
      1:13 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-14-2015 Mathematical Physics Seminar
      1:14 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-17-2017 Mathematical Physics Seminar
      1:14 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-18-2017 Social Science Applications Forum
      1:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-08-2015 Geometric Analysis Seminar
      1:16 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-06-2015 Geometric Analysis Seminar
      1:17 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:18 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-08-2015 Evolution Equations Seminar
      1:18 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:20 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:21 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      1:21 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-13-2015 Geometric Analysis Seminar
      1:22 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-19-2017 Random Matrix & Probability Theory Seminar
      1:22 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-10-2015 Evolution Equations Seminar
      1:23 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: 2016 Big Data Conference & Workshop
      1:24 pm
      11/01/2019-08/23/2016
      1 Oxford Street, Cambridge MA 02138

      ! LOCATION CHANGE: The conference will be in Science Center Hall C on Tuesday, Aug.23, 2016.

      The Center of Mathematical Sciences and Applications will be hosting a workshop on Big Data from August 12 – 21, 2016 followed by a two-day conference on Big Data from August 22 – 23, 2016.

      Big Data Conference features many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the second conference on Big Data the Center will host as part of our annual events. The 2015 conference was a huge success.

      The conference will be hosted at Harvard Science Center Hall A (Monday, Aug.22) & Hall C (Tuesday, Aug.23): 1 Oxford Street, Cambridge, MA 02138.

      The 2016 Big Data conference is sponsored by the Center of Mathematical Sciences and Applications at Harvard University and the Alfred P. Sloan Foundation.

      Conference Speakers:

      1. Jörn Boehnke, Harvard CMSA
      2. Joan Bruna, UC Berkeley [Video]
      3. Tamara Broderick, MIT [Video]
      4. Justin Chen, MIT [Video]
      5. Yiling Chen, Harvard University [Video]
      6. Amir Farbin, UT Arlington [Video]
      7. Doug Finkbeiner, Harvard University [Video]
      8. Andrew Gelman, Columbia University [Video]
      9. Nina Holden, MIT [Video]
      10. Elchanan Mossel, MIT
      11. Alex Peysakhovich, Facebook
      12. Alexander Rakhlin, University of Pennsylvania [Video]
      13. Neal Wadhwa, MIT [Video]
      14. Jun Yin, University of Wisconsin
      15. Harry Zhou, Yale University [Video]

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

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

      Please click here for registration.

      Conference Schedule:

      August 22 – Day 1
      8:30amBreakfast
      8:55amOpening remarks
      9:00am – 9:50amYiling Chen, “Machine Learning with Strategic Data Sources” [Video]
      9:50am – 10:40amAndrew Gelman, “Taking Bayesian Inference Seriously” [Video]
      10:40am – 11:10amBreak
      11:10am – 12:00pmHarrison Zhou, “A General Framework for Bayes Structured Linear Models” [Video]
      12:00pm – 1:30pmLunch
      1:30pm – 2:20pmDouglas Finkbeiner, “Mapping the Milky Way in 3D with star colors” [Video]
      2:20pm – 3:10pmNina Holden, “Sparse exchangeable graphs and their limits” [Video]
      3:10pm – 3:40pmBreak
      3:40pm – 4:30pmAlex Peysakhovich, “How social science methods inform personalization on Facebook News Feed” [Video]
      4:30pm – 5:20pmAmir Farbin, “Deep Learning in High Energy Physics” [Video]
      August 23 – Day 2
      8:45amBreakfast
      9:00am – 9:50amJoan Bruna Estrach, “Addressing Computational and Statistical Gaps with Deep Networks” [Video]
      9:50am – 10:40amJustin Chen & Neal Wadhwa, “Smaller Than the Eye Can See: Big Engineering from Tiny Motions in Video” [Video]
      10:40am – 11:10amBreak
      11:10am – 12:00pmAlexander Rakhlin, “How to Predict When Estimation is Hard: Algorithms for Learning on Graphs” [Video]
      12:00pm – 1:30pmLunch
      1:30pm – 2:20pmTamara Broderick, “Fast Quantification of Uncertainty and Robustness with Variational Bayes” [Video]
      2:20pm – 3:10pmElchanan Mossel, “Phylogenetic Reconstruction – a Rigorous Model of Deep Learning”
      3:10pm – 3:40pmBreak
      3:40pm – 4:30pmJörn Boehnke, “Amazon’s Price and Sales-rank Data: What can one billion prices on 150 thousand products tell us about the economy?”

      Workshop Participants:

      Richard Freeman’s Group:

      1. Sen Chai, ESSEC
      2. Brock Mendel, Harvard University
      3. Raviv Muriciano-Goroff, Stanford University
      4. Sifan Zhou, CMSA

      Scott Kominer’s Group:

      1. Bradly Stadie, UC Berkeley
      2. Neal Wadhwa, MIT [Video]
      3. Justin Chen

      Christopher Rogan’s Group:

      1. Amir Farbin, UT Arlington [Video]
      2. Paul Jackson, University of Adelaide

      For more information about the workshops, please reach out directly to the individual group leaders.

      This event is sponsored by CMSA Harvard University and the Alfred P. Sloan Foundation.

    • Seminars
      Seminars Colloquia & Seminar
      10-01-2015 Evolution Equations Seminar
      1:25 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-15-2015 Geometric Analysis Seminar
      1:26 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-16-2015 Random Matrix & Probability Theory Seminar
      1:27 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-23-2015 Random Matrix & Probability Theory Seminar
      1:29 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      5-3-2017 Random Matrix & Probability Theory Seminar
      1:29 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      1:30 pm-3:00 pm
      11/01/2019
    • Special Seminar
      1:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      5-2-2017 Social Sciences Application Forum
      1:30 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11/28/2018 Hodge Lecture
      1:30 pm
      11/01/2019
    • Seminars
      1:30 pm-3:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      1/23/2019 Hodge Seminar
      1:30 pm-3:00 pm
      11/01/2019
    • Special Seminar
      Special Seminar
      4/30/2018 Special Seminar
      1:30 pm-2:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      12/5/2018 Hodge Seminar
      1:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      11/14/2018 Hodge Seminar
      1:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      11/21/2018 Hodge Seminar
      1:30 pm
      11/01/2019
    • Colloquium
      1:31 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-28-2015 Mathematical Physics Seminar
      1:31 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-24-2017 Mathematical Physics Seminar
      1:31 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      1:32 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:33 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Concluding Conference of the Special Program on Nonlinear Equations, April 8 – 10, 2016
      1:34 pm
      11/01/2019-04/10/2016

      The Center of Mathematical Sciences and Applications will be hosting a concluding conference on April 8-10, 2016 to accompany the year-long program on nonlinear equations. The conference will have 15 speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

      Speakers:

      1. Lydia Bieri (University of Michigan)
      2. Luis Caffarelli (University of Texas at Austin)
      3. Mihalis Dafermos (Princeton University)
      4. Camillo De Lellis (Universität Zürich)
      5. Pengfei Guan (McGill University)
      6. Slawomir Kolodziej (Jagiellonian University)
      7. Melissa Liu (Columbia University)
      8. Duong H. Phong (Columbia University)
      9. Richard Schoen (UC Irvine)
      10. Cliff Taubes (Harvard University)
      11. Blake Temple (UC Davis)
      12. Valentino Tosatti (Northwestern University)
      13. Tai-Peng Tsai (University of British Columbia)
      14. Mu-Tao Wang (Columbia University)
      15. Xu-jia Wang (Australian National University)

      Please click NLE Conference Schedule with Abstracts for a downloadable schedule with talk abstracts.

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

      Schedule:

      April 8 – Day 1
      8:30amBreakfast
      8:45amOpening remarks
      9:00am – 10:00amCamillo De Lellis, “A Nash Kuiper theorem for $C^{1,1:5}$ isometric immersions of disks
      10:00am – 10:15amBreak
      10:15am – 11:15amXu-Jia Wang, “Monge’s mass transport problem
      11:15am – 11:30amBreak
      11:30am – 12:30pmPeng-Fei Guan, “The Weyl isometric embedding problem in general $3$ d Riemannian manifolds
      12:30pm – 2:00pmLunch
      2:00pm – 3:00pmBlake Temple, “An instability in the Standard Model of Cosmology
      3:00pm – 3:15pmBreak
      3:15pm – 4:15pmLydia Bieri, “The Einstein Equations and Gravitational Radiation
      4:15pm – 4:30pmBreak
      4:30pm – 5:30pmValentino Tosatti, “Adiabatic limits of Ricci flat Kahler metrics
      April 9 – Day 2
      8:45amBreakfast
      9:00am – 10:00amD.H. Phong, “On Strominger systems and Fu-Yau equations”
      10:00am – 10:15amBreak
      10:15am – 11:15amSlawomir Kolodziej, “Stability of weak solutions of the complex Monge-Ampère equation on compact Hermitian manifolds”
      11:15am – 11:30amBreak
      11:30am – 12:30pmLuis Caffarelli, “Non local minimal surfaces and their interactions”
      12:30pm – 2:00pmLunch
      2:00pm – 3:00pmMihalis Dafermos, “The interior of dynamical vacuum black holes and the strong cosmic censorship conjecture in general relativity”
      3:00pm – 3:15pmBreak
      3:15pm – 4:15pmMu-Tao Wang, “The stability of Lagrangian curvature flows”
      4:15pm – 4:30pmBreak
      4:30pm – 5:30pmMelissa Liu, “Counting curves in a quintic threefold”
      April 10 – Day 3
      8:45amBreakfast
      9:00am – 10:00amRick Schoen, “Metrics of fixed area on high genus surfaces with largest first eigenvalue”
      10:00am – 10:15amBreak
      10:15am – 11:15amCliff Taubes, “The zero loci of Z/2 harmonic spinors in dimensions 2, 3 and 4”
      11:15am – 11:30amBreak
      11:30am – 12:30pmTai-Peng Tsai, “Forward Self-Similar and Discretely Self-Similar Solutions of the 3D incompressible Navier-Stokes Equations”

      * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      10-22-2015 Evolution Equations Seminar
      1:37 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/11/2017 Mathematical Physics Seminar
      1:38 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9-18-17 Mathematical Physics Seminar
      1:39 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-17-2015 Evolution Equations Seminar
      1:39 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      9-27-17 RM&PT Seminar
      1:41 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9-27-17 Mathematical Physics Seminar
      1:42 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-23-17 Mathematical Physics Seminar
      1:43 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9/11/2019 Random Matrix
      1:45 pm-2:45 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-25-17 RMPT Seminars
      1:45 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:47 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-10-2017 RM & PT Seminar
      1:48 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:51 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-22-2015 Geometric Analysis Seminar
      1:52 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:52 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-30-2015 Random Matrix & Probability Theory Seminar
      1:53 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-13-2017 Mathematical Physics Seminar
      1:53 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:54 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-21-2015 Mathematical Physics Seminar
      1:54 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-15-17 RM & PT Seminar
      1:55 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-6-2017 RM & PT Seminar
      1:56 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      1:58 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      2/22/2019 Social Science Applications Forum
      2:00 pm
      11/01/2019
    • Math Science Lectures in Honor of Raoul Bott
      Math Science Lectures in Honor of Raoul Bott Event
      Math Science Lectures in Honor of Raoul Bott: Freddy Cachazo
      2:00 pm-5:00 pm
      11/01/2019-04/03/2018
      1 Oxford Street, Cambridge MA 02138
      Math Science Lectures in Honor of Raoul Bott

      DSC_0170-e1525711590120

      On April 2-3, the CMSA will be hosting two lectures by Freddy Cachazo (Perimeter Institute) on “Geometry and Combinatorics in Particle Interactions.”  This will be the first of the new annual Bott Math Science Lecture Series hosted by the CMSA.

      The lectures will take place from 4:30-5:30pm in Science Center, Hall D.

       

      Cachazo-e1519325938458

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-20-2017 RM & PT Seminar
      2:00 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02/26/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      Homological Mirror Symmetry Seminar
      2:00 pm-4:00 pm
      11/01/2019-09/15/2017

      The seminar series, Homological Mirror Symmetry, will be held on selected Thursdays from 2PM – 4pm in CMSA Building, 20 Garden Street, Room G10.

      The list of speakers is below and will be updated as details are confirmed.

      DateNameTitle
      09-15-16
      09-22-16Netanel Blaier, Brandeis  “Intro to HMS.”

      Abstract: This is the first talk of the seminar series. We survey the statement of Homological Mirror Symmetry (introduced by Kontsevich in 1994) and some known results, as well as briefly discussing its importance, and the connection to other formulations of Mirror Symmetry and the SYZ conjecture. Following that, we will begin to review the definition of the A-side (namely, the Fukaya category) in some depth. No background is assumed! Also, in the last half hour, we will divide papers and topics among participants.

      Lecture Slides

      09-29-16Netanel Blaier, Brandeisblaier4“Intro to HMS 2.”

      Abstract: In the second talk, we review (some) of the nitty-gritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of J-holomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya’s differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$-structures. We will try to demonstrate all concepts in the Morse theory ‘toy model’.

      Lecture Slides

      10-06-16

      Hansol Hong, CMSAhong

      Title: Homological mirror symmetry for elliptic curves

      Abstract:
      We survey the proof of homological mirror symmetry by Polishchuk and Zaslow. Some of more recent methods to prove HMS for elliptic curves will be discussed also,
      which use homological algebra techniques and formal deformation theory of Lagrangians etc.

      Notes

      Notes (Baris)

      10-13-16

      Yu-Wei Fan, Harvard

      s_yuwei_fan

      Title: Semi-flat mirror symmetry and Fourier-Mukai transform

      Abstract: We will review the semi-flat mirror symmetry setting in Strominger-Yau-Zaslow, and discuss the correspondence between special Lagrangian sections on the A-side and deformed Hermitian-Yang-Mills connections on the B-side using real Fourier-Mukai transform, following Leung-Yau-Zaslow.

       10-20-16

      Tim Large, MIT

      Title: “Symplectic cohomology and wrapped Fukaya categories”

      Abstract: While mirror symmetry was originally conjectured for compact manifolds, the phenomenon applies to non-compact manifolds as well. In the setting of Liouville domains, a class of open symplectic manifolds including affine varieties, cotangent bundles and Stein manifolds, there is an A-infinity category called the wrapped Fukaya category, which is easier to define and often more amenable to computation than the original Fukaya category. In this talk I will construct it, along with symplectic cohomology (its closed-string counterpart), and compute some examples. We will then discuss how compactifying a symplectic manifold corresponds, on the B-side of mirror symmetry, to turning on a Landau-Ginzburg potential.

      Notes

       10-27-16

      Philip Engel, Columbia

      picture

      Title: Mirror symmetry in the complement of an anticanonical divisor”

      According to the SYZ conjecture, the mirror of a Calabi-Yau variety can be constructed by dualizing the fibers of a special Lagrangian fibration. Following Auroux, we consider this rubric for an open Calabi-Yau variety X-D given as the complement of a normal crossings anticanonical divisor D in X. In this talk, we first define the moduli space of special Lagrangian submanfiolds L with a flat U(1) connection in X-D, and note that it locally has the structure of a Calabi-Yau variety. The Fukaya category of such Lagrangians is obstructed, and the degree 0 part of the obstruction on L defines a holomorphic function on the mirror. This “superpotential” depends on counts of holomorphic discs of Maslov index 2 bounded by L. We then restrict to the surface case, where there are codimension 1 “walls” consisting of Lagrangians which bound a disc of Maslov index 0. We examine how the superpotential changes when crossing a wall and discuss how one ought to “quantum correct” the complex structure on the moduli space to undo the discontinuity introduced by these discs.

      Notes

      11-03-16

      Yusuf Baris Kartal, MIT

      HMS for Del Pezzo surfaces

      I will present Auroux-Katzarkov-Orlov’s proof of one side of the homological mirror symmetry for Del Pezzo surfaces. Namely I will prove their derived categories are equivalent to the categories of vanishing cycles for certain LG-models together with B-fields. I plan to show how the general B-field corresponds to non-commutative Del Pezzo surfaces and time allowing may mention HMS for simple degenerations of Del Pezzo surfaces. The tools include exceptional collections( and mutations for degenerate case), explicit description of NC deformations, etc.

      11-10-16No seminar this week
       12-08-16

      Lino Amorim, Boston University

      Title: The Fukaya category of a compact toric manifold

      Abstract: In this talk I will discuss the Fukaya category of a toric manifold following the work of Fukaya-Oh-Ohta-Ono. I will start with an overview of the general structure of the Fukaya category of a compact symplectic manifold. Then I will consider toric manifolds in particular the Fano case and construct its mirror.

      Video

    • CMSA EVENT: Topological Insulators and Mathematical Science – Conference and Program
      2:00 pm-7:00 pm
      11/01/2019-09/17/2014

      The CMSA will be hosting a conference on the subject of topological insulators and mathematical science on September 15-17.  Seminars will take place each day from 2:00-7:00pm in Science Center Hall D, 1 Oxford Street, Cambridge, MA.

    • Seminars
      2:00 pm-4:00 pm
      11/01/2019

      References: 

      • D. Auroux, A beginner’s introduction to Fukaya categories. arXiv:1301.7056
      • I. Smith, A symplectic prolegomenon. arXiv:1401.0269
      • D. Auroux, “Topics in geometry: mirror symmetry”, Fall 2009 (MIT Math 18.969)
      • Nick Sheridan’s IAS and Jussieu lectures. 
      • Sheel Gantara “Topics in symplectic topology”, Spring 2016 (Stanford Math 257B)
    • Seminars
      Seminars Colloquia & Seminar
      1/8/2019 Topology Seminar
      2:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-29-17 RM & PT Seminar
      2:03 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Seminars
      Seminars Colloquia & Seminar
      09-24-2015 Evolution Equations Seminar
      2:03 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-28-2015 Special Random Matrix & Probability Theory Seminar
      2:05 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-18-2015 Random Matrix & Probability Theory Seminar
      2:07 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      9/25/2019 RM&PT Seminar
      2:08 pm
      11/01/2019
    • Colloquium
      2:08 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:10 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-29-2017 Mathematical Physics Seminar
      2:11 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Colloquium
      2:11 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      09-29-2015 Geometric Analysis Seminar
      2:14 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:14 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      10-28-2015 CMSA Special Seminar
      2:15 pm
      11/01/2019

      No additional detail for this event.

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      2:15 pm
      11/01/2019

      No additional detail for this event.

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      10-05-2015 Mathematical Physics Seminar
      2:16 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
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      12-6-2017 RM & PT Seminar
      2:16 pm
      11/01/2019

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      10-15-2015 Evolution Equations Seminar
      2:17 pm
      11/01/2019

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    • Mathematical Physics Seminar
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      12-6-2017 Mathematical Physics Seminar
      2:17 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-07-2015 Random Matrix & Probability Theory Seminar
      2:19 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:20 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-29-2015 Evolution Equations Seminar
      2:20 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-14-2015 Random Matrix & Probability Theory Seminar
      2:21 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      2:21 pm
      11/01/2019-03/06/2018

      During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th, from 1:00 to 3:00pm in room G10, CMSA Building.

      You can watch Prof. Sheshmani describe the series here.

      The Syllabus is as follows:

      Date………..TopicVideo/Audio
      1-25-2018Gromov-Witten invariants 

      Definition, examples via algebraic geometry I

      Video / Audio / Combined 


      *due to technical difficulties the audio and video are split for this lecture.

