CMSA

CMSA Q&A Seminar 3/5/2024
2024-03-05 12:30 - 13:30 (America/New_York) | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q and A Seminar

Speaker: Cumrun Vafa

Question: What is swampland?

High order WENO finite difference scheme for Einstein-Yang-Mills equations
2024-03-05 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Yuewen Chen, Tsinghua University
Title: High order WENO finite difference scheme for Einstein-Yang-Mills equations
Abstract: In this talk, we will show the convergence analysis of the first-order finite difference scheme for static spherically symmetric $SU(2)$ Einstein-Yang-Mills (EYM) equations. We also construct a new WENO scheme for EYM.

Strong bounds for arithmetic progressions
2024-03-04 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Raghu Meka (UCLA)
Title: Strong bounds for arithmetic progressions
Abstract: Suppose you have a set S of integers from {1,2,…,N} that contains at least N / C elements. Then for large enough N, must S contain three equally spaced numbers (i.e., a 3-term arithmetic progression)?
In 1953, Roth showed this is the case when C is roughly (log log N). Behrend in 1946 showed that C can be at most exp(sqrt(log N)). Since then, the problem has been a cornerstone of the area of additive combinatorics. Following a series of remarkable results, a celebrated paper from 2020 due to Bloom and Sisask improved the lower bound on C to C = (log N)^(1+c) for some constant c > 0.
This talk will describe a new work showing that C can be much closer to Behrend’s construction. Based on joint work with Zander Kelley.

AQFT Lecture Series
2024-03-01 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Peng Shan (Tsinghua)
Title: Skein algebras and quantized Coulomb branches
Abstract: In this talk, we explain how to attach a quantized Coulomb branch in the sense of Braverman-Finkelberg-Nakajima to a compact oriented surface of genus at most one, and compare it to the Kauffman bracket Skein algebra in some special cases. This is based on a joint work with Dylan Allegretti.

Contract Design in Combinatorial Settings
2024-03-01 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Tomer Ezra (Harvard CMSA)
Title: Contract Design in Combinatorial Settings
Abstract: We study two combinatorial settings of the contract design problem, in which a principal wants to delegate the execution of a costly task. In the first setting, the principal delegates the task to an agent that can take any subset of a given set of unobservable actions, each of which has an associated cost. The principal receives a reward which is a combinatorial function of the actions taken by the agent. In the second setting, we study the single-principal multi-agent contract problem, in which the principal motivates a team of agents to exert effort toward a given task. We design (approximately) optimal algorithms for both settings along with impossibility results for various classes of combinatorial functions.
This talk is based on joint works with Paul Duetting, Michal Feldman, Thomas Kesselheim and Maya Schlesinger.

AQFT Lecture Series
2024-03-01 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Chen Wan, Rutgers Newark
Title: Some examples of the relative Langlands duality
Abstract: In this talk I will discuss some examples of the relative Langlands duality (introduced by Ben-Zvi—Sakellaridis—Venkatesh) for strongly tempered spherical varieties. In some cases, I will introduce a relative trace formula comparison for the models and prove the fundamental lemma/smooth transfer. This is a joint work with Zhengyu Mao and Lei Zhang.

Fourth Annual Yip Lecture | Josh Tenenbaum | How to grow a mind from a brain: From guessing and betting to thinking and talking
2024-02-29 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Josh Tenenbaum gave the Fourth Annual Yip Lecture on February 29, 2024.
Title: How to grow a mind from a brain: From guessing and betting to thinking and talking
Time: 4:00-5:00 pm ET
Location: Harvard Science Center
The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

The previous Yip Lecture featured Andrew Strominger (Harvard), who spoke on Black Holes.

Directed motion in active matter: Frictiotaxis and flocking
2024-02-29 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Active Matter Seminar
Speaker: Ricard Alert, Max Planck Institute for the Physics of Complex Systems
Title: Directed motion in active matter: Frictiotaxis and flocking
Abstract: A key feature of active matter is its ability to move directionally, both as individual particles and collectively. I will discuss two examples of directed motion: one in cell migration, and one in collections of self-propelled colloids. First, I will show that cells lacking cell-substrate adhesions migrate along friction gradients. We call this phenomenon frictiotaxis, which is a new type of cell guidance. Second, I will present a new mechanism for flocking whereby self-propelled particles can align and move collectively despite turning away from each other.

Classifying curves on Fano varieties
2024-02-29 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Brian Lehmann (Boston College)
Title: Classifying curves on Fano varieties
Abstract: How can we understand the set of curves on a Fano variety? One perspective is provided by Geometric Manin’s Conjecture, a collection of conjectures with roots in arithmetic and topology. While I will mention some recent progress, the main focus will be developing a conceptual framework for thinking about our question.