       2-01-2018Gromov-Witten invariants 

      Virtual Fundamental Class I (definition)

      Video Audio / Combined 


      *due to technical difficulties the audio and video are split for this lecture

      2-13-2018Gromov-Witten invariants 

      Virtual Fundamental Class II (computation in some cases)

       2-15-2018Computing GW invariants 

      Three level GW classes

      Genus zero invariants of the projective plane

       2-20-2018Quantum Cohomology 

      Small Quantum Cohomology (Definition and Properties) I

      2-22-2018Quantum Cohomology 

      Small Quantum Cohomology (Definition and Properties) II

      2-27-2018Quantum Cohomology 

      Big Quantum Cohomology I

       3-1-2018Quantum Cohomology 

      Big Quantum Cohomology II

      GW potential

      WDVV equation

      3-6-2018GW invariants via Quantum Cohomology 

      The Quintic threefold case

      The P^2 case

      GW invariants via Quantum Cohomology 

      Dubrovin (quantum) connection

      Nakajima varieties 

      -Algebraic and symplectic reduction

      Nakajima varieties 

      Quasi maps to Nakajima varieties

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) I

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) II

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) III

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) I

       
      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) II

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) III

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) IV

       
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-21-2015 Random Matrix & Probability Theory Seminar
      2:22 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:23 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:24 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:29 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      10/3/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-28-2015 Random Matrix & Probability Theory Seminar
      2:30 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      11/31/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      11/01/2019
    • Seminars
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      10/18/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      11/01/2019
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      4/3/2019 Colloquium
      2:30 pm
      11/01/2019
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      3/11/2019 Social Science Applications Forum
      2:30 pm-4:00 pm
      11/01/2019
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      9/19/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      11/01/2019
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      9/26/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      11/01/2019
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      3/7/2019 Social Science Applications Forum
      2:30 pm-3:00 pm
      11/01/2019
    • Colloquium
      Colloquium Colloquia & Seminar
      4/10/2019 Colloquium
      2:30 pm
      11/01/2019
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      9/12/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      11/01/2019
    • Colloquium
      Colloquium Colloquia & Seminar
      2/27/2019 Colloquium
      2:30 pm-4:00 pm
      11/01/2019
    • General Relativity Seminar
      2:30 pm-3:30 pm
      11/01/2019-04/26/2020
    • Colloquium
      2:30 pm-3:00 pm
      11/01/2019
    • Colloquium
      2:32 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-19-2015 Mathematical Physics Seminar
      2:33 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      10-20-2015 Geometric Analysis Seminar
      2:35 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      10-26-2015 Mathematical Physics Seminar
      2:36 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      01-26-2018 Mirror Symmetry Seminar
      2:37 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      11-02-2015 Mathematical Physics Seminar
      2:37 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      11-03-2015 Geometric Analysis Seminar
      2:39 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-04-2015 Random Matrix & Probability Theory Seminar
      2:40 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      1-29-2018 Mathematical Physics Seminar
      2:42 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      Special Seminar
      1-30-2018 Special Seminar
      2:43 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      2:44 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      2-2-2018 Mirror Symmetry Seminar
      2:44 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      2:45 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:47 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      2:48 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-19-2015 Evolution Equations Seminar
      2:50 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-09-2015 CMSA Special Lecture
      2:51 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:54 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-09-2015 Mathematical Physics Seminar
      2:54 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      2:55 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:56 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-19-2015 Random Matrix and Probability Theory Seminar
      2:57 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      2:59 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-16-2015 Mathematical Physics Seminar
      2:59 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      2-27-2018 HMS Lecture
      3:00 pm-4:00 pm
      11/01/2019-03/01/2018
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12/5/2018 Random Matrix and Probability Theory Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4/17/2019 Fluid Dynamics Seminar
      3:00 pm
      11/01/2019
    • CMSA EVENT: 2018 Ding Shum Lecture
      3:00 pm-4:00 pm
      11/01/2019
      ding-shum-2018

       

      Screen-Shot-2018-06-14-at-1.41.25-PM

      On October 24, 2018, the CMSA will be hosting our second annual Ding Shum lecture. This event was made possible by the generous funding of Ding Lei and Harry Shum. Last year featured Leslie Valiant, who spoke on “learning as a Theory of Everything.”

      This year will feature Eric Maskin, who will speak on “How to Improve Presidential Elections: the Mathematics of Voting.” This lecture will take place from 5:00-6:00pm in Science Center, Hall D. 

      Pictures of the event can be found here.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/24/2018 RM & PT Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/7/2018 Random Matrix and Probability Theory Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/14/2018 RM & PT Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/28/2018 Random Matrix and Probability Theory Seminar
      3:00 pm
      11/01/2019
    • Seminars
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      10/23/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      1/31/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Special Seminar
      3:00 pm-4:30 pm
      11/01/2019-05/09/2019

      In the Spring 2019 Semester, the CMSA will be hosting a special lecture series on Derived algebraic/differential geometry run by Artan Sheshmani, with lectures given by Prof. Sheshmani and Dr. Dennis Borisov. The seminar will be held on Tuesdays and Thursdays from 3:00-4:30pm in CMSA, room G10.

      Click here for reference material

      Click here for a syllabus

      Schedule:

      Section 1: Basic setting of derived geometry

      The goal: To collect the minimum set of tools needed to do algebraic geometry in the derived context.

      2/05/2019Lecture 1: Model and с-categoriesVideo
      2/07/2019Lecture 2: Grothendieck topologies and homotopy descentVideo
      2/12/2019Lecture 3: Derived Artin stacksVideo 
      2/14/2019Lecture 4: Cotangent complexes

      Section 2: Loop spaces and differential forms

      The goal: This is the algebraic heart of the course – here we learn the homological techniques that are needed for shifted symplectic forms.

      2/19/2019Lecture 5: De Rham complexes and S1-equivariant schemes (loop spaces)Video
      2/21/2019Lecture 6: Chern characterVideo
      2/26/2019

      Room G02

      Lecture 7: Local structure of closed differential forms in the derived sense Part IVideo
      2/28/2019Lecture 8: Local structure of closed differential forms in the derived sense Part IIVideo
      3/05/2019Lecture 9: Cyclic homologyVideo

      Section 3: Shifted symplectic structures
      Goal: To see applications of the algebraic techniques from above in the geometric context of the actual moduli spaces.

      3/07/2019Lecture 10: Definition and existence resultsVideo
      3/12/2019Lecture 11: Lagrangians and Lagrangian fibrationsVideo
      3/14/2019

      Room G02

      Lecture 12: Lagrangians and Lagrangian fibrationsVideo
      3/26/2019Lecture 13: Intersections of LagrangiansVideo
      3/28/2019

      Room G02

      Lecture 14: Examples and applications 2 (Part I)Video
      4/02/2019Lecture 15: Examples and applications 2 (Part II)Video

      Section 4: Uhlenbeck–Yau construction and correspondence

      4/04/2019Lecture 16: Examples and applications 2 (Part III)Video
      4/09/2019

      Room G02

      Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)Video
    • Seminars
      Seminars Colloquia & Seminar
      2/7/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/13/2019 Special Algebraic Geometry Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/14/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2/20/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/6/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/8/2019 Special Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/20/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      Algebraic Geometry Seminar, Thursdays
      3:00 pm-4:00 pm
      11/01/2019

      This seminar will not be held in the Spring 2018 Semester.

      The Algebraic Geometry Seminar will be every Thursday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

      The schedule will be updated as details are confirmed.

       

       

      DateNameTitle/Abstract
      09-14-17 Yu-Wei Fan (Harvard Math)

      Entropy of an autoequivalence on Calami-Yau manifolds

      Abstract:  We will recall the notion of entropy of an autoequivalence on triangulated categories, and provide counterexamples of a conjecture by Kikuta-Takahashi.

      11-1-17

      *5:00pm, G10*

       Shamil Shakirov, Harvard Math

      Undulation invariants of plane curves

      Abstract: “One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem, described by Cayley and Salmon in 1852, is to determine whether or not a given plane curve of degree r > 3 has undulation points — the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r – 3)(3 r – 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries, and we conjecture a generalization for r = 5

      11-2-17

       

      Alexander Moll, IHES

      Hilbert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves

      ABSTRACT: By Grojnowski and Nakajima, Fock spaces are cohomology rings of Hilbert scheme of points in the plane.  On the other hand, by Pressley-Segal, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the Kähler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J.  First, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this Kähler structure.  Second, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = – e_1 e_2 that is invariant under e_2 <-> e_1.  As a corollary of Lehn’s theorem, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element.  Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin.  As time permits, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov’s BPS/CFT Correspondence.

      11-9-17  TBD  TBD
      11-16-17 TBD TBD
      11-23-17  TBD  TBD
      11-30-17  TBD  TBD
      12-7-17  TBD  TBD
      12-15-17  TBD  TBD
    • Seminars
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      4/24/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Fluid Dynamics Seminar
      Fluid Dynamics Seminar
      10/9/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/03/2018 RMPT Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      5/22/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      5/15/2019 Fluid Dynamics
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      5/1/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Special Seminar
      Special Seminar
      3-28-2018 Special Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      Dmytro Shklyrov HMS Focused Lecture Series
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/4/2019 Special Seminar
      3:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      11-17-2015 Geometric Analysis Seminar
      3:00 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9/18/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      11-23-2015 Mathematical Physics Seminar
      3:01 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar (2016-2017)
      3:01 pm
      11/01/2019-12/14/2017
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      DSC_0025-768x512

      The random matrix and probability theory will be every Wednesday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

    • CMSA EVENT: Working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017
      3:02 pm-3:03 pm
      11/01/2019-01/13/2017

      The Center of Mathematical Sciences and Applications will be hosting a working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Participants:

      Gerard Ben Arous, Courant Institute of Mathematical Sciences

      Alex Bloemendal, Broad Institute

      Arup Chakraburty, MIT

      Zhou Fan, Stanford University

      Alpha Lee, Harvard University

      Matthew R. McKay, Hong Kong University of Science and Technology (HKUST)

      David R. Nelson, Harvard University

      Nick Patterson, Broad Institute

      Marc Potters, Capital Fund management

      Yasser Roudi, IAS

      Tom Trogdon, UC Irvine

      Organizers:

      Michael Brenner, Lucy Colwell, Govind Menon, Horng-Tzer Yau

      Please click Program for a downloadable schedule with talk abstracts.

      Please note that breakfast & lunch will be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants should you need recommendations for dinner.

      Schedule:

      January 9 – Day 1
      9:30am – 10:00amBreakfast & Opening remarks
      10:00am – 11:00amMarc Potters, “Eigenvector overlaps and the estimation of large noisy matrices”
      11:00am – 12:00pmYasser Roudi
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 10 – Day 2
      8:30am – 9:00amBreakfast
      9:00am – 10:00amArup Chakraburty, “The mathematical analyses and biophysical reasons underlying why the prevalence of HIV strains and their relative fitness are simply correlated, and pose the challenge of building a general theory that encompasses other viruses where this is not true.”
      10:00am – 11:00amTom Trogdon, “On the average behavior of numerical algorithms”
      11:00am – 12:00pmDavid R. Nelson, “Non-Hermitian Localization in Neural Networks”
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 11 – Day 3
      8:30am – 9:00amBreakfast
      9:00am – 10:00amNick Patterson
      10:00am – 11:00amLucy Colwell
      11:00am – 12:00pmAlpha Lee
      12:00pm – 2:00pmLunch
      2:00pm-4:00pmAfternoon Discussion
      4:00pmGerard Ben Arous (Public Talk), “Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms
      January 12 – Day 4
      8:30am – 9:00amBreakfast
      9:00am – 10:00amGovind Menon
      10:00am – 11:00amAlex Bloemendal
      11:00am – 12:00pmZhou Fan, “Free probability, random matrices, and statistics”
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 13 – Day 5
      8:30am – 9:00amBreakfast
      9:00am – 12:00pmFree for Working
      12:00pm – 2:00pmLunch
      2:00pmFree for Working

      * This event is sponsored by CMSA Harvard University.

    • Colloquium
      3:03 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-24-2015 Geometric Analysis Seminar
      3:03 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-04-2016 Evolution Equations Seminar
      3:04 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      Hodge and Noether-Lefschetz Loci Seminar
      3:06 pm
      11/01/2019

      In the Fall 2018 Semester the CMSA will be hosting a seminar on Hodge and Noether-Lefschetz loci, with lectures given by Hossein Movasati (IMPA). The seminar will occur weekly on Wednesday at 1:30 in room G10 of the CMSA.

      The schedule below will be updated as talks are confirmed.

      DateTitle/Abstract
      11/7/2018

      Video

      Title: Hodge and Noether-Lefschetz loci

      Abstract: Hodge cycles are topological cycles which are conjecturally (the millennium Hodge conjecture) supported in algebraic cycles of a given smooth projective complex manifold. Their study in families leads to the notion of Hodge locus, which is also known as Noether-Lefschetz locus in the case of surfaces. The main aim of this mini course is to introduce a computational approach to the study of Hodge loci for hypersurfaces and near the Fermat hypersurface. This will ultimately lead to the verification of the variational Hodge conjecture for explicit examples of algebraic cycles inside hypersurfaces and also the verification of integral Hodge conjecture for examples of Fermat hypersurfaces. Both applications highly depend on computer calculations of rank of huge matrices. We also aim to review some classical results on this topic, such as Cattani-Deligne-Kaplan theorem on the algebraicity of the components of the hodge loci, Deligne’s absolute Hodge cycle theorem for abelian varieties etc.

      In the theoretical side another aim is to use the available tools in algebraic geometry and construct the moduli space of projective varieties enhanced with elements in their algebraic de Rham cohomology ring. These kind of moduli spaces have been useful in mathematical physics in order to describe the generating function of higher genus Gromov-Witten invariants, and it turns out that the Hodge loci in such moduli spaces are well-behaved, for instance, they are algebraic leaves of certain holomorphic foliations. Such foliations are constructed from the underlying Gauss-Manin connection. This lectures series involves many reading activities on related topics, and contributions by participants are most welcome.

      11/14/2018

      Video

      Title:  Integral Hodge conjecture for Fermat varieties

      Abstract: We describe an algorithm which verifies whether  linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this  confirms the integral Hodge conjecture for quartic and quintic Fermat fourfolds. Our algorithm is based on computation of the list of elementary divisors of both the lattice of linear algebraic cycles, and the lattice of Hodge cycles written in terms of  vanishing cycles, and observing that these two lists are the same. This is a joint work with E. Aljovin and R. Villaflor.

      11/21/2018

      Video

      Title:  Periods of algebraic cycles

      Abstract: The tangent space of the Hodge locus at a point can be described by the so called infinitesimal variation of Hodge structures and the cohomology class of Hodge cycles. For hypersurfaces of dimension $n$ and degree $d$ it turns out that one can describe it without any knowledge of cohomology theories and in a fashion which E. Picard in 1900’s wanted to study integrals/periods. The data of cohomology class is replaced with periods of Hodge cycles, and explicit computations of these periods, will give us a computer implementable description of the tangent space.  As an application of this we show that for examples of $n$ and $d$, the locus of hypersurfaces containing two linear cycles whose intersection is of low dimension, is a reduced component of the Hodge locus in the underlying parameter space.

      11/28/2018

      Video

      Title: Periods of Complete Intersection Algebraic Cycles

      Speaker: Roberto Villaflor

      Abstract: In order to compute periods of algebraic cycles inside even dimensional smooth degree d hypersurfaces of the projective space, we restrict ourselves to cycles supported in a complete intersection subvariety. When the description of the complete intersection is explicit, we can compute its periods, and furthermore its cohomological class. As an application, we can use this data to describe the Zariski tangent space of the corresponding Hodge locus, as the degree d part of some Artinian Gorenstein ideal of the homogeneous coordinate ring of the projective space. Using this description, we can show that for d>5, the locus of hypersurfaces containing two linear cycles, is a reduced component of the Hodge locus in the underlying parameter space.

      12/05/2018

      Room G02

      Title: Some explicit Hodge cycles

      Abstract: Explicit examples of Hodge cycles are due to D. Mumford and A. Weil in the case of CM abelian varieties. In this talk, I will describe few other examples for the Fermat variety. Effective verification of the Hodge conjecture for these cycles is not known.

      12/12/2018

      Video

      Title: A conjectural Hodge locus for cubic tenfold

      Abstract: In this talk we will consider the difference  of two linear algebraic cycles of dimension 5 inside a smooth cubic tenfold and such that the dimension of their intersection is 3. We will show some computer assisted evidences to the fact that the corresponding Hodge locus is bigger than the expected locus of algebraic deformations of the cubic tenfold together with its linear cycles. A similar discussion will be also presented for cubic six and eightfold,  for which we will prove that the corresponding second and third order infinitesimal Hodge loci are smooth. The main ingredient is a computer implementation of power series of periods of hypersurfaces.

      1/16/2019Title: Algebraic BCOV anomaly equation

      Abstract: We introduce the moduli space T of  non-rigid compact Calabi-Yau threefolds enhanced with differential forms and a Lie algebra of vector fields in T. This will be used in order to give a purely algebraic interpretation of topological string partition functions and the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation (joint work with M. Alim, E. Scheidegger, S.-T. Yau).  We will also define similar moduli spaces for even dimensional Calabi-Yau varieties, where we have the notion of Hodge locus.

      1/23/2019

      Video

      Title: A new model for modular curves

      Abstract: One of the non-trivial examples of a Hodge locus is the modular curve X_0(N), which is due to isogeny of elliptic curves (a Hodge/algebraic cycle in the product of two elliptic curves). After introducing the notion of enhanced moduli of elliptic curves, I will describe a new model for X_0(N) in the weighted projective space of dimension 4 and with weights (2,3,2,3,1). I will also introduce some elements in the defining ideal of such a model.

      The talk is based on the article arXiv:1808.01689.

      1/30/2019

      Video

      Title: Constant Yukawa couplings

      Abstract: In this talk I will first introduce algebraic Yukawa couplings for any moduli of enhanced Calabi-Yau n-folds. Then I will list many examples in support of the following conjecture. A moduli of Calabi-Yau n-folds is a quotient of a Hermitian symmetric domain (constructed from periods) by an arithmetic group if and only if the corresponding Yukawa couplings are constants.

      2/6/2019

      Video

      Title: Integrality properties of CY modular forms

      Abstract: The integrality of the coefficients of the mirror map is a central problem in the arithmetic of Calabi-Yau varieties and it has been investigated  by Lian-Yau (1996, 1998), Hosono-Lian-Yau (1996), Zudilin (2002), Kontsevich-Schwarz-Vologodsky (2006) Krattenthaler-Rivoal (2010). The central tool in most of these works has been the so called Dwork method.  In this talk we use this method and classify all hypergeometric differential equations with a maximal unipotent monodromy whose mirror map has integral coefficients.

      We also  give a computable condition on the parameters of a hypergeometric function which conjecturally computes all the primes which appear in the denominators of the coefficients of the mirror map. This is a joint work with Kh. Shokri.

      2/13/2019Title: Foliations and Hodge loci

      Abstract: In this talk I will introduce a holomorphic foliation in a larger parameter space attached to families of enhanced projective varieties. Irreducible components of the Hodge locus with constant periods are algebraic leaves of such a foliation. Under the hypothesis that these are all the algebraic leaves,  we get the fact that such algebraic leaves are defined over the algebraic closure of the base field and that Hodge classes are weak absolute in the sense of C. Voisin.

       

      References:

    • Seminars
      Seminars Colloquia & Seminar
      02-02-2016 Geometric Analysis Seminar
      3:06 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      3:06 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Data Analysis Workshop, April 4 – 8, 2016
      3:09 pm-3:10 pm
      11/01/2019-04/08/2016

      The Center of Mathematical Sciences and Applications will be hosting a 5-day workshop on Data Analysis and related areas on April 4 – 8, 2016.

      Workshop Locations:

      April 4 – 7 (Monday ~ Thursday)

      Room G10,
      20 Garden Street, Cambridge, MA 02138 

      April 8 (Friday)

      EPS Faculty Lounge, Room 409, 4th floor, Hoffman Lab
      20 Oxford Street, Cambridge, MA 02138

       Participants:

      • Peter Hubyers (Harvard University)
      • Eli Tziperman (Harvard University)
      • Andrew Rhines (University of Washington)
      • Karen McKinnon (UCAR)
      • Douglas MacMartin (Caltech)
      • Thomas Laepple (Alfred Wegener Institute)
      • Yossi Ashkenazy (Ben-Gurion University)
      • Marlene Kretschamer (Potsdam Institute for Climate Impact Research)
      • Natesh Pillai (Harvard University)
      • Judah Cohen (Atmospheric and Environmental Research)
      • Cristian Proistosescu (Harvard University)

      Please click Workshop Agenda for a downloadable agenda.