10-27-2016 Homological Mirror Symmetry Seminar
2024-02-27 19:03

AQFT Lecture Series
2024-02-27 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Wei Zhang (MIT)
Title: Shtuka special cycles and their generating series

CMSA Q&A Seminar 2/27/2024
2024-02-27 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar

Speaker: Dan Freed

Question: What are Higgs bundles?

On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
2024-02-27 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Nishanth Gudapati, Clark University
Title: On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
Abstract: The Kerr black hole stability problem is an important open problem in general relativity. In this talk, I will focus on the role of energy methods in the axisymmetric stability of Kerr black hole spacetimes. In particular, I will discuss the construction and the application of a positive Hamiltonian energy for axially symmetric Maxwell and Einstein perturbations of sub-extremal Kerr black hole spacetimes.

Factorization algebras in quite a lot of generality
2024-02-26 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Clark Barwick, University of Edinburgh
Title: Factorization algebras in quite a lot of generality
Abstract: The objects of arithmetic geometry are not manifolds. Some concepts from differential geometry admit analogues in arithmetic, but they are not straightforward. How then can we hope to make precise sense of quantum field theories on these objects? I will propose the beginnings of a mathematical framework via a general theory of factorization algebras. A new feature is a subtle piece of additional structure on our objects – what I call a world-structure – that is ordinarily left implicit.

AQFT Lecture Series
2024-02-26 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Omer Offen (Brandeis)
Title: Period integrals of automorphic forms and the residue method
Abstract: I will discuss some aspects of period integrals of automorphic forms via examples. In particular, the residue method of Jacquet and Rallis and its recent application, joint with Friedberg and Ginzburg, to study new periods on the residual automorphic spectrum of the symplectic group.

Integrability and Hidden Symmetries in Black Hole Dynamics
2024-02-23 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Uri Kol (Harvard CMSA)
Title: Integrability and Hidden Symmetries in Black Hole Dynamics
Abstract: The last decade has produced a number of remarkable discoveries, such as the first direct observation of gravitational waves by the LIGO/Virgo collaboration and the first black hole image taken by the Event Horizon Telescope. These discoveries mark the beginning of a new precision era in black hole physics, which is expected to develop further by future experiments such as LISA, the Einstein Telescope and Cosmic Explorer.

In the era of precision black hole measurements, there is a need for precision theoretical methods and accurate predictions. In this talk I will describe an integrable sector of the gravitational scattering problem – analogous to the hydrogen atom in quantum mechanics – in which exact predictions can be made, and the implications for astrophysical black holes and binary mergers.

Spontaneously Broken (-1)-form symmetries
2024-02-23 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Motoo Suzuki (Harvard)
Title: Spontaneously Broken (-1)-form symmetries
Abstract: Spontaneous breaking of symmetries leads to universal phenomena. We extend this notion to (−1)-form U(1) symmetries. The spontaneous breaking is diagnosed by a dependence of the vacuum energy on a constant background field θ, which can be probed by the topological susceptibility. This leads to a reinterpretation of the Strong CP problem as arising from a spontaneously broken instantonic symmetry in QCD. We discuss how known solutions to the problem are unified in this framework and explore some, so far unsuccessful, attempts to find new solutions. I will also talk about our ongoing work on the explicit breaking by monopoles.

Geometric origins of values of the Riemann Zeta functions at positive integers
2024-02-22 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Yan Zhou, Northeastern
Title: Geometric origins of values of the Riemann Zeta functions at positive integers
Abstract: Given a Fano manifold, Iritani proposed that the asymptotic behavior of solutions to the quantum differential equation of the Fano should be given by the so-called ‘Gamma class’ in its cohomology ring. Later, Abouzaid-Ganatra-Iritani-Sheridan reformulated the ‘Gamma conjecture’ for Calabi-Yau manifolds via the tropical SYZ mirror symmetry and proposed that values of the Riemann Zeta function at positive integers have geometric origins in the tropical periods and singularities of the SYZ geometry. In this talk, we will first review the content of the Gamma conjecture. Then, we will discuss the first step of generalizing AGIS’ approach to Gamma conjecture for the Gross-Siebert mirror families of a Fano manifold in dimension 2 cases, based on joint work with Bohan Fang and Junxiao Wang.

Computers and mathematics in partial differential equations: New developments and challenges
2024-02-21 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Javier Gomez Serrano, Brown University
Title: Computers and mathematics in partial differential equations: new developments and challenges
Abstract: In this talk I will address the interaction between traditional and more modern mathematics and how computers have helped over the last decade providing rigorous (computer-assisted) proofs in the context of partial differential equations. I will also describe new exciting future directions in the field. No background is assumed.