      * This event is sponsored by CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      02-11-2016 Evolution Equations Seminar
      3:09 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      3:09 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2-16-2018 RM & PT Seminar
      3:09 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Colloquium
      3:11 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-03-2016 Random Matrix & Probability Theory Seminar
      3:11 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      3:13 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 RMPT Seminar
      3:15 pm-4:15 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/9/2019 RM & PT Seminar
      3:15 pm-4:15 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/30/2019 Random Matrix and Probability Theory Seminar
      3:15 pm-4:15 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/16/2019 RM & PT Seminar
      3:15 pm
      11/01/2019
    • Colloquium
      3:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-16-2016 Geometric Analysis Seminar
      3:16 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-15-2016 Mathematical Physics Seminar
      3:17 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-18-2016 Evolution Equations Seminar
      3:19 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-22-2016 Mathematical Physics Seminar
      3:20 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-23-2016 Geometric Analysis Seminar
      3:22 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-24-2016 Random Matrix & Probability Theory
      3:23 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Mini-workshop on SYZ and Homological Mirror Symmetry
      3:23 pm
      11/01/2019-12/02/2016

      The Center of Mathematical Sciences and Applications will be hosting a 4-day workshop on SYZ and Homological Mirror Symmetry and related areas on November 28 – December 2, 2016 at Harvard CMSA Building: Room G10, 20 Garden Street, Cambridge, MA 02138.

      Organizers:

      Bong Lian (Brandeis University), Siu-Cheong Lau (Boston University), Shing-Tung Yau (Harvard University)

      Speakers:

      1. Conan Leung, Chinese University of Hong Kong
      2. Junwu Tu, University of Missouri
      3. Jingyu Zhao, Columbia University
      4. David Treumann, Boston College
      5. Hiro Lee Tanaka, Harvard University
      6. Fabian Haiden, Harvard University
      7. Hansol Hong, Harvard CMSA/Brandeis University
      8. Netanel Blaier, Harvard CMSA/Brandeis University
      9. Garret Alston, The University of Oklahoma

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

      Conference Schedule:

      Monday, November 28 – Day 1
      10:30am –11:30amHiro Lee Tanaka“Floer theory through spectra”
      Lunch
      1:00pm – 2:30pmFabian Haiden“Categorical Kahler Geometry”
       2:30pm-2:45pm Break
      2:45pm – 4:15pmFabian Haiden“Categorical Kahler Geometry”
      4:30pm – 5:15pmGarret Alston“Potential Functions of Non-exact fillings”
      Tuesday, November 29 – Day 2
      10:30am –11:30amConan Leung, “Remarks on SYZ”
      Lunch
      1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
       2:30pm-2:45pm Break
      2:45pm – 4:15pmHiro Lee Tanaka“Floer theory through spectra”
      4:30pm – 5:15pmHansol Hong, “Mirror Symmetry for punctured Riemann surfaces and gluing construction”
      Wednesday, November 30 – Day 3
      10:30am –11:30amJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
      Lunch
      1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
       2:30-2:45pm Break
      2:45pm – 4:15pmDavid Treumann, “Invariants of Lagrangians via microlocal sheaf theory”
      Thursday, December 1 – Day 4
      10:30am –11:30amDavid Treumann“Some examples in three dimensions”
      Lunch
      1:00pm – 2:30pmJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
       2:30-2:45pm Break
      2:45pm – 3:30pmNetanel Blaier, “The quantum Johnson homomorphism, and the symplectic mapping class group of 3-folds”

      * This event is sponsored by the Simons Foundation and CMSA Harvard University.

    • Colloquium
      3:25 pm
      11/01/2019

      During the Spring 2021 semester, and until further notice, all seminars will take place virtually.

      The 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually, using zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed.

      To learn how to attend, please fill out this form.

      Information on previous colloquia can be found here.

      Spring 2021:

      DateSpeakerTitle/Abstract
      1/27/2021Evelyn Tang (Max Planck Institute for Dynamics and Self-Organization)

      Slides

      Video

      Title: Topology protects chiral edge currents in stochastic systems

      Abstract: Living systems can exhibit time-scales much longer than those of the underlying components, as well as collective dynamical behavior. How such global behavior is subserved by stochastic constituents remains unclear. I will present two-dimensional stochastic networks that consist of out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. I will discuss the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, stochastic growth and shrinkage, and synchronization.

      2/3/2021André Luiz de Gouvêa (Northwestern)

      Video

      Title: The Brave Nu World

      Abstract: Neutrinos are the least understood of the fundamental particles that make up the so-called Standard Model of Particle Physics. Measuring neutrino properties and identifying how they inform our understanding of nature at the smallest distant scales is among the highest priorities of particle physics research today. I will discuss our current understanding of neutrinos, concentrating on the observation of neutrino oscillations and neutrino masses, along with all the open questions that came of these discoveries from the end of the 20th century.

      2/10/2021Mykhaylo Shkolnikov (Princeton)

      Video

      Title: Probabilistic approach to free boundary problems and applications

      Abstract: We will discuss a recently developed probabilistic approach to (singular) free boundary problems, such as the supercooled Stefan problem. The approach is based on a new notion of solution, referred to as probabilistic, which arises naturally in the context of large system limits of interacting particle systems. In the talk, I will give an example of how such interacting particle systems arise in applications (e.g., finance), then obtain a solution of a free boundary problem in the large system limit, and discuss how this solution can be analyzed mathematically (thereby answering natural questions about the systemic risk in financial systems and neural synchronization in the brain). The talk is based on recent and ongoing joint works with Sergey Nadtochiy, Francois Delarue, Jiacheng Zhang and Xiling Zhang

      2/17/2021
      9:00 – 10:00PM ET
      C. Seshadhri (UC Santa Cruz)

      Video

      Title: Studying the (in)effectiveness of low dimensional graph embeddings

      Abstract: Low dimensional graph embeddings are a fundamental and popular tool used for machine learning on graphs. Given a graph, the basic idea is to produce a low-dimensional vector for each vertex, such that “similarity” in geometric space corresponds to “proximity” in the graph. These vectors can then be used as features in a plethora of machine learning tasks, such as link prediction, community labeling, recommendations, etc. Despite many results emerging in this area over the past few years, there is less study on the core premise of these embeddings. Can such low-dimensional embeddings effectively capture the structure of real-world (such as social) networks? Contrary to common wisdom, we mathematically prove and empirically demonstrate that popular low-dimensional graph embeddings do not capture salient properties of real-world networks. We mathematically prove that common low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, which have been widely established to be empirically true for real-world networks. Empirically, we observe that the embeddings generated by popular methods fail to recreate the triangle structure of real-world networks, and do not perform well on certain community labeling tasks. (Joint work with Ashish Goel, Caleb Levy, Aneesh Sharma, and Andrew Stolman.)

      2/24/2021David Ben-Zvi (U Texas)

      Video

      Title: Electric-Magnetic Duality for Periods and L-functions

      Abstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory.
      A fundamental aspect of the Langlands correspondence — the relative Langlands program — studies the representation of L-functions of Galois representations as integrals of automorphic forms. However, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don’t seem to line up.
      We present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely, we rewrite the relative Langlands program as duality in the presence of supersymmetric boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.

      3/3/2021

      9:00pm ET

      Omer Tamuz (Caltech)Title: Monotone Additive Statistics

      Abstract: How should a random quantity be summarized by a single number? We study mappings from random variables to real numbers, focussing on those with the following two properties: (1) monotonicity with respect to first-order stochastic dominance, and (2) additivity for sums of independent random variables. This problem turns out to be connected to the following question: Under what conditions on the random variables X and Y does there exist an independent Z so that X + Z first-order stochastically dominates Y + Z?

      (Joint work with Tobias Fritz, Xiaosheng Mu, Luciano Pomatto and Philipp Strack.)

      3/10/2021

      9:00pm ET

      Piotr Indyk (MIT)Title: Learning-Based Sampling and Streaming

      Abstract: Classical algorithms typically provide “one size fits all” performance, and do not leverage properties or patterns in their inputs. A recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. In this talk I will present two examples of this type, in the context of streaming and sampling algorithms. In particular, I will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (ICLR’19), and (b) sampling algorithms for estimating the support size of a distribution (ICLR’21). Both algorithms use an ML-based predictor that, given a data item, estimates the number of times the item occurs in the input data set. (The talk will cover material from papers co-authored with T Eden, CY Hsu, D Katabi, S Narayanan, R Rubinfeld, S Silwal, T Wagner and A Vakilian.

      3/17/2021
      9:00pm ET
      Chiu-Chu Melissa Liu (Columbia)Title: Topological Recursion and Crepant Transformation Conjecture

      Abstract: The Crepant Transformation Conjecture (CTC), first proposed by Yongbin Ruan and later refined/generalized by others, relates Gromov-Witten (GW) invariants of K-equivalent smooth varieties or smooth Deligne-Mumford stacks. We will outline a proof of all-genus open and closed CTC for symplectic toric Calabi-Yau 3-orbifolds based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong. Our proof relies on the Remodeling Conjecture (proposed by Bouchard-Klemm-Marino-Pasquetti and proved in full generality by Fang, Zong and the speaker) relating open and closed GW invariants of a symplectic toric Calabi-Yau 3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin Topological Recursion.

      3/24/2021Weinan E (Princeton)

      Video

      Title: Machine Learning and PDEs

      Abstract: I will discuss two topics:
      (1) Machine learning-based algorithms and “regularity” theory for very high dimensional PDEs;
      (2) Formulating machine learning as PDE (more precisely, integral-differental equation) problems.

      3/31/2021Thore Graepel (DeepMind/UCL)

      Video

      Title: From AlphaGo to MuZero – Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model

      Abstract: Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a perfect simulator is available. However, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. MuZero learns a model that, when applied iteratively, predicts the quantities most directly relevant to planning: the reward, the action-selection policy, and the value function. When evaluated on 57 different Atari games – the canonical video game environment for testing AI techniques, in which model-based planning approaches have historically struggled – our new algorithm achieved a new state of the art. When evaluated on Go, chess and shogi, without any knowledge of the game rules, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.

      4/7/2021Kui Ren (Columbia)Title: Inversion via Optimization: Revisiting the Classical Least-Squares Formulation of Inverse Problems

      Abstract: The classical least-squares formulation of inverse problems has provided a successful framework for the computational solutions of those problems. In recent years, modifications and alternatives have been proposed to overcome some of the disadvantages of this classical formulation in dealing with new applications. This talk intends to provide an (likely biased) overview of the recent development in constructing new least-squares formulations for model and data-driven solutions of inverse problems.

      4/14/2021Siu-Cheong Lau (Boston U)Title: An algebro-geometric formulation of computing machines

      Abstract: Neural network in machine learning has obvious similarity with quiver representation theory.  The main gap between the two subjects is that network functions produced from two isomorphic quiver representations are not equal, due to the presence of non-linear activation functions which are not equivariant under the automorphism group.  This violates the important math/physics principle that isomorphic objects should produce the same results.  In this talk, I will introduce a general formulation using moduli spaces of framed modules of (noncommutative) algebra and fix this gap.  Metrics over the moduli space are crucial.  I will also explain uniformization between spherical, Euclidean and hyperbolic moduli.

      4/21/2021Vasco Carvalho (Cambridge)Title: The Economy as a Complex Production Network
      Abstract: A modern economy is an intricately linked web of specialized production units, each relying on the flow of inputs from their suppliers to produce their own output, which in turn is routed towards other downstream units. From this production network vantage point we: (i) present the theoretical foundations for the role of such input linkages as a shock propagation channel and as a mechanism for transforming micro-level shocks into macroeconomic, economy-wide fluctuations (ii) selectively survey both empirical and simulation-based studies that attempt to ascertain the relevance and quantitative bite of this argument and (time permitting) (iii) discuss a range of domains where this networked production view is currently being extended to.
      4/28/2021

      9:00 – 10:00pm ET

      Shamit Kachru (Stanford)

      Slides

      Title: K3 Metrics from String Theory

      Abstract: Calabi-Yau manifolds have played a central role in important developments in string theory and mathematical physics.  Famously, they admit Ricci flat metrics — but the proof of that fact is not constructive, and the metrics remain mysterious.  K3 is perhaps the simplest non-trivial compact Calabi-Yau space.  In this talk, I describe two different methods of constructing (smooth, Ricci flat) K3 metrics, and a string theory duality which relates them.  The duality re-sums infinite towers of disc instanton corrections via a purely classical infinite-dimensional hyperkahler quotient construction, which can be practically implemented.


      Fall 2020:

      DateSpeakerTitle/Abstract
      9/23/2020David Kazhdan (Hebrew University)Title: On Applications of Algebraic Combinatorics to Algebraic Geometry

      Abstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.

      10/7/2020

      10:00am

      Mariangela Lisanti (Princeton University)

      Video

      Title: Mapping the Milky Way’s Dark Matter Halo with Gaia

      Abstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium, as typically assumed, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments, which search for the interactions of these particles in terrestrial targets.

      10/14/2020Gil Kalai (Hebrew University and IDC Herzliya)

      Video

      Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers

      Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to
      a) My general argument “against” quantum computers,
      b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
      Relevant papers:
      Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.
      wordpress.com/2019/11/stat-quantum2.pdf

      Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.
      wordpress.com/2020/08/laws-blog2.pdf

      Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.
      wordpress.com/2019/09/main-pr.pdf

      10/21/2020Marta Lewicka (University of Pittsburgh)

      Video

      Title: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models

      Abstract: We propose results that relate the following two contexts:
      (i) Given a Riemann metric G on a thin plate, we study the question of what is its closest isometric immersion, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.
      (ii) We perform the full scaling analysis of E^h, in the context of dimension reduction as the plate’s thickness h goes to 0, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).
      For each n, we identify conditions for the validity of the corresponding scaling, in terms of the vanishing of Riemann curvatures of G up to appropriate orders, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth, swelling, shrinkage, plasticity, etc. Our results display the interaction of calculus of variations,
      geometry and mechanics of materials in the prediction of patterns and shape formation.

      10/28/2020Jonathan Heckman (University of Pennsylvania)

      Video

      Title: Top Down Approach to Quantum Fields

      Abstract: Quantum Field theory (QFT) is the common language of particle physicists, cosmologists, and condensed matter physicists. Even so, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory, highlighting in particular the special role of seemingly “exotic”  higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs, and are now using this to extra observables from strongly correlated systems in theories with more than four spacetime dimensions, as well as in spacetimes with four or fewer spacetime dimensions. Along the way, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems

      11/4/2020
      9:00pm ET
      Surya Ganguli (Stanford)

      Video

      Title: Weaving together machine learning, theoretical physics, and neuroscience through mathematics

      Abstract: An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning, theoretical physics, and neuroscience.  The unification of these fields will likely enable us to exploit the power of complex systems analysis, developed in theoretical physics and applied mathematics, to elucidate the design principles governing neural systems, both biological and artificial, and deploy these principles to develop better algorithms in machine learning.  We will give several vignettes in this direction, including:  (1) determining the best optimization problem to solve in order to perform regression in high dimensions;  (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) developing interpretable machine learning to derive and understand state of the art models of the retina; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) delineating fundamental theoretical limits on the energy, speed and accuracy with which non-equilibrium sensors can detect signals
      Selected References:
      M. Advani and S. Ganguli, Statistical mechanics of optimal convex inference in high dimensions, Physical Review X, 6, 031034, 2016.
      M. Advani and S. Ganguli, An equivalence between high dimensional Bayes optimal inference and M-estimation, NeurIPS, 2016.
      A.K. Lampinen and S. Ganguli, An analytic theory of generalization dynamics and transfer learning in deep linear networks, International Conference on Learning Representations (ICLR), 2019.
      H. Tanaka, A. Nayebi, N. Maheswaranathan, L.M. McIntosh, S. Baccus, S. Ganguli, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction, NeurIPS 2019.
      S. Deny, J. Lindsey, S. Ganguli, S. Ocko, The emergence of multiple retinal cell types through efficient coding of natural movies, Neural Information Processing Systems (NeurIPS) 2018.
      B. Sorscher, G. Mel, S. Ganguli, S. Ocko, A unified theory for the origin of grid cells through the lens of pattern formation, NeurIPS 2019.
      Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
      S.E. Harvey, S. Lahiri, and S. Ganguli, A universal energy accuracy tradeoff in nonequilibrium cellular sensing, https://arxiv.org/abs/2002.10567

      11/11/2020Kevin Buzzard (Imperial College London)

      Video

      Title: Teaching proofs to computers

      Abstract: A mathematical proof is a sequence of logical statements in a precise language, obeying some well-defined rules. In that sense it is very much like a computer program. Various computer tools have appeared over the last 50 years which take advantage of this analogy by turning the mathematical puzzle of constructing a proof of a theorem into a computer game. The newest tools are now capable of understanding some parts of modern research mathematics. In spite of this, these tools are not used in mathematics departments, perhaps because they are not yet capable of telling mathematicians *something new*.
      I will give an overview of the Lean theorem prover, showing what it can currently do. I will also talk about one of our goals: using Lean to make practical tools which will be helpful for future researchers in pure mathematics.

      11/18/2020Jose A. Scheinkman (Columbia)

      Video

      Title: Re-pricing avalanches

      Abstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive.  Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper, we show that a state-dependent  pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment.  These fluctuations, in turn, cause fluctuations  in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)

      11/25/2020

      10:45am

      Eric J. Heller (Harvard)

      Video

      Title: Branched Flow

      Abstract: In classical and quantum  phase space flow, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In  evolution under smooth, random, weakly deflecting  but persistent perturbations, a remarkable regime develops, called branched flow. Lying between the first cusp catastrophes at the outset, leading to fully chaotic  statistical flow much later, lies the visually beautiful regime of branched flow.  It applies to tsunami wave propagation, freak wave formation, light propagation, cosmic microwaves arriving from pulsars, electron flow in metals and devices, sound propagation in the atmosphere and oceans, the large scale structure of the universe, and much more. The mathematical structure of this flow is only partially understood, involving exponential instability coexisting with “accidental” stability. The flow is qualitatively universal, but this has not been quantified.  Many questions arise, including the scale(s) of the random medium,  and the time evolution of manifolds and “fuzzy” manifolds in phase space.  The classical-quantum (ray-wave)  correspondence in this flow is only partially understood.  This talk will be an introduction to the phenomenon, both visual and mathematical, emphasizing unanswered questions

      12/2/2020Douglas Arnold (U of Minnesota)

      Video

      Title: Preserving geometry in numerical discretization

      Abstract: An important design principle for numerical methods for differential equations is that the discretizations preserve key geometric, topological, and algebraic structures of the original differential system.  For ordinary differential equations, such geometric integrators were developed at the end of the last century, enabling stunning computations in celestial mechanics and other applications that would have been impossible without them.  Since then, structure-preserving discretizations have been developed for partial differential equations.  One of the prime examples has been the finite element exterior calculus or FEEC, in which the structures to preserve are related to Hilbert complexes underlying the PDEs, the de Rham complex being a canonical example.  FEEC has led to highly successful new numerical methods for problems in fluid mechanics, electromagnetism, and other applications which relate to the de Rham complex.  More recently, new tools have been developed which extend the applications of FEEC far beyond the de Rham complex, leading to progress in discretizations of problems from solid mechanics, materials science, and general relativity.

      12/9/2020Manuel Blum and Lenore Blum (Carnegie Mellon)

      Video

      Title: What can Theoretical Computer Science Contribute to the Discussion of Consciousness?

      Abstract: The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We study consciousness from the perspective of theoretical computer science. This is done by formalizing the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. We give a precise formal definition of a Conscious Turing Machine (CTM), also called Conscious AI, in the spirit of Alan Turing’s simple yet powerful definition of a computer. We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness.
      After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness, the range of related concepts that the model explains easily and naturally, and the extent of the theory’s agreement with scientific evidence

    • Seminars
      Seminars Colloquia & Seminar
      02-25-2016 Evolution Equations Seminar
      3:25 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-03-2016 Evolution Equations Seminar
      3:26 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-29-2016 Geometric Analysis Seminar
      3:27 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-5-2018 Mathematical Physics Seminar
      3:27 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Seminars
      Seminars Colloquia & Seminar
      04-07-2016 Evolution Equations Seminar
      3:28 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: JDG 2017 Conference, April 28 – May 2, 2017
      3:29 pm
      11/01/2019-05/02/2017

      In celebration of the Journal of Differential Geometry’s 50th anniversary, the Harvard Math Department will be hosting the Tenth Conference on Geometry and Topology (JDG 2017) from April 28 – May 2, 2017.