Math Science Lectures in Honor of Raoul Bott: Maggie Miller: Fibered ribbon knots vs. major 4D conjectures
2024-02-20 16:00 - 17:30 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Fibered ribbon knots vs. major 4D conjectures
Location: Harvard University Science Center Hall A & via Zoom webinar
Dates: Feb 20 & 22, 2024
Time: 4:00-5:30 pm
Maggie Miller is an assistant professor in the mathematics department at the University of Texas at Austin and a Clay Research Fellow.
This is the fourth annual Math Science Lecture Series held in Honor of Raoul Bott.
Talk topic: Fibered ribbon knots vs. major 4D conjectures

Feb. 20, 2024
Title: Fibered ribbon knots and the Poincaré conjecture
Abstract: A knot is “fibered” if its complement in S^3 is the total space of a bundle over the circle, and ribbon if it bounds a smooth disk into B^4 with no local maxima with respect to radial height. A theorem of Casson-Gordon from 1983 implies that if a fibered ribbon knot does not bound any fibered disk in B^4, then the smooth 4D Poincaré conjecture is false. I’ll show that unfortunately (?) many ribbon disks bounded by fibered knots are fibered, giving some criteria for extending fibrations and discuss how one might search for non-fibered examples.

Feb. 22, 2024
Title: Fibered knots and the slice-ribbon conjecture
Abstract: The slice-ribbon conjecture (Fox, 1962) posits that if a knot bounds any smooth disk into B^4, it also bounds a ribbon disk. The previously discussed work of Casson-Gordon yields an obstruction to many fibered knots being ribbon, yielding many interesting potential counterexamples to this conjecture — if any happy to bound a non-ribbon disk. In 2022, Dai-Kong-Mallick-Park-Stoffregen showed that unfortunately( ?) many of these knots don’t bound a smooth disk into B^4 and thus can’t disprove the conjecture. I’ll show a simple alternate proof that a certain interesting knot (the (2,1)-cable of the figure eight) isn’t slice and discuss remaining open questions. This talk is joint with Paolo Aceto, Nickolas Castro, JungHwan Park, and Andras Stipsicz.

Talk Chair: Cliff Taubes (Harvard Mathematics)
Moderator: Freid Tong (Harvard CMSA)

Raoul Bott (9/24/1923 – 12/20/2005) is known for the Bott periodicity theorem, the Morse–Bott functions, and the Borel–Bott–Weil theorem.

CMSA Q&A Seminar 2/20/2024
2024-02-20 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q and A Seminar

Speaker: Solomon Friedberg, Boston College

Question: What is the Langlands program?

Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes
2024-02-20 09:30 - 10:30 | Virtual
General Relativity Seminar
Speaker: He Mei, Shenzhen University
Title: Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes
Abstract: In this talk, I will present a work on the long time dynamics of solutions to the defocusing semilinear wave equations on the Schwarzschild black hole spacetimes. For sufficiently smooth and localized initial data, we show that the solution decays in the domain of outer communication. The proof relies on a vector field method of Dafermos-Rodnianski together with Strichartz estimates for linear waves by Marzuola-Metcalfe-Tataru-Tohaneanu.

Symmetries and algebraicity in the flux landscape
2024-02-16 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Damian van de Heisteeg (Harvard CMSA)
Title: Symmetries and algebraicity in the flux landscape
Abstract: In this talk I consider potentials coming from fluxes in string theory. The minima of these potentials trace out special loci in the moduli space of Calabi-Yau manifolds. I discuss the structure that underlies these minima from a Hodge-theoretic point of view.

Programmable Simulations of Molecules and Materials with present-day Reconfigurable Quantum Processors
2024-02-16 10:30 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Susanne Yelin (Harvard)
Title: Programmable Simulations of Molecules and Materials with present-day Reconfigurable Quantum Processors
Abstract: Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. We introduce a simulation framework for strongly correlated quantum systems that can be represented by model spin Hamiltonians. Our approach leverages reconfigurable qubit architectures to programmably simulate real-time dynamics and introduces an algorithm for extracting chemically relevant spectral properties via classical co-processing of quantum measurement results. We develop a digital-analog simulation toolbox for efficient Hamiltonian time evolution utilizing digital Floquet engineering and hardware-optimized multi-qubit operations to accurately realize complex spin-spin interactions, and as an example present an implementation proposal based on Rydberg atom arrays. Then, we show how detailed spectral and other relevant chemical information can be extracted from these dynamics through snapshot measurements and single-ancilla control, enabling the evaluation of excitation energies and finite-temperature susceptibilities from a single-dataset. To illustrate the approach, we show how this method can be used to compute key properties of a polynuclear transition-metal catalyst and 2D magnetic materials.