      Registration and additional information on the conference can be found at http://abel.harvard.edu/jdg/index.html.

      Confirmed Speakers

      * This event is co-sponsored by Lehigh University and partially supported by the National Science Foundation.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2-23-2018 RM & PT Seminar
      3:30 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Seminars
      Seminars Colloquia & Seminar
      4/4/2019 General Relativity Seminar
      3:30 pm-4:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      02-29-2016 Social Science Application Forum
      3:30 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/14/2019 General Relativity Seminar
      3:30 pm-4:30 pm
      11/01/2019
    • Colloquium
      3:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/15/2019 Spacetime Seminar
      3:30 pm-5:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/10/2019 Spacetime Seminar
      3:30 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/17/2018 RM & PT Seminar
      3:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      02-29-2016 Mathematical Physics Seminar
      3:31 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-01-2016 Geometric Analysis Seminar
      3:32 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-10-2016 Evolution Equations Seminar
      3:34 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Working Conference on Materials and Data Analysis, March 27-30, 2017
      3:34 pm
      11/01/2019-03/30/2017

      The Center of Mathematical Sciences and Applications will be hosting a 5-day working Conference on Materials and Data Analysis and related areas, March 27-30, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Photos of the event can be found on CMSA’s Blog.

       Participants:

      Organizers:

      * This event is sponsored by CMSA Harvard University.

      Schedule:

      Monday, March 27

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amKieron Burke, University of California, IrvineBackground in DFT and electronic structure calculations
      10:00am – 11:00amKieron Burke, University of California, Irvine

      The density functionals machines can learn

      11:00am – 12:00pmSadasivan Shankar, Harvard UniversityA few key principles for applying Machine Learning to Materials (or Complex Systems) — Scientific and Engineering Perspectives

      Tuesday, March 28

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amRyan Adams, HarvardTBA
      10:00am – 11:00amGábor Csányi, University of Cambridge

      Interatomic potentials using machine learning: accuracy, transferability and chemical diversity

      11:00am – 1:00pmLunch Break
      1:00pm – 2:00pmEvan Reed, Stanford UniversityTBA

       Wednesday, March 29 

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amPatrick Riley, GoogleThe Message Passing Neural Network framework and its application to molecular property prediction
      10:00am – 11:00amJörg Behler, University of GöttingenTBA
      11:00am – 12:00pmEkin Doğuş Çubuk, Stanford UniversTBA
      4:00pmLeslie Greengard, Courant InstituteInverse problems in acoustic scattering and cryo-electron microscopy

      CMSA Colloquium

      Thursday, March 30

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amMatthias Rupp, Fitz Haber Institute of the Max Planck SocietyTBA
      10:00am – 11:00amPetros Koumoutsakos, Radcliffe Institute for Advanced Study, HarvardTBA
      11:00am – 1:00pmLunch Break
      1:00pm – 2:00pmDennis Sheberla, Harvard UniversityRapid discovery of functional molecules by a high-throughput virtual screening
    • CMSA EVENT: Workshop on Discrete and Topological Models for Effective Field Theories, January 9-13, 2017
      3:35 pm-3:36 pm
      11/01/2019-01/13/2017

      The Center of Mathematical Sciences and Applications will be hosting a Workshop on “Discrete and Topological Models for Effective Field Theories,” January 9-13, 2017.  The workshop will be hosted in G02 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Titles, abstracts and schedule will be provided nearer to the event.

      Participants:

      Dan Freed, UT Austin

      Anton Kapustin, California Institute of Technology

      Alexei Y. Kitaev, California Institute of Technology

      Greg Moore, Rutgers University

      Constantin Teleman, University of Oxford

      Organizers:

      Mike Hopkins, Shing-Tung Yau

      * This event is sponsored by CMSA Harvard University.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-09-2016 Random Matrix & Probability Theory
      3:35 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-23-2016 Random Matrix & Probability Theory
      3:37 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-04-2016 Social Science Applications Forum
      3:38 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Working Conference on Covariance Analysis in Biology, May 1-4, 2017
      3:40 pm-3:41 pm
      11/01/2019-05/02/2017

      The Center of Mathematical Sciences and Applications will be hosting a working Conference on Covariance Analysis in Biology, May 1-4, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      This event is open and free.  If you would like to attend, please register here to help us keep a headcount. A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Speakers:

      Orr Ashenberg, Fred Hutchinson Cancer Research Center

      John Barton, Massachusetts Institute of Technology

      Simona Cocco, Laboratoire de Physique Statistique de l’ENS

      Sean Eddy, Harvard University

      Efthimios Kaxiras, Harvard University

      Michael Laub, Massachusetts Institute of Technology

      Debora S. Marks, Harvard University

      Govind Menon, Brown University

      Rémi Monasson, Laboratoire de Physique Théorique de l’ENS

      Andrew Murray, Harvard University

      Ilya Nemenman, Emory College

      Chris Sander, Dana-Farber Cancer Institute, Harvard Medical School

      Dave Thirumalai, University of Texas at Austin

      Martin Weigt, IBPS, Université Pierre et Marie Curie

      Matthieu Wyart, EPFL

      More speakers will be confirmed soon.

       

      Schedule:

      (Please click here for a downloadable version of the schedule.)

      Please note that the schedule for both days is currently tentative and is subject to change.

      May 1, Monday

      TimeSpeakerTopic
      9:00-10:00amSean EddyTBA
      10:00-11:00amMike LaubTBA
      11:00am-12:00pmIlya NemenmanTBA
      May 2, Tuesday
      TimeSpeakerTopic
      9:00-10:00amOrr AshenbergTBA
      10:00-11:00amDebora MarksTBA
      11:00am-12:00pmMartin WeigtTBA
      4:30pm-5:30pmSimona CoccoCMSA Colloquia

       

      May 3, Wednesday
      TimeSpeakerTopic
      9:00-10:00amAndrew MurrayTBA
      10:00-11:00amMatthieu WyartTBA
      11:00am-12:00pmRémi MonassonTBA

       

      May 4, Thursday
      TimeSpeakerTopic
      9:00-10:00amDavid ThirumalaiTBA
      10:00-11:00amChris SanderTBA
      11:00am-12:00pmJohn BartonTBA

       

      Organizers:

      Michael Brenner, Lucy Colwell, Elena Rivas, Eugene Shakhnovich

      * This event is sponsored by CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      03-07-2016 Mathematical Physics Seminar
      3:41 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2-26-2018 Mathematical Physics Seminar
      3:42 pm
      11/01/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-11-2016 Random Matrix & Probability Theory
      3:42 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: A Celebration of Symplectic Geometry: 15 Years of JSG, June 5-6, 2017
      3:44 pm
      11/01/2019-05/04/2017

      In celebration of the Journal of Symplectic Geometry’s 15th anniversary, the Center of Mathematical Sciences and Applications will be hosting A Celebration of Symplectic Geometry: 15 Years of JSG on June 5-6, 2017.

      To register for this event, please click here.

      Confirmed speakers:

      The conference is co-organized by Denis Auroux and Victor Guillemin. Additional information on the conference will be announced closer to the event.

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

      Schedule:

      The schedule for both days is currently tentative and is subject to change. A pdf version of the schedule can also be downloaded here.

      June 5, Monday (Full day)

      TimeSpeakerTopic
      8:30am – 9:0amBreakfast
      9:00am – 10:00amJonathan WeitsmanTitle: On the geometric quantization of (some) Poisson manifolds
      10:30am – 11:30amEckhard MeinrenkenTitle: On Hamiltonian loop group spaces

      Abstract: Let G be a compact Lie group. We explain a construction of an LG-equivariant spinor module over any Hamiltonian loop group space with proper moment map. It may be regarded as its `canonical spin-c structure’. We show how to reduce to finite dimensions, resulting in actual spin-s structure on transversals, as well as twisted spin-c structures for the associated quasi-hamiltonian space. This is based on joint work with Yiannis Loizides and Yanli Song.

      11:30am – 1:30pmBreak
      1:30pm – 2:30pmAna Rita PiresTitle: Infinite staircases in symplectic embedding problems

      Abstract: McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with Cristofaro-Gardiner, Holm and Mandini.

      Video

      3:00pm – 4:00pmSobhan SeyfaddiniTitle: Rigidity of conjugacy classes in groups of area-preserving homeomorphisms

      Abstract: Motivated by understanding the algebraic structure of groups of area-preserving homeomorphims F. Beguin, S. Crvoisier, and F. Le Roux were lead to the following question: Can the conjugacy class of a Hamiltonian homeomorphism be dense? We will show that one can rule out existence of dense conjugacy classes by simply counting fixed points. This is joint work with Le Roux and Viterbo.

      4:30pm – 5:30pmRoger CasalsTitle: Differential Algebra of Cubic Graphs
      Abstract: In this talk we will associate a combinatorial dg-algebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations and examples. From there we study the Legendrian surfaces behind these constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.Video

      June 6, Tuesday (Full day)

      TimeSpeakerTopic
      8:30am – 9:00amBreakfast
      9:00am – 10:00amAlejandro UribeTitle: Semi-classical wave functions associated with isotropic submanifolds of phase space

      Abstract: After reviewing fundamental ideas on the quantum-classical correspondence, I will describe how to associate spaces of semi-classical wave functions to isotropic submanifolds of phase space satisfying a Bohr-Sommerfeld condition. Such functions have symbols that are symplectic spinors, and they satisfy a symbol calculus under the action of quantum observables. This is the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin, and it is joint work with Victor Guillemin and Zuoqin Wang. I will inlcude applications and open questions.

      Video

      10:30am – 11:30amAlisa KeatingTitle: Symplectomorphisms of exotic discs

      Abstract: It is a theorem of Gromov that the group of compactly supported symplectomorphisms of R^4, equipped with the standard symplectic form, is contractible. While nothing is known in higher dimensions for the standard symplectic form, we show that for some exotic symplectic forms on R^{4n}, for all but finitely n, there exist compactly supported symplectomorphisms that are smoothly non-trivial. The principal ingredients are constructions of Milnor and Munkres, a symplectic and contact version of the Gromoll filtration, and Borman, Eliashberg and Murphy’s work on existence of over-twisted contact structures. Joint work with Roger Casals and Ivan Smith.

      Video

      11:30am – 1:30pmBreak
      1:30pm – 2:30pmChen HeTitle: Morse theory on b-symplectic manifolds

      Abstract: b-symplectic (or log-symplectic) manifolds are Poisson manifolds equipped with symplectic forms of logarithmic singularity. Following Guillemin, Miranda, Pires and Scott’s introduction of Hamiltonian group actions on b-symplectic manifolds, we will survey those classical results of Hamiltonian geometry to the b-symplectic case.

      Video

      3:00pm – 4:00pmYael KarshonTitle: Geometric quantization with metaplectic-c structures

      Abstract: I will present a variant of the Kostant-Souriau geometric quantization procedure that uses metaplectic-c structures to incorporate the “half form correction” into the prequantization stage. This goes back to the late 1970s but it is not widely known and it has the potential to generalize and improve upon recent works on geometric quantization.

      Video


    • Seminars
      Seminars Colloquia & Seminar
      03-08-2016 Geometric Analysis Seminar
      3:44 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-21-2016 Mathematical Physics Seminar
      3:46 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-24-2016 Evolution Equations Seminar
      3:47 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: 2017 Big Data Conference
      3:47 pm
      11/01/2019-08/19/2017
      1 Oxford Street, Cambridge MA 02138

      The Center of Mathematical Sciences and Applications will be hosting a conference on Big Data from August 18 – 19, 2017, in Hall D of the Science Center at Harvard University.

      The Big Data Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the third conference on Big Data the Center will host as part of our annual events, and is co-organized by Richard Freeman, Scott Kominers, Jun Liu, Horng-Tzer Yau and Shing-Tung Yau.

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

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

      Confirmed Speakers:

       

      Following the conference, there will be a two-day workshop from August 20-21. The workshop is organized by Scott Kominers, and will feature:

      • Jörn Boehnke, Harvard University
      • Nikhil Naik, Harvard University
      • Bradly Stadie, Open AI, University of California, Berkeley

       

      Conference Schedule

      A PDF version of the schedule below can also be downloaded here.

      August 18, Friday (Full day)

      TimeSpeakerTopic
      8:30 am – 9:00 amBreakfast
      9:00 am – 9:40 amMohammad Akbarpour

      Video

      Title: Information aggregation in overlapping generations and the emergence of experts

      Abstract: We study a model of social learning with “overlapping generations”, where agents meet others and share data about an underlying state over time. We examine under what conditions the society will produce individuals with precise knowledge about the state of the world. There are two information sharing regimes in our model: Under the full information sharing technology, individuals exchange the information about their point estimates of an underlying state, as well as their sources (or the precision of their signals) and update their beliefs by taking a weighted average. Under the limited information sharing technology, agents only observe the information about the point estimates of those they meet, and update their beliefs by taking a weighted average, where weights can depend on the sequence of meetings, as well as the labels. Our main result shows that, unlike most social learning settings, using such linear learning rules do not guide the society (or even a fraction of its members) to learn the truth, and having access to, and exploiting knowledge of the precision of a source signal are essential for efficient social learning (joint with Amin Saberi & Ali Shameli).

      9:40 am – 10:20 amLucas Janson

      Video

      Title: Model-Free Knockoffs For High-Dimensional Controlled Variable Selection

      Abstract: Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new framework of model-free knockoffs, which reads from a different perspective the knockoff procedure (Barber and Candès, 2015) originally designed for controlling the false discovery rate in linear models. The key innovation of our method is to construct knockoff variables probabilistically instead of geometrically. This enables model-free knockoffs to deal with arbitrary (and unknown) conditional models and any dimensions, including when the dimensionality p exceeds the sample size n, while the original knockoffs procedure is constrained to homoscedastic linear models with n greater than or equal to p. Our approach requires the design matrix be random (independent and identically distributed rows) with a covariate distribution that is known, although we show our procedure to be robust to unknown/estimated distributions. As we require no knowledge/assumptions about the conditional distribution of the response, we effectively shift the burden of knowledge from the response to the covariates, in contrast to the canonical model-based approach which assumes a parametric model for the response but very little about the covariates. To our knowledge, no other procedure solves the controlled variable selection problem in such generality, but in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case-control study of Crohn’s disease in the United Kingdom, making twice as many discoveries as the original analysis of the same data.

      Slides

      10:20 am – 10:50 amBreak
      10:50 pm – 11:30 pmNoureddine El Karoui

      Video

      Title: Random matrices and high-dimensional statistics: beyond covariance matrices

      Abstract: Random matrices have played a central role in understanding very important statistical methods linked to covariance matrices (such as Principal Components Analysis, Canonical Correlation Analysis etc…) for several decades. In this talk, I’ll show that one can adopt a random-matrix-inspired point of view to understand the performance of other widely used tools in statistics, such as M-estimators, and very common methods such as the bootstrap. I will focus on the high-dimensional case, which captures well the situation of “moderately” difficult statistical problems, arguably one of the most relevant in practice. In this setting, I will show that random matrix ideas help upend conventional theoretical thinking (for instance about maximum likelihood methods) and highlight very serious practical problems with resampling methods.

      11:30 am – 12:10 pmNikhil Naik

      Video

      Title: Understanding Urban Change with Computer Vision and Street-level Imagery

      Abstract: Which neighborhoods experience physical improvements? In this work, we introduce a computer vision method to measure changes in the physical appearances of neighborhoods from time-series street-level imagery. We connect changes in the physical appearance of five US cities with economic and demographic data and find three factors that predict neighborhood improvement. First, neighborhoods that are densely populated by college-educated adults are more likely to experience physical improvements. Second, neighborhoods with better initial appearances experience, on average, larger positive improvements. Third, neighborhood improvement correlates positively with physical proximity to the central business district and to other physically attractive neighborhoods. Together, our results illustrate the value of using computer vision methods and street-level imagery to understand the physical dynamics of cities.

      (Joint work with Edward L. Glaeser, Cesar A. Hidalgo, Scott Duke Kominers, and Ramesh Raskar.)

      12:10 pm – 12:25 pmVideo #1

      Video #2

      Data Science Lightning Talks
      12:25 pm – 1:30 pmLunch
      1:30 pm – 2:10 pmTracy Ke

      Video

      Title: A new SVD approach to optimal topic estimation

      Abstract: In the probabilistic topic models, the quantity of interest—a low-rank matrix consisting of topic vectors—is hidden in the text corpus matrix, masked by noise, and Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank matrix and the singular vectors of the text corpus matrix are usually complicated and hard to spell out, so how to use SVD for learning topic models faces challenges.

      We overcome the challenge by revealing a surprising insight: there is a low-dimensional simplex structure which can be viewed as a bridge between the low-rank matrix of interest and the SVD of the text corpus matrix, and which allows us to conveniently reconstruct the former using the latter. Such an insight motivates a new SVD-based approach to learning topic models.

      For asymptotic analysis, we show that under a popular topic model (Hofmann, 1999), the convergence rate of the l1-error of our method matches that of the minimax lower bound, up to a multi-logarithmic term. In showing these results, we have derived new element-wise bounds on the singular vectors and several large deviation bounds for weakly dependent multinomial data. Our results on the convergence rate and asymptotical minimaxity are new. We have applied our method to two data sets, Associated Process (AP) and Statistics Literature Abstract (SLA), with encouraging results. In particular, there is a clear simplex structure associated with the SVD of the data matrices, which largely validates our discovery.

      2:10 pm – 2:50 pmAlbert-László Barabási

      Video

      Title: Taming Complexity: From Network Science to Controlling Networks

      Abstract: The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here we explore the controllability of an arbitrary complex network, identifying the set of driver nodes whose time-dependent control can guide the system’s entire dynamics. We apply these tools to several real networks, unveiling how the network topology determines its controllability. Virtually all technological and biological networks must be able to control their internal processes. Given that, issues related to control deeply shape the topology and the vulnerability of real systems. Consequently unveiling the control principles of real networks, the goal of our research, forces us to address series of fundamental questions pertaining to our understanding of complex systems.

       

      2:50 pm – 3:20 pmBreak
      3:20 pm – 4:00 pmMarena Lin

      Video

      Title: Optimizing climate variables for human impact studies

      Abstract: Estimates of the relationship between climate variability and socio-economic outcomes are often limited by the spatial resolution of the data. As studies aim to generalize the connection between climate and socio-economic outcomes across countries, the best available socio-economic data is at the national level (e.g. food production quantities, the incidence of warfare, averages of crime incidence, gender birth ratios). While these statistics may be trusted from government censuses, the appropriate metric for the corresponding climate or weather for a given year in a country is less obvious. For example, how do we estimate the temperatures in a country relevant to national food production and therefore food security? We demonstrate that high-resolution spatiotemporal satellite data for vegetation can be used to estimate the weather variables that may be most relevant to food security and related socio-economic outcomes. In particular, satellite proxies for vegetation over the African continent reflect the seasonal movement of the Intertropical Convergence Zone, a band of intense convection and rainfall. We also show that agricultural sensitivity to climate variability differs significantly between countries. This work is an example of the ways in which in-situ and satellite-based observations are invaluable to both estimates of future climate variability and to continued monitoring of the earth-human system. We discuss the current state of these records and potential challenges to their continuity.

      4:00 pm – 4:40 pmAlex Peysakhovich Title: Building a cooperator

      Abstract: A major goal of modern AI is to construct agents that can perform complex tasks. Much of this work deals with single agent decision problems. However, agents are rarely alone in the world. In this talk I will discuss how to combine ideas from deep reinforcement learning and game theory to construct artificial agents that can communicate, collaborate and cooperate in productive positive sum interactions.

      4:40 pm – 5:20 pmTze Leung Lai

      Video

      Title: Gradient boosting: Its role in big data analytics, underlying mathematical theory, and recent refinements

      Abstract: We begin with a review of the history of gradient boosting, dating back to the LMS algorithm of Widrow and Hoff in 1960 and culminating in Freund and Schapire’s AdaBoost and Friedman’s gradient boosting and stochastic gradient boosting algorithms in the period 1999-2002 that heralded the big data era. The role played by gradient boosting in big data analytics, particularly with respect to deep learning, is then discussed. We also present some recent work on the mathematical theory of gradient boosting, which has led to some refinements that greatly improves the convergence properties and prediction performance of the methodology.