Quantum Algebra of Chern-Simons Matrix Model and Large N Limit
2024-02-14 16:00 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Sen Hu (Shanghai Institute for Mathematics and Interdisciplinary Study)
Title: Quantum Algebra of Chern-Simons Matrix Model and Large N Limit
Abstract: In this talk we discuss the algebra of quantum observables of the Chern-Simons matrix model which was originally proposed by Susskind and Polychronakos to describe electrons in fractional quantum Hall effects. We establish the commutation relations for its generators and study the large N limit of its representation. We show that the large N limit algebra is isomorphic to the uniform in N algebra studied by Costello, which is conjecturally isomorphic to the deformed double current algebra studied by Guay. Under appropriate scaling limit, we show that the large N limit algebra degenerates to a Lie algebra which admits a surjective map to the affine Lie algebra of u(p). This leads to a complete proof of the large N emergence of the u(p) current algebra as proposed by Dorey, Tong and Turner. This also suggests a rigorous derivation of edge excitation of a fractional quantum Hall droplet. This is a joint work with Si Li, Dongheng Ye and Yehao Zhou (arXiv: 2308.14046).

What Algorithms can Transformers Learn? A Study in Length Generalization
2024-02-14 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Preetum Nakkiran, Apple
Title: What Algorithms can Transformers Learn? A Study in Length Generalization
Abstract: Large language models exhibit many surprising “out-of-distribution” generalization abilities, yet also struggle to solve certain simple tasks like decimal addition. To clarify the scope of Transformers’ out-of-distribution generalization, we isolate this behavior in a specific controlled setting: length-generalization on algorithmic tasks. Eg: Can a model trained on 10 digit addition generalize to 50 digit addition? For which tasks do we expect this to work?
Our key tool is the recently-introduced RASP language (Weiss et al 2021), which is a programming language tailor-made for the Transformer’s computational model. We conjecture, informally, that: Transformers tend to length-generalize on a task if there exists a short RASP program that solves the task for all input lengths. This simple conjecture remarkably captures most known instances of length generalization on algorithmic tasks, and can also inform design of effective scratchpads. Finally, on the theoretical side, we give a simple separating example between our conjecture and the “min-degree-interpolator” model of learning from Abbe et al. (2023).
Joint work with Hattie Zhou, Arwen Bradley, Etai Littwin, Noam Razin, Omid Saremi, Josh Susskind, and Samy Bengio. To appear in ICLR 2024.

Characteristic Initial Value Problem for the 3D Compressible Euler Equations
2024-02-13 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Sifan Yu, NUS
Title: Characteristic Initial Value Problem for the 3D Compressible Euler Equations
Abstract: We present the first result for the characteristic initial value problem of the compressible Euler equations in three space dimensions without any symmetry assumption. We allow presence of vorticity and consider any equation of state. Compared to the standard Cauchy problem, where initial data can be freely prescribed on a constant-time hypersurface, we formulate the problem by distinguishing between the “free-component” and the “constrained-component” of the initial data. The latter is to be solved by the “free-component” utilizing the properties of the compressible Euler equations on the initial null hypersurfaces. Then, we establish a priori estimates, followed by a local well-posedness and a continuation criterion argument. Moreover, we prove a regularity theory in Sobolev norms. Our analysis critically relies on the vectorfield method due to the nature of the problem. This is a joint work with Jared Speck.

Machine Learning and Scientific Computing: There is plenty of room in the middle
2024-02-12 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Petros Koumoutsakos, Harvard SEAS
Title: Machine Learning and Scientific Computing: There is plenty of room in the middle
Abstract: Over the last thirty years we have experienced more than a billion-fold increase in hardware capabilities and a dizzying pace of acquiring and transmitting massive amounts of data. Scientific Computing and, more lately, Artificial Intelligence (AI) has been key beneficiaries of these advances. In this talk I would outline the need for bridging the decades long advances in Scientific Computing with those of AI. I will use examples from fluid mechanics to argue for forming alloys of AI and simulations for their prediction and control. I will present novel algorithms for learning the Effective Dynamics (LED) of complex systems and a fusion of multi- agent reinforcement learning and scientific computing (SciMARL) for modeling and control of turbulent flows. I will also show our recent work on Optimizing a Discrete Loss (ODIL) that outperforms popular techniques such as PINNs by several orders of magnitude.
I will juxtapose successes and failures and argue that the proper fusion of scientific computing and AI expertise are essential to advance scientific frontiers.

AQFT Lecture Series | David Ben-Zvi
2024-02-09 15:30 - 16:30, 2024-02-09 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Arithmetic Quantum Field Theory Program Lecture Series
Speaker: David Ben-Zvi
Topic: The Langlands program via arithmetic QFT
Abstract: Structures in QFT (like factorization for observables and functorial QFT for states and their relation to geometric / deformation quantization) that are sufficiently algebraic and formal to allow for arithmetic analogs.