      August 19, Saturday (Full day)

      TimeSpeakerTopic
      8:30 am – 9:00 amBreakfast
      9:00 am – 9:40 amNatesh Pillai

      Video

      Title: Accelerating MCMC algorithms for Computationally Intensive Models via Local Approximations

      Abstract: We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler’s exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this article: when the likelihood has some local regularity, the number of model evaluations per Markov chain Monte Carlo (MCMC) step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ordinary differential equation (ODE) and partial differential equation (PDE) inference problems, with both synthetic and real data.

      9:40 am – 10:20 amRavi Jagadeesan

      Video

      Title: Designs for estimating the treatment effect in networks with interference

      Abstract: In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring” on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide range of interference functions encountered in applications, we show both by theory and simulations that the classical Neymanian estimator for the direct effect has desirable properties for our designs. This further extends to settings where homophily is present in addition to interference.

      10:20 am – 10:50 amBreak
      10:50 am – 11:30 amAnnie Liang

      Video

      Title: The Theory is Predictive, but is it Complete? An Application to Human Generation of Randomness

      Abstract: When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? This question is difficult to answer, because in general we do not know how much “predictable variation” there is in the problem. In this paper, we consider approaches motivated by machine learning algorithms as a means of constructing a benchmark for the best attainable level of prediction.  We illustrate our methods on the task of predicting human-generated random sequences. Relative to a theoretical machine learning algorithm benchmark, we find that existing behavioral models explain roughly 15 percent of the predictable variation in this problem. This fraction is robust across several variations on the problem. We also consider a version of this approach for analyzing field data from domains in which human perception and generation of randomness has been used as a conceptual framework; these include sequential decision-making and repeated zero-sum games. In these domains, our framework for testing the completeness of theories provides a way of assessing their effectiveness over different contexts; we find that despite some differences, the existing theories are fairly stable across our field domains in their performance relative to the benchmark. Overall, our results indicate that (i) there is a significant amount of structure in this problem that existing models have yet to capture and (ii) there are rich domains in which machine learning may provide a viable approach to testing completeness (joint with Jon Kleinberg and Sendhil Mullainathan).

      11:30 am – 12:10 pmZak Stone

      Video

      Title: TensorFlow: Machine Learning for Everyone

      Abstract: We’ve witnessed extraordinary breakthroughs in machine learning over the past several years. What kinds of things are possible now that weren’t possible before? How are open-source platforms like TensorFlow and hardware platforms like GPUs and Cloud TPUs accelerating machine learning progress? If these tools are new to you, how should you get started? In this session, you’ll hear about all of this and more from Zak Stone, the Product Manager for TensorFlow on the Google Brain team.

      12:10 pm – 1:30 pmLunch
      1:30 pm – 2:10 pmJann Spiess

      Video

      Title: (Machine) Learning to Control in Experiments

      Abstract: Machine learning focuses on high-quality prediction rather than on (unbiased) parameter estimation, limiting its direct use in typical program evaluation applications. Still, many estimation tasks have implicit prediction components. In this talk, I discuss accounting for controls in treatment effect estimation as a prediction problem. In a canonical linear regression framework with high-dimensional controls, I argue that OLS is dominated by a natural shrinkage estimator even for unbiased estimation when treatment is random; suggest a generalization that relaxes some parametric assumptions; and contrast my results with that for another implicit prediction problem, namely the first stage of an instrumental variables regression.

      2:10 pm – 2:50 pmBradly StadieTitle: Learning to Learn Quickly: One-Shot Imitation and Meta Learning

      Abstract: Many reinforcement learning algorithms are bottlenecked by data collection costs and the brittleness of their solutions when faced with novel scenarios.
      We will discuss two techniques for overcoming these shortcomings. In one-shot imitation, we train a module that encodes a single demonstration of a desired behavior into a vector containing the essence of the demo. This vector can subsequently be utilized to recover the demonstrated behavior. In meta-learning, we optimize a policy under the objective of learning to learn new tasks quickly. We show meta-learning methods can be accelerated with the use of auxiliary objectives. Results are presented on grid worlds, robotics tasks, and video game playing tasks.

      2:50 pm – 3:20 pmBreak
      3:20 pm – 4:00 pmHau-Tieng Wu

      Video

      Title: When Medical Challenges Meet Modern Data Science

      Abstract: Adaptive acquisition of correct features from massive datasets is at the core of modern data analysis. One particular interest in medicine is the extraction of hidden dynamics from a single observed time series composed of multiple oscillatory signals, which could be viewed as a single-channel blind source separation problem. The mathematical and statistical problems are made challenging by the structure of the signal which consists of non-sinusoidal oscillations with time varying amplitude/frequency, and by the heteroscedastic nature of the noise. In this talk, I will discuss recent progress in solving this kind of problem by combining the cepstrum-based nonlinear time-frequency analysis and manifold learning technique. A particular solution will be given along with its theoretical properties. I will also discuss the application of this method to two medical problems – (1) the extraction of a fetal ECG signal from a single lead maternal abdominal ECG signal; (2) the simultaneous extraction of the instantaneous heart/respiratory rate from a PPG signal during exercise; (3) (optional depending on time) an application to atrial fibrillation signals. If time permits, the clinical trial results will be discussed.

      4:00 pm – 4:40 pmSifan Zhou

      Video

      Title: Citing People Like Me: Homophily, Knowledge Spillovers, and Continuing a Career in Science

      Abstract: Forward citation is widely used to measure the scientific merits of articles. This research studies millions of journal article citation records in life sciences from MEDLINE and finds that authors of the same gender, the same ethnicity, sharing common collaborators, working in the same institution, or being geographically close are more likely (and quickly) to cite each other than predicted by their proportion among authors working on the same research topics. This phenomenon reveals how social and geographic distances influence the quantity and speed of knowledge spillovers. Given the importance of forward citations in academic evaluation system, citation homophily potentially put authors from minority group at a disadvantage. I then show how it influences scientists’ chances to survive in the academia and continue publishing. Based on joint work with Richard Freeman.

       

      To view photos and video interviews from the conference, please visit the CMSA blog.

       

    • Seminars
      Seminars Colloquia & Seminar
      12-07-2015 Mathematical Physics Seminar
      3:49 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-22-2016 Geometric Analysis Seminar
      3:51 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      10/16/2019 Colloquium
      4:00 pm
      11/01/2019
    • Yip Lecture Series
      Yip Lecture Series Event
      Yip Annual Lecture
      4:00 pm-5:00 pm
      11/01/2019
      1 Oxford Street, Cambridge MA 02138

      On April 18, 2019 Harvard CMSA hosted the inaugural Yip lecture. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Peter Galison (Harvard Physics).

      The lecture was held from 4:00-5:00pm in Science Center, Hall A.

      Credit:Bronzwaer/Davelaar/Moscibrodzka/Falcke/Radboud University
    • Seminars
      4:00 pm-5:00 pm
      11/01/2019

    • Math Science Lectures in Honor of Raoul Bott
      Math Science Lectures in Honor of Raoul Bott Event
      Math Science Lectures in Honor of Raoul Bott: Mina Aganagic
      4:00 pm
      11/01/2019-04/10/2019
      1 Oxford Street, Cambridge MA 02138

      On April 9 and 10, 2019 the CMSA hosted two lectures by Mina Aganagic (UC Berkeley).  This was the second annual Math Science Lecture Series held in honor of Raoul Bott.

      The lectures took place in Science Center, Hall C

      “Two math lessons from string theory”

      Lecture 1:

       

       

       

       

       

      April 9, 2019

      Title: “Lesson on Integrability”

       

      Abstract: The quantum Knizhnik-Zamolodchikov (qKZ) equation is a difference generalization of the famous Knizhnik-Zamolodchikov (KZ) equation. The problem to explicitly capture the monodromy of the qKZ equation has been open for over 25 years. I will describe the solution to this problem, discovered jointly with Andrei Okounkov. The solution comes from the geometry of Nakajima quiver varieties and has a string theory origin.

      Part of the interest in the qKZ monodromy problem is that its solution leads to integrable lattice models, in parallel to how monodromy matrices of the KZ equation lead to knot invariants. Thus, our solution of the problem leads to a new, geometric approach, to integrable lattice models. There are two other approaches to integrable lattice models, due to Nekrasov and Shatashvili and to Costello, Witten and Yamazaki. I’ll describe joint work with Nikita Nekrasov which explains how string theory unifies the three approaches to integrable lattice models.

      Lecture 2:

       

       

       

       

       

      April 10, 2019

      Title: “Lesson on Knot Categorification”

       

      Abstract: An old problem is to find a unified approach to the knot categorification problem. The new string theory perspective on the qKZ equation I described in the first talk can be used to derive two geometric approaches to the problem.

      The first approach is based on a category of B-type branes on resolutions of slices in affine Grassmannians. The second is based on a category of A-branes in a Landau-Ginzburg theory. The relation between them is two dimensional (equivariant) mirror symmetry. String theory also predicts that a third approach to categorification, based on counting solutions to five dimensional Haydys-Witten equations, is equivalent to the first two.

      This talk is mostly based on joint work with Andrei Okounkov.

       

      Information about last year’s Math Science Bott lecture can be found here. 

      Aganagic

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      03-28-2016 Mathematical Physics Seminar
      4:08 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-06-2016 Random Matrix & Probability Theory
      4:10 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-30-2016 Random Matrix & Probability Theory Seminar
      4:11 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-14-2016 Evolution Equations Seminar
      4:13 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-12-2016 Geometric Analysis Seminar
      4:14 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Special Seminar
      4:15 pm
      11/01/2019
    • Seminars
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      03-31-2016 Evolution Equations Seminar
      4:15 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      4:15 pm-5:15 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      Duality String Seminar, Thursdays
      4:15 pm-6:00 pm
      11/01/2019-10/12/2016

      The Duality String  Seminar is held every Thursday at 4:15pm in Jefferson Lab, 453.

      For details, please visit the website.

      * The Duality String Seminar is sponsored by the Center of Mathematical Sciences and Applications’ Cheng Yu-Tong Fund, for Research at the Interface of Mathematics and Physics.

    • Seminars
      Seminars Colloquia & Seminar
      04-04-2016 Mathematical Physics Seminar
      4:20 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      04-05-2016 Geometric Analysis Seminar
      4:21 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      04-11-2016 Mathematical Physics Seminar
      4:22 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      04-07-2016 Evolution Equations Seminar
      4:24 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
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      04-06-2016 Seminar on General Relativity
      4:25 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-11-2016 Random Matrix & Probability Theory Seminar
      4:28 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-13-2016 General Relativity Seminar
      4:29 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:30 pm
      11/01/2019
    • Seminars
      4:30 pm-5:30 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2/14/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      Colloquium Colloquia & Seminar
      2/20/2019 Colloquium
      4:30 pm-5:00 pm
      11/01/2019
    • Colloquium
      Colloquium Colloquia & Seminar
      2/13/2019 Colloquium
      4:30 pm-5:00 pm
      11/01/2019
    • Seminars
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Seminars
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      1/30/2019 Colloquium
      4:30 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/4/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      11/01/2019
    • Seminars
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      10/3/2019 RM & PT Seminar
      4:30 pm-5:00 pm
      11/01/2019
    • Seminars
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      4/24/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Seminars
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      10/9/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Seminars
      4:30 pm-5:30 pm
      11/01/2019
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      4/17/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
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      10/2/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      9/18/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      04-20-2016 General Relativity Seminar
      4:30 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      3/20/2019 Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm-5:30 pm
      11/01/2019
    • Colloquium
      4:30 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3/28/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      04-18-2016 Social Science Application Forum
      4:31 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:33 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-19-2016 Geometric Analysis Seminar
      4:33 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-18-2016 Mathematical Physics Seminar
      4:34 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:34 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-21-2016 Evolution Equations Seminar
      4:35 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:36 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-20-2016 Random Matrix & Probability Theory Seminar
      4:37 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-26-2016 Geometric Analysis Seminar
      4:38 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:39 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-25-2016 Mathematical Physics Seminar
      4:39 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      4:41 pm
      11/01/2019
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-27-2016 Random Matrix & Probability Theory Seminar
      4:42 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-27-2016 General Relativity Seminar
      4:44 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-28-2016 CMSA Special Seminar
      4:45 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-28-2016 Evolution Equations Seminar
      4:46 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-04-2016 General Relativity Seminar
      4:48 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-29-2016 CMSA Special Seminar
      4:49 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      05-02-2016 Mathematical Physics Seminar
      4:50 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-05-2016 Evolution Equations Seminar
      4:51 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-25-2016 General Relativity Seminar
      4:52 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      4:54 pm
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
      4:58 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      5:00 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      2018 HMS Focused Lecture Series
      5:00 pm
      11/01/2019

      As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester. The lectures will take place  on Tuesdays and Thursdays in the CMSA Building, 20 Garden Street, Room G10.

      The schedule will be updated below.

      DateSpeakerTitle/Abstract
      January 23, 25, 30 and February 1 

      3-5pm

      *Room G10*

      Ivan Losev 

      (Northeastern)

      Title: BGG category O: towards symplectic duality 

      Abstract: We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson, Ginzburg and Soergel on the Koszul duality for such categories, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting.

      Approximate (optimistic) plan of the lectures:

      1) Preliminaries and BGG category O.

      2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem.

      3) Localization theorem continued. Soergel modules.

      4) Koszul algebras and Koszul duality for categories O.

      Time permitting: other instances of Symplectic duality.

      Prerequisites:

      Semi-simple Lie algebras and their finite dimensional representation theory.

      Some  Algebraic geometry. No prior knowledge of category O/ Geometric

      Representation theory is assumed.

      Scanned from a Xerox Multifunction Device

      February 27, 

      and March 1

      3-5pm

      Colin Diemer 

      (IHES)

      Title: Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS. 

      Abstract: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau’s the role of the mirror map is well-appreciated. In these talks I’ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov, Kontsevich, Pantev), the interplay of the topology  of LG models with autoequivalence relations in the Calabi-Yau setting, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we’ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster).

      March 6 and 8 

      4-5pm

      Adam Jacob 

      (UC Davis)

      Title: The deformed Hermitian-Yang-Mills equation 

      Abstract: In this series I will discuss the deformed Hermitian-Yang-Mills equation, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible, and cover joint work with T.C. Collins and S.-T. Yau.

      March 6, 8, 13, 15 

      3-4pm

      Dmytro Shklyarov 

      (TU Chemnitz)

      Title: On categories of matrix factorizations and their homological invariants 

      Abstract: The talks will cover the following topics:

      1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements.

      2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the “classical” mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models.

      3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data, namely, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type, open varieties, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which, just as their non-equivariant cousins, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds.

      April 10 & 12 

      3-4pm

      Mauricio Romo 

      (IAS)

      Title: Gauged Linear Sigma Models, Supersymmetric Localization and Applications 

      Abstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with  CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs).

      Lecture notes

      April 17, 19, 26 

      3-5pm

      Andrew  Harder 

      (University of Miami)

      Title: Perverse sheaves of categories on surfaces 

      Abstract: Perverse sheaves of categories on a Riemann surface S are systems of categories and functors which are encoded by a graphs on S, and which satisfy conditions that resemble the classical characterization of perverse sheaves on a disc.

      I’ll review the basic ideas behind Kapranov and Schechtman’s notion of a perverse schober and generalize this to perverse sheaves of categories on a punctured Riemann surface. Then I will give several examples of perverse sheaves of categories in both algebraic geometry, symplectic geometry, and category theory. Finally, I will describe how one should be able to use related ideas to prove homological mirror symmetry for certain noncommutative deformations of projective 3-space.

       

      May 15, 17 

      1-3pm

      Charles Doran 

      (University of Alberta)

      Lecture One:
      Title: Picard-Fuchs uniformization and Calabi-Yau geometry
      Abstract:
      Part 1:  We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties, with emphasis on Calabi-Yau manifolds.  Specializing to the case of K3 surfaces, we explore general results on “Picard-Fuchs uniformization” of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces.  As an application, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces.
      Part 2:  We next consider families with one natural complex structure modulus, (e.g., elliptic curves, rank 19 K3 surfaces, b_1=4 Calabi-Yau threefolds, …), where the Picard-Fuchs equations are ODEs.  What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces?  Using Hodge theory and parabolic cohomology, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space.  In particular, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau.

       

      Lecture Two:
      Title: Calabi-Yau fibrations: construction and classification
      Abstract:

      Part 1:  Codimension one Calabi-Yau submanifolds induce fibrations, with the periods of the total space relating to those of the fibers and the structure of the fibration.  We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals.

      Part 2:  We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces.  The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces.  When the total space of the fibration is a Calabi-Yau threefold, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations.  The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1.

    • CMSA EVENT: Noga Alon Public Talk, 9-7-17
      5:00 pm-6:00 pm
      11/01/2019

      Noga Alon (Tel Aviv University) will be giving a public talk on September 7, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

      Title: Graph Coloring: Local and Global

      Abstract: Graph Coloring is arguably the most popular subject in Discrete Mathematics, and its combinatorial, algorithmic and computational aspects have been studied intensively. The most basic notion in the area, the chromatic number of a graph, is an inherently global property. This is demonstrated by the hardness of computation or approximation of this invariant as well as by the existence of graphs with arbitrarily high chromatic number and no short cycles. The investigation of these graphs had a profound impact on Graph Theory and Combinatorics. It combines combinatorial, probabilistic, algebraic and topological techniques with number theoretic tools. I will describe the rich history of the subject focusing on some recent results.

    • CMSA EVENT: 2017 Ding Shum Lecture
      5:00 pm-6:00 pm
      11/01/2019
      1 Oxford Street, Cambridge MA 02138

      Leslie Valiant will be giving the inaugural talk of the Ding Shum Lectures on Tuesday, October 10 at 5:00 pm in Science Center Hall D, Cambridge, MA.

      Learning as a Theory of Everything

      Abstract: We start from the hypothesis that all the information that resides in living organisms was initially acquired either through learning by an individual or through evolution. Then any unified theory of evolution and learning should be able to characterize the capabilities that humans and other living organisms can possess or acquire. Characterizing these capabilities would tell us about the nature of humans, and would also inform us about feasible targets for automation. With this purpose we review some background in the mathematical theory of learning. We go on to explain how Darwinian evolution can be formulated as a form of learning. We observe that our current mathematical understanding of learning is incomplete in certain important directions, and conclude by indicating one direction in which further progress would likely enable broader phenomena of intelligence and cognition to be realized than is possible at present.

       

    • CMSA EVENT: Jennifer Chayes Public Talk, 11-02-17
      5:00 pm-6:00 pm
      11/01/2019

      Jennifer Chayes (Microsoft Research) will be giving a public talk on November 02, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

      Title: Network Science: From the Online World to Cancer Genomics

      Abstract: Everywhere we turn these days, we find that networks can be used to describe relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage many human diseases. In this talk, I look quite generally at some of the models we are using to describe these networks, processes we are studying on the networks, algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. I’ll discuss in some detail particular applications to cancer genomics, applying network algorithms to suggest possible drug targets for certain kinds of cancer.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      05-11-2016 Random Matrix & Probability Theory Seminar
      5:00 pm
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
      5:02 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      06-01-2016 Random Matrix & Probability Theory Seminar
      5:03 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      06-08-2016 Random Matrix & Probability Theory Seminar
      5:04 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      07-12-2016 Chinese Economy Seminar
      5:06 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      07-19-2016 Chinese Economy Seminar
      5:07 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      08-02-2016 China Gazetteer Seminar
      5:08 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-12-2016 Mathematical Physics Seminar
      5:10 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-19-2016 Mathematical Physics Seminar
      5:11 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-21-2016 Random Matrix & Probability Theory Seminar
      5:13 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      Colloquium Colloquia & Seminar
      3/27/2019 Colloquium
      5:15 pm-6:15 pm
      11/01/2019
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-23-2018 Math Physics
      5:15 pm
      11/01/2019

      No additional detail for this event.

    • Colloquium
      Colloquium Colloquia & Seminar
      2/13/2019 Colloquium
      5:15 pm-6:15 pm
      11/01/2019
    • Seminars
      Seminars Colloquia & Seminar
      4-16-2018 Social Science Applications Forum
      5:16 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-20-2018 Social Science Applications Forum
      5:18 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-26-16 Mathematical Physics Seminar
      5:32 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-28-2016 Random Matrix & Probability Theory Seminar
      5:35 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      5:36 pm
      11/01/2019

      As part of the Program on Topological Aspects of Condensed Mattera weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

      DateSpeakerTitle/Abstract
      8/29/2018Zeng-Cheng GuTitle: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory

      Abstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.

      9/10/2018Dominic Else, MIT

      Video

      Title: Phases and topology in periodically driven (Floquet) systems

      Abstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.

      9/17/2018Adrian Po, MIT

      Video

      Title: A modern solution to the old problem of symmetries in band theory

      Abstract: There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants.

      9/24/2018Maxim MetlitskiTitle: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs

      Abstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.

      10/1/2018Cancelled
      10/9/2018

      Tuesday

      3:00-4:30pm

      Sagar VijayTitle: Fracton Phases of Matter

      Abstract:  Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped, point-like excitations (“fractons”) that are strictly immobile at zero temperature, and by degenerate ground-states that are locally indistinguishable.  Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions, and these states of matter are a gateway for exploring mechanisms for quantum information storage, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases, constructions of these states using well-studied two-dimensional topological phases, and a model in which the fracton excitations carry a protected internal degeneracy, which provides a natural generalization of non-Abelian anyons to three spatial dimensions.  I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.

      10/15/2018Ethan LakeTitle: A primer on higher symmetries

      Abstract: The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.

      10/22/2018

      Room G02

      Yin-Chen He, PerimeterTitle: Emergent QED3 and QCD3 in condensed matter system

      Abstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.

      10/29/2018Dominic Williamson, Yale

      Video

      Title: Symmetry and topological order in tensor networks

      Abstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.

      11/13/2018

      Tuesday

      3:00-4:30pm

      Jason Alicea, CaltechTitle: Time-crystalline topological superconductors
      11/19/2018X. G. Wen, MIT

      Video

      Title: A classification of 3+1D topological orders

      Abstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.

      12/3/2018

      *Room G02*

      Claudio Chamon, Boston UniversityTitle: Many-body scar states with topological properties in 1D, 2D, and 3D.

      Abstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies.

      12/10/2018

      Room G02

      Anders Sandvik, Boston University and Institute of Physics, CAS, BeijingTitle: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets

      Abstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.

      1/8/2019Lukasz Fidkowski, Univ. of Washington

      Video

      Title: Non-trivial quantum cellular automata in 3 dimensions

      Abstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom.  This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.

      3/18/2019Ari Turner, Technion

      Video

      Title:  Trapping Excitations at Phantasmagoric Wave Vectors

      Abstract:  This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this, and also introduce “finite fields”, which are the number systems one needs to define exponentials mod. 2.

      4/1/2019Yi-Zhuang You (UCSD)Title: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points

      Abstract: Noether’s theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s  theorem at the deconfined quantum critical point (DQCP), which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.

      4/8/2019Adam Nahum (Oxford)Title: Emergent statistical mechanics of entanglement in random unitary circuits

      Abstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.

      4/16/2019

      Lyman 425

      1:30pm

      Xie Chen (Calthech)Title: Foliated Fracton Order

      Abstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk, I will present a new framework, which we call the “foliated fracton order”, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models, but also points to the direction of search for interesting new features.

      4/24/2019

      10:30am

      Michael Freedman (Microsoft Station Q)

      Video

      Title: Quantum cellular automata in higher dimensions

      Abstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.

      4/26/2019

      10:30am

      Maissam Barkeshli (University of Maryland)

      Video

      Title: Relative anomalies in (2+1)D symmetry enriched topological states

      Abstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.

      5/3/2019Yuan-Ming Lu (Ohio State)Title: Spontaneous symmetry breaking from anyon condensation

      Abstract: In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

      5/9/2019

      10:30am

      Michael Zaletel (UC Berkeley)Title: Three-partite entanglement in CFTs and chiral topological orders

      Abstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement, multi-partite entanglement is far richer, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure, the “entanglement of purification,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders, and solicit the audience’s help in proving or disproving it.

      5/28/2019

      10:30am

      Masaki Oshikawa (U Tokyo)Title: Gauge invariance, polarization, and conductivity

       

      Abstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors, and also to general constraints on the electric conductivity.

      7/18/2019Eslam Khalaf (Harvard)

      Title: Dynamical correlations in anomalous disordered wires

      Abstract: In a (multichannel) disordered wire, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case, the classical dynamics are described by diffusion + drift, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.
      The problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.
      The mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.
    • Seminars
      Seminars Colloquia & Seminar
      Spacetime and Quantum Mechanics Seminar
      5:38 pm
      11/01/2019

      As part of the program on Spacetime and Quantum Mechanics, the CMSA will be hosting a weekly seminar on Thursdays at 2:30pm in room G10.

      DateSpeakerTitle/Abstract
      9/12/2019Pasha Pylyavskyy (University of Minnesota)Title: Vector-relation configurations and plabic graphs
      19/18/2019

      2:00pm

      G02

      Francis Brown (University of Oxford)Title: Amplitudes, Polylogs and Moduli Spaces
      9/19/2019Chuck Doran (University of Alberta)Title: Calabi-Yau geometry of the N-loop sunset Feynman integrals

      Abstract: I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals.

      Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli.

      These include: (1) an iterated fibration structure which allows one to “bootstrap” both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (“jump loci”) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via “creative telescoping”; and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties.

      Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev.

      9/26/2019Tomasz Taylor (Northeastern)Title: Celestial Amplitudes
      10/3/2019Simon Caron-Huot (McGill)Title: Poincare Duals of Feynman Integrals
      10/10/2019

      3:30pm

      Yutin Huang (National Taiwan University)Title: Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian
      10/15/2019

      Tuesday

      3:30pm

       

      Sergey Fomin (Univ. of Michigan)

       

      Title: “Morsifications and mutations” (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston). 
      10/18/2019

      Friday 

      G02

      Sebastian Franco (The City College of New York)Title: Graded quivers, generalized dimer models, and topic geometry
      10/31/2019Junjie Rao (Albert Einstein Institute)Title: All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
      11/1/2019

      SC 232

      1:30pm

      George Lusztig (MIT)Title: Total positivity in Springer fibres
      11/12/2019

      Tuesday

      G02

      3:30pm

       

      Pierpaolo Mastrolia (University of Padova)

      Title: Feynman Integrals and Intersection Theory
      11/14/2019

      G02

      Pierpaolo Mastrolia (University of Padova)Title: Feynman Integrals and Intersection Theory Pt. II
      11/21/2019Cristian Vergu (Niels Bohr Institute)Title: The Octagonal Alphabet
      11/26/2019Stephan Stieberger (IAS)Title: Strings on the Celestial Sphere
      12/4/2019Hadleigh Frost (Oxford)Title: BCJ numerators, $\mathcal{M}_{0,n}$, and ABHY

      Abstract: We relate the BCJ numerator Jacobi property to the classical fact that the top homology group of $\mathcal{M}_{0,n}$ is isomorphic to a component of the free Lie algebra. We describe ways to get BCJ numerators, and caution that the BCJ Jacobi property doesn’t imply the existence of what has been called a ‘kinematic algebra.’

       12/5/2019David Kosower (IAS)Title: From scattering amplitudes to classical observables
      12/10/2019Ramis Movassagh (MIT)Title: Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law

      Abstract: In recent years, there has been a surge of activities in proposing “exactly solvable” quantum spin chains with surprising high amount of ground state entanglement–exponentially more than the critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $\sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and ‘generic’ aspects of local spin chains.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-05-2016 Random Matrix & Probability Theory Seminar
      5:41 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/10/2018 Math-Physics Seminar
      5:41 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      5:42 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3/14/2019 Random Matrix and Probability Theory Seminar
      5:45 pm
      11/01/2019
    • Seminars
      5:48 pm
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
      5:52 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/17/2018 Math-Physics Seminar
      5:53 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/24/2018 Math-Physics Seminar
      5:55 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      5:56 pm
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
      5:59 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Workshop on Additive Combinatorics, Oct. 2-6, 2017
      6:00 pm-6:01 pm
      11/01/2019-10/06/2017

      The workshop on additive combinatorics will take place October 2-6, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      Additive combinatorics is a mathematical area bordering on number theory, discrete mathematics, harmonic analysis and ergodic theory. It has achieved a number of successes in pure mathematics in the last two decades in quite diverse directions, such as:

      • The first sensible bounds for Szemerédi’s theorem on progressions (Gowers);
      • Linear patterns in the primes (Green, Tao, Ziegler);
      • Construction of expanding sets in groups and expander graphs (Bourgain, Gamburd);
      • The Kakeya Problem in Euclidean harmonic analysis (Bourgain, Katz, Tao).

      Ideas and techniques from additive combinatorics have also had an impact in theoretical computer science, for example

      • Constructions of pseudorandom objects (eg. extractors and expanders);
      • Constructions of extremal objects (eg. BCH codes);
      • Property testing (eg. testing linearity);
      • Algebraic algorithms (eg. matrix multiplication).

      The main focus of this workshop will be to bring together researchers involved in additive combinatorics, with a particular inclination towards the links with theoretical computer science. Thus it is expected that a major focus will be additive combinatorics on the boolean cube (Z/2Z)^n , which is the object where the exchange of ideas between pure additive combinatorics and theoretical computer science is most fruitful. Another major focus will be the study of pseudorandom phenomena in additive combinatorics, which has been an important contributor to modern methods of generating provably good randomness through deterministic methods. Other likely topics of discussion include the status of major open problems (the polynomial Freiman-Ruzsa conjecture, inverse theorems for the Gowers norms with bounds, explicit correlation bounds against low degree polynomials) as well as the impact of new methods such as the introduction of algebraic techniques by Croot–Pach–Lev and Ellenberg–Gijswijt.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Ben GreenSwastik KoppartyRyan O’DonnellTamar Ziegler.

      Monday, October 2

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast 
      9:30-10:20amJacob FoxTower-type bounds for Roth’s theorem with popular differences

      Abstract: A famous theorem of Roth states that for any $\alpha > 0$ and $n$ sufficiently large in terms of $\alpha$, any subset of $\{1, \dots, n\}$ with density $\alpha$ contains a 3-term arithmetic progression. Green developed an arithmetic regularity lemma and used it to prove that not only is there one arithmetic progression, but in fact there is some integer $d > 0$ for which the density of 3-term arithmetic progressions with common difference $d$ is at least roughly what is expected in a random set with density $\alpha$. That is, for every $\epsilon > 0$, there is some $n(\epsilon)$ such that for all $n > n(\epsilon)$ and any subset $A$ of $\{1, \dots, n\}$ with density $\alpha$, there is some integer $d > 0$ for which the number of 3-term arithmetic progressions in $A$ with common difference $d$ is at least $(\alpha^3-\epsilon)n$. We prove that $n(\epsilon)$ grows as an exponential tower of 2’s of height on the order of $\log(1/\epsilon)$. We show that the same is true in any abelian group of odd order $n$. These results are the first applications of regularity lemmas for which the tower-type bounds are shown to be necessary.

      The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

      10:20-11:00amCoffee Break 
      11:00-11:50amYufei ZhaoTower-type bounds for Roth’s theorem with popular differences

      Abstract:  Continuation of first talk by Jacob Fox. The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

      12:00-1:30pmLunch 
      1:30-2:20pmJop BriëtLocally decodable codes and arithmetic progressions in random settings

      Abstract: This talk is about a common feature of special types of error correcting codes, so-called locally decodable codes (LDCs), and two problems on arithmetic progressions in random settings, random differences in Szemerédi’s theorem and upper tails for arithmetic progressions in a random set in particular. It turns out that all three can be studied in terms of the Gaussian width of a set of vectors given by a collection of certain polynomials. Using a matrix version of the Khintchine inequality and a lemma that turns such polynomials into matrices, we give an alternative proof for the best-known lower bounds on LDCs and improved versions of prior results due to Frantzikinakis et al. and Bhattacharya et al. on arithmetic progressions in the aforementioned random settings.

      Joint work with Sivakanth Gopi

      2:20-3:00pmCoffee Break 
      3:00-3:50pmFernando Shao

      Large deviations for arithmetic progressions

      Abstract: We determine the asymptotics of the log-probability that the number of k-term arithmetic progressions in a random subset of integers exceeds its expectation by a constant factor. This is the arithmetic analog of subgraph counts in a random graph. I will highlight some open problems in additive combinatorics that we encountered in our work, namely concerning the “complexity” of the dual functions of AP-counts.

      4:00-6:00pmWelcome Reception

      Tuesday, October 3

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amEmanuele ViolaInterleaved group products

      Authors: Timothy Gowers and Emanuele Viola

      Abstract: Let G be the special linear group SL(2,q). We show that if (a1,a2) and (b1,b2) are sampled uniformly from large subsets A and B of G^2 then their interleaved product a1 b1 a2 b2 is nearly uniform over G. This extends a result of Gowers (2008) which corresponds to the independent case where A and B are product sets. We obtain a number of other results. For example, we show that if X is a probability distribution on G^m such that any two coordinates are uniform in G^2, then a pointwise product of s independent copies of X is nearly uniform in G^m, where s depends on m only. Similar statements can be made for other groups as well.

      These results have applications in computer science, which is the area where they were first sought by Miles and Viola (2013).

      10:20-11:00amCoffee Break
      11:00-11:50amVsevolod LevOn Isoperimetric Stability

      Abstract: We show that a non-empty subset of an abelian group with a small edge boundary must be large; in particular, if $A$ and $S$ are finite, non-empty subsets of an abelian group such that $S$ is independent, and the edge boundary of $A$ with respect to $S$ does not exceed $(1-c)|S||A|$ with a real $c\in(0,1]$, then $|A|\ge4^{(1-1/d)c|S|}$, where $d$ is the smallest order of an element of $S$. Here the constant $4$ is best possible.

      As a corollary, we derive an upper bound for the size of the largest independent subset of the set of popular differences of a finite subset of an abelian group. For groups of exponent $2$ and $3$, our bound translates into a sharp estimate for the additive  dimension of the popular difference set.

      We also prove, as an auxiliary result, the following estimate of possible independent interest: if $A\subseteq{\mathbb Z}^n$ is a finite, non-empty downset, then, denoting by $w(z)$ the number of non-zero components of the vector $z\in\mathbb{Z}^n$, we have   $$ \frac1{|A|} \sum_{a\in A} w(a) \le \frac12\, \log_2 |A|. $$

      12:00-1:30pmLunch
      1:30-2:20pmElena GrigorescuNP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem

      Abstract: I will discuss the complexity of decoding Reed-Solomon codes, and some results establishing NP-hardness for asymptotically smaller decoding radii than the maximum likelihood decoding radius. These results follow from the study of a generalization of the classical Subset Sum problem to higher moments, which may be of independent interest. I will further discuss a connection with the Prouhet-Tarry-Escott problem studied in Number Theory, which turns out to capture a main barrier in extending our techniques to smaller radii.

      Joint work with Venkata Gandikota and Badih Ghazi.

      2:20-3:00pmCoffee Break
      3:00-3:50pmSean PrendivillePartition regularity of certain non-linear Diophantine equations.

      Abstract:  We survey some results in additive Ramsey theory which remain valid when variables are restricted to sparse sets of arithmetic interest, in particular the partition regularity of a class of non-linear Diophantine equations in many variables.

      Wednesday, October 4

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast 
      9:30-10:20amOlof SisaskBounds on capsets via properties of spectra

      Abstract: A capset in F_3^n is a subset A containing no three distinct elements x, y, z satisfying x+z=2y. Determining how large capsets can be has been a longstanding problem in additive combinatorics, particularly motivated by the corresponding question for subsets of {1,2,…,N}. While the problem in the former setting has seen spectacular progress recently through the polynomial method of Croot–Lev–Pach and Ellenberg–Gijswijt, such progress has not been forthcoming in the setting of the integers. Motivated by an attempt to make progress in this setting, we shall revisit the approach to bounding the sizes of capsets using Fourier analysis, and in particular the properties of large spectra. This will be a two part talk, in which many of the ideas will be outlined in the first talk, modulo the proof of a structural result for sets with large additive energy. This structural result will be discussed in the second talk, by Thomas Bloom, together with ideas on how one might hope to achieve Behrend-style bounds using this method.

      Joint work with Thomas Bloom.

      10:20-11:00amCoffee Break 
      11:00-11:50amThomas BloomBounds on capsets via properties of spectra

      This is a continuation of the previous talk by Olof Sisask.

      12:00-1:30pmLunch 
      1:30-2:20pmHamed HatamiPolynomial method and graph bootstrap percolation

      Abstract: We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori and multidimensional grids (in particular hypercubes). The former answers a question of Morrison and Noel, and the latter provides an alternative and simpler proof for one of their main results. This is based on a joint work with Lianna Hambardzumyan and Yingjie Qian.

      2:20-3:00pmCoffee Break
      3:00-3:50pmArnab BhattacharyyaAlgorithmic Polynomial Decomposition

      Abstract: Fix a prime p. Given a positive integer k, a vector of positive integers D = (D_1, …, D_k) and a function G: F_p^k → F_p, we say a function P: F_p^n → F_p admits a (k, D, G)-decomposition if there exist polynomials P_1, …, P_k: F_p^n -> F_p with each deg(P_i) <= D_i such that for all x in F_p^n, P(x) = G(P_1(x), …, P_k(x)). For instance, an n-variate polynomial of total degree d factors nontrivially exactly when it has a (2, (d-1, d-1), prod)-decomposition where prod(a,b) = ab.

      When show that for any fixed k, D, G, and fixed bound d, we can decide whether a given polynomial P(x_1, …, x_n) of degree d admits a (k,D,G)-decomposition and if so, find a witnessing decomposition, in poly(n) time. Our approach is based on higher-order Fourier analysis. We will also discuss improved analyses and algorithms for special classes of decompositions.

      Joint work with Pooya Hatami, Chetan Gupta and Madhur Tulsiani.

      Thursday, October 5

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amMadhur TulsianiHigher-order Fourier analysis and approximate decoding of Reed-Muller codes

       Abstract: Decomposition theorems proved by Gowers and Wolf provide an appropriate notion of “Fourier transform” for higher-order Fourier analysis. I will discuss some questions and techniques that arise from trying to develop polynomial time algorithms for computing these decompositions.

      I will discuss constructive proofs of these decompositions based on boosting, which reduce the problem of computing these decompositions to a certain kind of approximate decoding problem for codes. I will also discuss some earlier and recent works on this decoding problem.

      Based on joint works with Arnab Bhattacharyya, Eli Ben-Sasson, Pooya Hatami, Noga Ron-Zewi and Julia Wolf.

      10:20-11:00amCoffee Break
      11:00-11:50amJulia WolfStable arithmetic regularity

      The arithmetic regularity lemma in the finite-field model, proved by Green in 2005, states that given a subset A of a finite-dimensional vector space over a prime field, there exists a subspace H of bounded codimension such that A is Fourier-uniform with respect to almost all cosets of H. It is known that in general, the growth of the codimension of H is required to be of tower type depending on the degree of uniformity, and that one must allow for a small number of non-uniform cosets.

      Our main result is that, under a natural model-theoretic assumption of stability, the tower-type bound and non-uniform cosets in the arithmetic regularity lemma are not necessary.  Specifically, we prove an arithmetic regularity lemma for k-stable subsets in which the bound on the codimension of the subspace is a polynomial (depending on k) in the degree of uniformity, and in which there are no non-uniform cosets.

      This is joint work with Caroline Terry.

      12:00-1:30pmLunch 
      1:30-2:20pmWill Sawin

      Constructions of Additive Matchings

      Abstract: I will explain my work, with Robert Kleinberg and David Speyer, constructing large tri-colored sum-free sets in vector spaces over finite fields, and how it shows that some additive combinatorics problems over finite fields are harder than corresponding problems over the integers. 

      2:20-3:00pmCoffee Break
      3:00-3:50pmMei-Chu ChangArithmetic progressions in multiplicative groups of finite fields

      Abstract:   Let G be a multiplicative subgroup of the prime field F_p of size |G|> p^{1-\kappa} and r an arbitrarily fixed positive integer. Assuming \kappa=\kappa(r)>0 and p large enough, it is shown that any proportional subset A of G contains non-trivial arithmetic progressions of length r.

      Friday, October 6

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amAsaf FerberOn a resilience version of the Littlewood-Offord problem

      Abstract:  In this talk we consider a resilience version of the classical Littlewood-Offord problem. That is, consider the sum X=a_1x_1+…a_nx_n, where the a_i-s are non-zero reals and x_i-s are i.i.d. random variables with     (x_1=1)= P(x_1=-1)=1/2. Motivated by some problems from random matrices, we consider the question: how many of the x_i-s  can we typically allow an adversary to change without making X=0? We solve this problem up to a constant factor and present a few interesting open problems.

      Joint with: Afonso Bandeira (NYU) and Matthew Kwan (ETH, Zurich).

      10:20-11:00amCoffee Break
      11:00-11:50amKaave HosseiniProtocols for XOR functions and Entropy decrement

      Abstract: Let f:F_2^n –> {0,1} be a function and suppose the matrix M defined by M(x,y) = f(x+y) is partitioned into k monochromatic rectangles.  We show that F_2^n can be partitioned into affine subspaces of co-dimension polylog(k) such that f is constant on each subspace. In other words, up to polynomial factors, deterministic communication complexity and parity decision tree complexity are equivalent.

      This relies on a novel technique of entropy decrement combined with Sanders’ Bogolyubov-Ruzsa lemma.

      Joint work with Hamed Hatami and Shachar Lovett

      12:00-1:30pmLunch
      1:30-2:20pmGuy Kindler

      From the Grassmann graph to Two-to-Two games

      Abstract: In this work we show a relation between the structure of the so called Grassmann graph over Z_2 and the Two-to-Two conjecture in computational complexity. Specifically, we present a structural conjecture concerning the Grassmann graph (together with an observation by Barak et. al., one can view this as a conjecture about the structure of non-expanding sets in that graph) which turns out to imply the Two-to-Two conjecture.

      The latter conjecture its the lesser-known and weaker sibling of the Unique-Games conjecture [Khot02], which states that unique games (a.k.a. one-to-one games) are hard to approximate. Indeed, if the Grassmann-Graph conjecture its true, it would also rule out some attempts to refute the Unique-Games conjecture, as these attempts provide potentially efficient algorithms to solve unique games, that would actually also solve two-to-two games if they work at all.

      These new connections between the structural properties of the Grassmann graph and complexity theoretic conjectures highlight the Grassmann graph as an interesting and worthy object of study. We may indicate some initial results towards analyzing its structure.

      This is joint work with Irit Dinur, Subhash Khot, Dror Minzer, and Muli Safra.

    • CMSA EVENT: Current Developments In Mathematics 2018
      6:00 pm-5:00 pm
      11/01/2019-11/17/2018
      CDM2018

      Current Developments in Mathematics 2018 Conference.

      Friday, Nov. 16, 2018 2:15 pm – 6:00 pm

      Saturday, Nov. 17, 2018  9:00 am – 5:00 pm

      Harvard University Science Center, Hall B

      Visit the conference page here 

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/01/2018 Math-Physics Seminar
      6:01 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Fluid turbulence and Singularities of the Euler/ Navier Stokes equations
      6:02 pm
      11/01/2019-03/15/2018
      Fluid turbulence

      The Workshop on Fluid turbulence and Singularities of the Euler/ Navier Stokes equations will take place on March 13-15, 2019. This is the first of two workshop organized by Michael Brenner, Shmuel Rubinstein, and Tom Hou. The second, Machine Learning for Multiscale Model Reduction, will take place on March 27-29, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

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

      List of registrants

      Speakers: 

    • General Relativity Seminar
      6:03 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/08/2018 Math-Physics Seminar
      6:04 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      6:05 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Blockchain Conference
      6:05 pm
      11/01/2019-01/25/2018
      Blockchain

      On January 24-25, 2019 the Center of Mathematical Sciences will be hosting a conference on distributed-ledger (blockchain) technology. The conference is intended to cover a broad range of topics, from abstract mathematical aspects (cryptography, game theory, graph theory, theoretical computer science) to concrete applications (in accounting, government, economics, finance, management, medicine). The talks will take place in Science Center, Hall D.

      https://youtu.be/FyKCCutxMYo

      List of registrants

      Photos

      Speakers: 

    • Special Seminar
      6:06 pm
      11/01/2019

      No additional detail for this event.

    • CMSA EVENT: Workshop on Algebraic Methods in Combinatorics
      6:07 pm
      11/01/2019-11/17/2017

      The workshop on Algebraic Methods in Combinatorics will take place November 13-17, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      The main focus of the workshop is the application of algebraic method to study problems in combinatorics.  In recent years there has been a large number of results in which the use of algebraic technique has resulted in significant improvements to long standing open problems. Such problems include the finite field Kakeya problem, the distinct distance problem of Erdos and, more recently, the cap-set problem. The workshop will include talks on all of the above mentioned problem as well as on recent development in related areas combining combinatorics and algebra.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Zeev DvirLarry Guth, and Shubhangi Saraf.

      Click here for a list of registrants.

      Monday, Nov. 13

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Jozsef Solymosi

       

      On the unit distance problem

      Abstract: Erdos’ Unit Distances conjecture states that the maximum number of unit distances determined by n points in the plane is almost linear, it is O(n^{1+c}) where c goes to zero as n goes to infinity. In this talk I will survey the relevant results and propose some questions which would imply that the maximum number of unit distances is o(n^{4/3}). 

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

       

      Orit RazIntersection of linear subspaces in R^d and instances of the PIT problem 

      Abstract: In the talk I will tell about a new deterministic, strongly polynomial time algorithm which can be viewed in two ways. The first is as solving a derandomization problem, providing a deterministic algorithm to a new special case of the PIT (Polynomial Identity Testing) problem. The second is as computing the dimension of the span of a collection of flats in high dimensional space. The talk is based on a joint work with Avi Wigderson.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Andrew Hoon Suk

      Ramsey numbers: combinatorial and geometric

      Abstract:  In this talk, I will discuss several results on determining the tower growth rate of Ramsey numbers arising in combinatorics and in geometry.  These results are joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Janos Pach, and Benny Sudakov.

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Josh Zahl

      Cutting curves into segments and incidence geometry

      4:00-6:00pmWelcome Reception

      Tuesday, Nov. 14

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Péter Pál Pach

      Polynomials, rank and cap sets

      AbstractIn this talk we will look at a new variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like $\mathbb{Z}_4^n$ and $\mathbb{F}_q^n$ are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets and mention further applications of the method.

      10:30-11:00amCoffee Break
      11:00-12:00pmJordan Ellenberg

      The Degeneration Method

      Abstract:  In algebraic geometry, a very popular way to study (nice, innocent, nonsingular) varieties is to degenerate them to (weird-looking, badly singular, nonreduced) varieties (which are actually not even varieties but schemes.)  I will talk about some results in combinatorics using this approach (joint with Daniel Erman) and some ideas for future applications of the method.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Larry GuthThe polynomial method in Fourier analysis

      Abstract: This will be a survey talk about how the polynomial method helps to understand problems in Fourier analysis.  We will review some applications of the polynomial method to problems in combinatorial geometry.  Then we’ll discuss some problems in Fourier analysis, explain the analogy with combinatorial problems, and discuss how to adapt the polynomial method to the Fourier analysis setting.

       

      2:30-3:00pm

      Coffee Break
      3:00-4:00pmOpen Problem

      Wednesday, Nov. 15

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

       

      Avi Wigderson

      The “rank method” in arithmetic complexity: Lower bounds and barriers to lower bounds

      Abstract: Why is it so hard to find a hard function? No one has a clue! In despair, we turn to excuses called barriers. A barrier is a collection of lower bound techniques, encompassing as much as possible from those in use, together with a  proof that these techniques cannot prove any lower bound better than the state-of-art (which is often pathetic, and always very far from what we expect for complexity of random functions).

      In the setting of  Boolean computation of Boolean functions (where P vs. NP is the central open problem),  there are several famous barriers which provide satisfactory excuses, and point to directions in which techniques may be strengthened.

      In the setting of Arithmetic computation of polynomials and tensors (where  VP vs. VNP is the central open problem) we have no satisfactory barriers, despite some recent interesting  attempts.

      This talk will describe a new barrier for the Rank Method in arithmetic complexity, which encompass most lower bounds in this field. It also encompass most lower bounds on tensor rank in algebraic geometry (where the the rank method is called Flattening).

      I will describe the rank method, explain how it is used to prove lower bounds, and then explain its limits via the new barrier result. As an example, it shows that while the best lower bound on the tensor rank of any explicit 3-dimensional tensor of side n (which is achieved by a rank method) is 2n, no rank method can prove a lower bound which exceeds 8n

      (despite the fact that a random such tensor has rank quadratic in n).

      No special background knowledge is assumed. The audience is expected to come up with new lower bounds, or else, with new excuses for their absence.

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Venkat Guruswami

      Subspace evasion, list decoding, and dimension expanders

       Abstract: A subspace design is a collection of subspaces of F^n (F = finite field) most of which are disjoint from every low-dimensional subspace of F^n. This notion was put forth in the context of algebraic list decoding where it enabled the construction of optimal redundancy list-decodable codes over small alphabets as well as for error-correction in the rank-metric. Explicit subspace designs with near-optimal parameters have been constructed over large fields based on polynomials with structured roots. (Over small fields, a construction via cyclotomic function fields with slightly worse parameters is known.) Both the analysis of the list decoding algorithm as well as the subspace designs crucially rely on the *polynomial method*.

      Subspace designs have since enabled progress on linear-algebraic analogs of Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In particular, they yield an explicit construction of constant-degree dimension expanders over large fields. While constructions of such dimension expanders are known over any field, they are based on a reduction to a highly non-trivial form of vertex expanders called monotone expanders. In contrast, the subspace design approach is simpler and works entirely within the linear-algebraic realm. Further, in recent (ongoing) work, their combination with rank-metric codes yields dimension expanders with expansion proportional to the degree.

      This talk will survey these developments revolving around subspace designs, their motivation, construction, analysis, and connections.

      (Based on several joint works whose co-authors include Chaoping Xing, Swastik Kopparty, Michael Forbes, Nicolas Resch, and Chen Yuan.)

      12:00-1:30pmLunch
      1:30-2:30pm

       

      David Conlon

      Finite reflection groups and graph norms

      Abstract: For any given graph $H$, we may define a natural corresponding functional $\|.\|_H$. We then say that $H$ is norming if $\|.\|_H$ is a semi-norm. A similar notion $\|.\|_{r(H)}$ is defined by $\| f \|_{r(H)} := \| | f | \|_H$ and $H$ is said to be weakly norming if $\|.\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. Using results from the theory of finite reflection groups, we identify a much larger class of weakly norming graphs. This result includes all previous examples of weakly norming graphs and adds many more. We also discuss several applications of our results. In particular, we define and compare a number of generalisations of Gowers’ octahedral norms and we prove some new instances of Sidorenko’s conjecture. Joint work with Joonkyung Lee.

       

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Laszlo Miklós Lovasz

      Removal lemmas for triangles and k-cycles.

      Abstract: Let p be a fixed prime. A k-cycle in F_p^n is an ordered k-tuple of points that sum to zero; we also call a 3-cycle a triangle. Let N=p^n, (the size of F_p^n). Green proved an arithmetic removal lemma which says that for every k, epsilon>0 and prime p, there is a delta>0 such that if we have a collection of k sets in F_p^n, and the number of k-cycles in their cross product is at most a delta fraction of all possible k-cycles in F_p^n, then we can delete epsilon times N elements from the sets and remove all k-cycles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in particular, asked whether a polynomial bound holds. Despite considerable attention, prior to our work, the best known bound for any k, due to Fox, showed that 1/delta can be taken to be an exponential tower of twos of height logarithmic in 1/epsilon (for a fixed k).

      In this talk, we will discuss recent work on Green’s problem. For triangles, we prove an essentially tight bound for Green’s arithmetic triangle removal lemma in F_p^n, using the recent breakthroughs with the polynomial method. For k-cycles, we also prove a polynomial bound, however, the question of the optimal exponent is still open.

      The triangle case is joint work with Jacob Fox, and the k-cycle case with Jacob Fox and Lisa Sauermann.

      Thursday, Nov. 16

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Janos PachLet’s talk about multiple crossings

      Abstract: Let k>1 be a fixed integer. It is conjectured that any graph on n vertices that can be drawn in the plane without k pairwise crossing edges has O(n) edges. Two edges of a hypergraph cross each other if neither of them contains the other, they have a nonempty intersection, and their union is not the whole vertex set. It is conjectured that any hypergraph on n vertices that contains no k pairwise crossing edges has at most O(n) edges. We discuss the relationship between the above conjectures and explain some partial answers, including a recent result of Kupavskii, Tomon, and the speaker, improving a 40 years old bound of Lomonosov.

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Misha Rudnev

      Few products, many sums

      Abstract: This is what I like calling “weak Erd\H os-Szemer\’edi conjecture”, still wide open over the reals and in positive characteristic. The talk will focus on some recent progress, largely based on the ideas of I. D. Shkredov over the past 5-6 years of how to use linear algebra to get the best out of the Szemer\’edi-Trotter theorem for its sum-product applications. One of the new results is strengthening (modulo the log term hidden in the $\lesssim$ symbol) the textbook Elekes inequality

      $$

      |A|^{10} \ll |A-A|^4|AA|^4

      $$

      to

      $$|A|^{10}\lesssim |A-A|^3|AA|^5.$$

      The other is the bound 

      $$E(H) \lesssim |H|^{2+\frac{9}{20}}$$ for additive energy of sufficiently small multiplicative subgroups in $\mathbb F_p$.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Adam Sheffer

      Geometric Energies: Between Discrete Geometry and Additive Combinatorics

      Abstract: We will discuss the rise of geometric variants of the concept of Additive energy. In recent years such variants are becoming more common in the study of Discrete Geometry problems. We will survey this development and then focus on a recent work with Cosmin Pohoata. This work studies geometric variants of additive higher moment energies, and uses those to derive new bounds for several problems in Discrete Geometry.  

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Boris Bukh

      Ranks of matrices with few distinct entries

      Abstract: Many applications of linear algebra method to combinatorics rely on the bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these application. I will also present a classification of sets L for which no low-rank matrix with entries in L exists.

      Friday, Nov. 17

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Benny Sudakov

      Submodular minimization and set-systems with restricted intersections

      AbstractSubmodular function minimization is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint types under which it remains efficiently solvable. The arguably most relevant non-trivial constraint class for which polynomial algorithms are known are parity constraints, i.e., optimizing submodular function only over sets of odd (or even) cardinality. Parity constraints capture classical combinatorial optimization problems like the odd-cut problem, and they are a key tool in a recent technique to efficiently solve integer programs with a constraint matrix whose subdeter-minants are bounded by two in absolute value.

      We show that efficient submodular function minimization is possible even for a significantly larger class than parity constraints, i.e., over all sets (of any given lattice) of cardinality r mod m, as long as m is a constant prime power. To obtain our results, we combine tools from Combinatorial Optimization, Combinatorics, and Number Theory. In particular, we establish an interesting connection between the correctness of a natural algorithm, and the non-existence of set systems with specific intersection properties.

      Joint work with M. Nagele and R. Zenklusen

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Robert Kleinberg 

      Explicit sum-of-squares lower bounds via the polynomial method

      AbstractThe sum-of-squares (a.k.a. Positivstellensatz) proof system is a powerful method for refuting systems of multivariate polynomial inequalities, i.e. proving that they have no solutions. These refutations themselves involve sum-of-squares (sos) polynomials, and while any unsatisfiable system of inequalities has a sum-of-squares refutation, the sos polynomials involved might have arbitrarily high degree. However, if a system admits a refutation where all polynomials involved have degree at most d, then the refutation can be found by an algorithm with running time polynomial in N^d, where N is the combined number of variables and inequalities in the system.

      Low-degree sum-of-squares refutations appear throughout mathematics. For example, the above proof search algorithm captures as a special case many a priori unrelated algorithms from theoretical computer science; one example is Goemans and Williamson’s algorithm to approximate the maximum cut in a graph. Specialized to extremal graph theory, they become equivalent to flag algebras. They have also seen practical use in robotics and optimal control.

      Therefore, it is of interest to identify “hard” systems of low-degree polynomial inequalities that have no solutions but also have no low-degree sum-of-squares refutations. Until recently, the only known examples were either not explicit (i.e., known to exist by non-constructive means such as the probabilistic method) or not robust (i.e., a system is constructed which is not refutable by degree d sos polynomials, but becomes refutable when perturbed by an amount tending to zero with d). We present a new family of instances derived from the cap-set problem, and we show a super-constant lower bound on the degree of its sum-of-squares refutations. Our instances are both explicit and robust.

      This is joint work with Sam Hopkins.

      12:00-1:30pmLunch

       

    • Special Seminar
      6:10 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      6:11 pm-6:12 pm
      11/01/2019-10/25/2016

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/10/2018 RM & PT Seminar
      6:11 pm
      11/01/2019

      No additional detail for this event.

    • General Relativity Seminar
      6:12 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-03-16 Mathematical Physics Seminar
      6:13 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/15/2018 Topology Seminar
      6:14 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/15/2018 Math Physics Seminar
      6:15 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-12-2016 Random Matrix & Probability Theory Seminar
      6:16 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      6:17 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-24-2016 Random Matrix & Probability Theory Seminar
      6:18 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/30/2018 RM & PT Seminar
      6:19 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      6:19 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/26/2018 Social Science Applications Forum
      6:20 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-19-2016 Random Matrix & Probability Theory Seminar
      6:22 pm
      11/01/2019

      No additional detail for this event.

    • Member Seminar
      6:24 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/22/2018 Mathematical Physics Seminar
      6:24 pm
      11/01/2019
    • Member Seminar
      6:26 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-26-2016 Random Matrix & Probability Theory Seminar
      6:27 pm
      11/01/2019

      No additional detail for this event.

    • Member Seminar
      6:29 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-24-16 Mathematical Physics Seminar
      6:30 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      6:32 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      6:34 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-01-2016 Social Sciences Applications Forum
      6:36 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-19-2016 Random Matrix & Probability Theory Seminar
      6:37 pm
      11/01/2019

      No additional detail for this event.

    • Member Seminar
      6:40 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-17-16 Mathematical Physics Seminar
      6:41 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-26-2016 Random Matrix & Probability Theory Seminar
      6:46 pm
      11/01/2019

      No additional detail for this event.

    • Member Seminar
      6:52 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-24-16 Mathematical Physics Seminar
      6:53 pm
      11/01/2019

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      6:54 pm
      11/01/2019

      No additional detail for this event.

    • Special Seminar
      6:59 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-01-2016 Social Sciences Applications Forum
      7:00 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      7:03 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-31-16 Mathematical Physics Seminar
      7:05 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12/10/2018 Mathematical Physics Seminar
      8:42 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      12/10/2018 Topology Seminar
      8:43 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      12/12/2018 Hodge Seminar
      8:43 pm
      11/01/2019

      No additional detail for this event.

    • Mathematical Physics Seminar
      8:45 pm
      11/01/2019

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      1/16/2019 Hodge Seminar
      8:46 pm
      11/01/2019

      No additional detail for this event.

    • Fluid Dynamics Seminar
      Fluid Dynamics Seminar
      4/3/2019 Fluid Dynamics Seminar
      8:54 pm
      11/01/2019

      No additional detail for this event.

    • Program
      9:39 pm
      11/01/2019-12/18/2014

      arge random matrices provide some of the simplest models for large, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a rigorous understanding of universality in the case of orthogonal, Hermitian, or symplectic matrices with independent entries, resolving a conjecture of Wigner-Dyson-Mehta dating back 50 years. These new developments have exploited techniques from a wide range of mathematical areas in addition to probability, including combinatorics, partial differential equations, and hydrodynamic limits. It is hoped that these new techniques will be useful in the analysis of universal behaviour in matrix ensembles with more complicated structure such as random regular graph models, or 2D matrix ensembles, as well as more physically relevant systems such as band matrices and random Schroedinger-type Hamiltonians. For some of these models, results in the direction of universality have already been obtained.

      Here is a partial list of the mathematicians who are participating in this program

    • Program
      9:44 pm
      11/01/2019-12/28/2013

      During Academic year 2018-19, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines.

      As part of the Program, the CMSA will be hosting two workshops:

      .

      Additionally, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

      Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program
      NameTentative Visiting Dates

      Jason Alicea

      11/12/2018-11/16/2018
      Maissam Barkeshli4/22/2019 – 4/26/2019
      Xie Chen4/15-17/2019 4/19-21/2019 4/24-30/2019

      Lukasz Fidkowski

      1/7/2019-1/11/2019

      Zhengcheng Gu

      8/15/2018-8/30/2018 & 5/9/2019-5/19/2019

      Yin Chen He

      10/14/2018-10/27/2018
      Anton Kapustin8/26/2018-8/30/2018 & 3/28/2019-4/5/2019

      Michael Levin

      3/11/2019-3/15/2019
      Yuan-Ming Lu4/29/2019-6/01/2019

      Adam Nahum

      4/2/2019- 4/19/2019

      Masaki Oshikawa

      4/22/2019-5/22/2019
      Chong Wang 10/22/2018-11/16/2018

      Juven Wang

      4/1/2019-4/16/2019
      Cenke Xu 8/26/2018-10/1/2018

      Yi-Zhuang You

      4/1/2019-4/19/2019

      Mike Zaletel

      5/1/2019-5/10/2019
    • Program
      9:45 pm-9:46 pm
      11/01/2019-12/31/2010

      During Academic year 2018-19, the CMSA will be hosting a Program on Mathematical Biology.

      Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape.

      In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. And in mathematics and computation, there has been a revolution in terms of posing and solving problems at the intersection of computational geometry, statistics and inference.  So, how far are we from realizing a descriptive, predictive and controllable theory of biological shape?

      In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems

      The CMSA will be hosting three workshops as part of this program. The Workshop on Morphometrics, Morphogenesis and Mathematics will take place on October 22-26. 

      A workshop on Morphogenesis: Geometry and Physics will take place on December 3-6, 2018.

      A workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

    • Program
      9:48 pm
      11/01/2019-12/31/2010

      Recent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during fall 2019, with between 20-30 participants. They will also invite 10-20 longer-term visitors throughout the semester. Additionally, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10.

      Organizers:

      .

      Workshops:

       

      Here is a partial list of the mathematicians and physicists who have indicated that they will attend part or all of this special program as a visitor:

    • Program
      9:49 pm
      11/01/2019-12/23/2010

      The Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry, Symplectic geometry, Arithmetic geometry, Quantum topology and mathematical aspects of high energy physics, specially string theory with the goal of proving the homological mirror symmetry conjecture (HMS) in full generality and explore its applications. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model). We are happy to announce that the Simons Foundation has agreed to renew funding for the HMS collaboration program for three additional years.

      A brief induction of the Brandeis-Harvard CMSA HMS/SYZ research agenda and team members are as follow:


      Directors:


      Shing-Tung Yau (Harvard University)

      Born in Canton, China, in 1949, S.-T. Yau grew up in Hong Kong, and studied in the Chinese University of Hong Kong from 1966 to 1969. He did his PhD at UC Berkeley from 1969 to 1971, as a student of S.S. Chern. He spent a year as a postdoc at the Institute for Advanced Study in Princeton, and a year as assistant professor at SUNY at Stony Brook. He joined the faculty at Stanford in 1973. On a Sloan Fellowship, he spent a semester at the Courant Institute in 1975. He visited UCLA the following year, and was offered a professorship at UC Berkeley in 1977. He was there for a year, before returning to Stanford. He was a plenary speaker at the 1978 ICM in Helsinki. The following year, he became a faculty member at the IAS in Princeton. He moved to UCSD in 1984. Yau came to Harvard in 1987, and was appointed the Higgins Professor of Mathematics in 1997. He has been at Harvard ever since. Yau has received numerous prestigious awards and honors throughout his career. He was named a California Scientist of the Year in 1979. In 1981, he received a Oswald Veblen Prize in Geometry and a John J. Carty Award for the Advancement of Science, and was elected a member of the US National Academy of Sciences. In 1982, he received a Fields Medal for “his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex MongeAmpre equations”. He was named Science Digest, America’s 100 Brightest Scientists under 40, in 1984. In 1991, he received a Humboldt Research Award from the Alexander von Humboldt Foundation in Germany. He was awarded a Crafoord Prize in 1994, a US National Medal of Science in 1997, and a China International Scientific and Technological Cooperation Award, for “his outstanding contribution to PRC in aspects of making progress in sciences and technology, training researchers” in 2003. In 2010, he received a Wolf Prize in Mathematics, for “his work in geometric analysis and mathematical physics”. Yau has also received a number of research fellowships, which include a Sloan Fellowship in 1975-1976, a Guggenheim Fellowship in 1982, and a MacArthur Fellowship in 1984-1985. Yau’s research interests include differential and algebraic geometry, topology, and mathematical physics. As a graduate student, he started to work on geometry of manifolds with negative curvature. He later became interested in developing the subject of geometric analysis, and applying the theory of nonlinear partial differential equations to solve problems in geometry, topology, and physics. His work in this direction include constructions of minimal submanifolds, harmonic maps, and canonical metrics on manifolds. The most notable, and probably the most influential of this, was his solution of the Calabi conjecture on Ricci flat metrics, and the existence of Kahler-Einstein metrics. He has also succeeded in applying his theory to solve a number of outstanding conjectures in algebraic geometry, including Chern number inequalities, and the rigidity of complex structures of complex projective spaces. Yau’s solution to the Calabi conjecture has been remarkably influential in mathematical physics over the last 30 years, through the creation of the theory of Calabi-Yau manifolds, a theory central to mirror symmetry. He and a team of outstanding mathematicians trained by him, have developed many important tools and concepts in CY geometry and mirror symmetry, which have led to significant progress in deformation theory, and on outstanding problems in enumerative geometry. Lian, Yau and his postdocs have developed a systematic approach to study and compute period integrals of CY and general type manifolds. Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula of Candelas et al for worldsheet instantons on the quintic threefold. In the course of understanding mirror symmetry, Strominger, Yau, and Zaslow proposed a new geometric construction of mirror symmetry, now known as the SYZ construction. This has inspired a rapid development in CY geometry over the last two decades. In addition to CY geometry and mirror symmetry, Yau has done influential work on nonlinear partial differential equations, generalized geometry, Kahler geometry, and general relativity. His proof of positive mass conjecture is a widely regarded as a cornerstone in the classical theory of general relativity. In addition to publishing well over 350 research papers, Yau has trained more than 60 PhD students in a broad range of fields, and mentored dozens of postdoctoral fellows over the last 40 years.


      Professor Bong Lian (Brandeis University)

      BongBorn in Malaysia in 1962, Bong Lian completed his PhD in physics at Yale University under the direction of G. Zuckerman in 1991. He joined the permanent faculty at Brandeis University in 1995, and has remained there since. Between 1995 and 2013, he had had visiting research positions at numerous places, including the National University of Taiwan, Harvard University, and Tsinghua University. Lian received a J.S. Guggenheim Fellowship in 2003. He was awarded a Chern Prize at the ICCM in Taipei in 2013, for his “influential and fundamental contributions in mathematical physics, in particular in the theory of vertex algebras and mirror symmetry.” He has also been co-Director, since 2014, of the Tsinghua Mathcamp, a summer outreach program launched by him and Yau for mathematically talented teenagers in China. Since 2008, Lian has been the President of the International Science Foundation of Cambridge, a non-profit whose stated mission is “to provide financial and logistical support to scholars and universities, to promote basic research and education in mathematical sciences, especially in the Far East.” Over the last 20 years, he has mentored a number of postdocs and PhD students. His research has been supported by an NSF Focused Research Grant since 2009. Published in well over 60 papers over 25 years, Lian’s mathematical work lies in the interface between representation theory, Calabi-Yau geometry, and string theory. Beginning in the late 80’s, Lian, jointly with Zuckerman, developed the theory of semi-infinite cohomology and applied it to problems in string theory. In 1994, he constructed a new invariant (now known as the Lian- Zuckerman algebra) of a topological vertex algebra, and conjectured the first example of a G algebra in vertex algebra theory. The invariant has later inspired a new construction of quantum groups by I. Frenkel and A. Zeitlin, as semi-infinite cohomology of braided vertex algebras, and led to a more recent discovery of new relationships between Courant algebroids, A-algebras, operads, and deformation theory of BV algebras. In 2010, he and his students Linshaw and Song developed important applications of vertex algebras in equivariant topology. Lian’s work in CY geometry and mirror symmetry began in early 90’s. Using a characteristic p version of higher order Schwarzian equations, Lian and Yau gave an elementary proof that the instanton formula of Candelas et al implies Clemens’s divisibility conjecture for the quintic threefold, for infinitely many degrees. In 1996, Lian (jointly with Hosono and Yau) answered the so-called Large Complex Structure Limit problem in the affirmative in many important cases. Around the same year, they announced their hyperplane conjecture, which gives a general formula for period integrals for a large class of CY manifolds, extending the formula of Candelas et al. Soon after, Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula. In 2003, inspired by mirror symmetry, Lian (jointly with Hosono, Oguiso and Yau) discovered an explicit counting formula for Fourier-Mukai partners, and settled an old problem of Shioda on abelian and K3 surfaces. Between 2009 and 2014, Lian (jointly with Bloch, Chen, Huang, Song, Srinivas, Yau, and Zhu) developed an entirely new approach to study the so-called Riemann-Hilbert problem for period integrals of CY manifolds, and extended it to general type manifolds. The approach leads to an explicit description of differential systems for period integrals with many applications. In particular, he answered an old question in physics on the completeness of Picard-Fuchs systems, and constructed new differential zeros of hypergeometric functions.


      Denis Auroux (Harvard University)

      AurouxDenis Auroux’s research concerns symplectic geometry and its applications to mirror symmetry. While his early work primarily concerned the topology of symplectic 4-manifolds, over the past decade Auroux has obtained pioneering results on homological mirror symmetry outside of the Calabi-Yau setting (for Fano varieties, open Riemann surfaces, etc.), and developed an extension of the SYZ approach to non-Calabi-Yau spaces.After obtaining his PhD in 1999 from Ecole Polytechnique (France), Auroux was employed as Chargé de Recherche at CNRS and CLE Moore Instructor at MIT, before joining the faculty at MIT in 2002 (as Assistant Professor from 2002 to 2004, and as Associate Professor from 2004 to 2009, with tenure starting in 2006). He then moved to UC Berkeley as a Full Professor in 2009.
      Auroux has published over 30 peer-reviewed articles, including several in top journals, and given 260 invited presentations about his work. He received an Alfred P. Sloan Research Fellowship in 2005, was an invited speaker at the 2010 International Congress of Mathematicians, and in 2014 he was one of the two inaugural recipients of the Poincaré Chair at IHP. He has supervised 10 PhD dissertations, won teaching awards at MIT and Berkeley, and participated in the organization of over 20 workshops and conferences in symplectic geometry and mirror symmetry.




      Senior Personnel:

      Artan Sheshmani (Harvard CMSA)

      unnamedArtan Sheshmani’s research is focused on enumerative algebraic geometry and mathematical aspects of string theory. He is interested in applying techniques in algebraic geometry, such as, intersection theory, derived category theory, and derived algebraic geometry to construct and compute the deformation invariants of algebraic varieties, in particular Gromov-Witten (GW) or Donaldson-Thomas (DT) invariants. In the past Professor Sheshmani has worked on proving modularity property of certain DT invariants of K3-fibered threefolds (as well as their closely related Pandharipande-Thomas (PT) invariants), local surface threefolds, and general complete intersection Calabi-Yau threefolds. The modularity of DT/PT invariants in this context is predicted in a famous conjecture of  string theory called S-duality modularity conjecture, and his joint work has provided the proof to some cases of it, using degenerations, virtual localizations, as well as wallcrossing techniques. Recently, Sheshmani has focused on proving a series of dualities relating the various enumerative invariants over threefolds, notably the GW invariants and invariants that arise in topological gauge theory. In particular in his joint work with Gholampour, Gukov, Liu, Yau he studied DT gauge theory and its reductions to D=4 and D=2 which are equivalent to local theory of surfaces in Calabi-Yau threefolds. Moreover, in a recent joint work with Yau and Diaconescu, he has studied the construction and computation of DT invariants of Calabi-Yau fourfolds via a suitable derived categorical reduction of the theory to the DT theory of threefolds. Currently Sheshmani is interested in a wide range of problems in enumerative geometry of CY varieties in dimensions 3,4,5.

      Artan has received his PhD and Master’s degrees in pure mathematics under Sheldon Katz and Thomas Nevins from the University of Illinois at Urbana Champaign (USA) in 2011 and 2008 respectively. He holds a Master’s degree in Solid Mechanics (2004) and two Bachelor’s degrees, in Mechanical Engineering and Civil Engineering from the Sharif University of Technology, Tehran, Iran.  Artan has been a tenured Associate Professor of Mathematics with joint affiliation at Harvard CMSA and center for Quantum Geometry of Moduli Spaces (QGM), since 2016. Before that he has held visiting Associate Professor and visiting Assistant Professor positions at MIT.

      An Huang (Brandeis University)

      unnamedThe research of An Huang since 2011 has been focused on the interplay between algebraic geometry, the theory of special functions and mirror symmetry. With S. Bloch, B. Lian, V. Srinivas, S.-T. Yau, X. Zhu, he has developed the theory of tautological systems, and has applied it to settle several important problems concerning period integrals in relation to mirror symmetry. With B. Lian and X. Zhu, he has given a precise geometric interpretation of all solutions to GKZ systems associated to Calabi-Yau hypersurfaces in smooth Fano toric varieties. With B. Lian, S.-T. Yau, and C.-L. Yu, he has proved a conjecture of Vlasenko concerning an explicit formula for unit roots of the zeta functions of hypersurfaces, and has further related these roots to p-adic interpolations of complex period integrals. Beginning in 2018, with B. Stoica and S.-T. Yau, he has initiated the study of p-adic strings in curved spacetime, and showed that general relativity is a consequence of the self-consistency of quantum p-adic strings. One of the goals of this study is to understand p-adic A and B models.

      An Huang received his PhD in Mathematics from the University of California at Berkeley in 2011. He was a postdoctoral fellow at the Harvard University Mathematics Department, and joined Brandeis University as an Assistant Professor in Mathematics in 2016.



      Siu Cheong Lau (Boston University)
      unnamed

      The research interest of Siu Cheong Lau lies in SYZ mirror symmetry, symplectic and algebraic geometry.  His thesis work has successfully constructed the SYZ mirrors for all toric Calabi-Yau manifolds based on quantum corrections by open Gromov-Witten invariants and their wall-crossing phenomenon.  In collaboration with N.C. Leung, H.H. Tseng and K. Chan, he derived explicit formulas for the open Gromov-Witten invariants for semi-Fano toric manifolds which have an obstructed moduli theory.  It has a beautiful relation with mirror maps and Seidel representations.   Recently he works on a local-to-global approach to SYZ mirror symmetry.  In joint works with C.H. Cho and H. Hong, he developed a noncommutative local mirror construction for immersed Lagrangians, and a natural gluing method to construct global mirrors.  The construction has been realized in various types of geometries including orbifolds, focus-focus singularities and pair-of-pants decompositions of Riemann surfaces.

      Siu-Cheong Lau has received the Doctoral Thesis Gold Award (2012) and the Best Paper Silver Award (2017) at the International Congress of Chinese Mathematicians.  He was awarded the Simons Collaboration Grant in 2018.  He received a Certificate of Teaching Excellence from Harvard University in 2014.


      Affiliates:

      • Netanel Rubin-Blaier (Cambridge)
      • Kwokwai Chan (Chinese University of Hong Kong)
      • Mandy Cheung (Harvard University, BP)
      • Chuck Doran (University of Alberta)
      • Honsol Hong (Yonsei University)
      • Shinobu Hosono (Gakushuin University, Japan)
      • Conan Leung (Chinese University of Hong Kong)
      • Yu-shen Lin (Boston University)
      • Hossein Movassati (IMPA Brazil)
      • Arnav Tripathhy (Harvard University, BP)

       

      Postdocs:

      • Dennis Borisov
      • Tsung-Ju Lee
      • Dingxin Zhang
      • Jingyu Zhao
      • Yang Zhou

      Jobs:

      Postdoctoral Fellowship in Algebraic Geometry

      Postdoctoral Fellowship in Mathematical Sciences

       

      To learn about previous programming as part of the Simons Collaboration, click here.

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  • CMSA EVENT: Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks
    11:19 am
    11/12/2019-11/14/2019
    Dynamics-12-x-18-683x1024

    On November 12-14, 2019 the CMSA will be hosting a workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Biological cells are the fundamental units of life, and predictive modeling of cellular dynamics is essential for understanding a myriad of biological processes and functions. Rapid advances in technologies have made it possible for biologists to measure many variables and outputs from complex molecular and cellular networks with various inputs and environmental conditions. However, such advances are far ahead of the development of mathematical theory, models and methods needed to secure a deep understanding of how high-level robust behaviors emerge from the interactions in complex structures, especially in dynamic and stochastic environments. This workshop will bring together mathematicians and biological scientists involved in developing mathematical theories and methods for understanding, predicting and controlling dynamic behavior of molecular and cellular networks. Particular emphasis will be placed on efforts directed towards discovering underlying biological principles that govern function, adaptation and evolution, and on the development of associated mathematical theories.

    Organizers: Jeremy Gunawardena (Harvard) and Ruth Williams (University of California, San Diego)

    A limited amount of funding is available to help in defraying the travel costs of early career researchers, women, and underrepresented minorities, participating the workshop. Early career researchers are researchers who received their Ph.D. in 2014 or later, or who are Ph.D. students expecting to complete their Ph.D. by the end of 2020.

    To apply, please send a CV, a statement of why you wish to attend, and, if you are a grad student, a letter of support from your advisor to Sarah LaBauve at slabauve@math.harvard.edu

    All applications received by 5pm, EDT, October 28, 2019 will receive full consideration.

    Speakers: 

    Videos from the workshop can be found in the Youtube playlist.

  • Seminars

    Seminars Colloquia & Seminar
    11/12/2019 Spacetime Seminar

    3:30 pm
    11/12/2019
  • Seminars

    Seminars Colloquia & Seminar
    11/13/2019 Colloquium

    4:30 pm-5:30 pm
    11/12/2019
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  • CMSA EVENT: Current Developments in Mathematics 2019
    1:30 pm-5:00 pm
    11/22/2019-11/23/2019
    CDM-POSTER-2019.email_-662x1024

     

    cdmFriday, Nov. 22, 2019 1:30 pm – 5:20 pm

    Saturday, Nov. 23, 2019  9:00 am – 5:00 pm

    Harvard University Science Center, Hall C

    Speakers:

    ·      Svetlana Jitomirskaya (UC Irvine)

    ·      Subash Khot (NYU)

    ·      Jun Li (Stanford)

    ·      André Neves (Chicago)

    ·      Geordie Williamson (U Sidney)

    Free and open to the public – registration is required.
    Please register in advance online at www.math.harvard.edu/cdm

    CDM_2019-agenda-791x1024

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  • Seminars

    Seminars Colloquia & Seminar
    11/1/2019 General Relativity Seminar

    10:30 am-11:30 am
    11/01/2019
  • CMSA EVENT: Learning from health data in the million genome era
    11:26 am
    11/01/2019

    On November 12019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system.

    Speakers: 

    • Heidi Rehm, Ph.D.
      Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform.
    • Saiju Pyarajan, Ph.D.
      Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS
    • Tianxi Cai, Sci.D
      John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health
    • Susan Redline, M.D., M.P.H
      Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center
    • Avinash Sahu, Ph.D.
      Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health
    • Peter J. Park, Ph.D.
      Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School
    • David Roberson
      Community Engagement Manager, Seven Bridges

    Registration & Schedule

  • General Relativity Seminar
    2:30 pm-3:30 pm
    11/01/2019-04/26/2020
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