CMSA

CMSA Q&A Seminar 3/19/2024
2024-03-19 12:30 - 13:30 (America/New_York) | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q and A Seminar

Speaker: Arthur Jaffe, Harvard University

Question: What is mathematical picture language?

Scattering Rigidity Problem
2024-03-19 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Jin Jia, Hunan University
Title: Scattering Rigidity Problem
Abstract: If the asymptotic behavior of a solution to a nonlinear equation is the same as that of a solution to its linearized equation, it is called a scattering solution. Scattering phenomena are widely observed near steady-state solutions of various mathematical physics equations, such as water wave equations, Einstein equations, MHD equations, and Vlasov-Poisson equations. This report takes these equations as examples to provide the definition of scattering operator and its relation to radiation fields. It explains the concepts of scattering rigidity problem and scattering completeness problem, and introduces the latest discoveries of the speaker in the general solution approach to scattering rigidity problem.

Koszul duality & twisted holography for asymptotically flat spacetimes
2024-03-18 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Natalie Paquette, University of Washington
Title: Koszul duality & twisted holography for asymptotically flat spacetimes
Abstract: Koszul duality has been understood in recent years to characterize order-type defects in twists of supersymmetric field theories. This notion has been generalized, from a physical point of view, by studying couplings between D-branes and closed string theories in the topological string. Computing the D-brane backreaction, and studying the resulting open/closed string duality, is the purview of the twisted holography program. Twisted holography seeks to study supersymmetric sectors of the AdS/CFT correspondence using these methods, and leverage the appropriate generalization of Koszul duality to elucidate the bulk/boundary map. When applying these methods to a topological string configuration on twistor space, one can construct an instance of twisted holography in which a 2d chiral algebra, supported on the “celestial sphere”, is dual to a 4d theory in an asymptotically flat spacetime. This is the first such top-down example of holography in a 4d asymptotically flat spacetime. This talk describes joint work done, variously, with Kevin Costello, Brian Williams, and Atul Sharma.

AQFT Lecture Series
2024-03-18 13:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Xinwen Zhu (Stanford)
Title: The tame categorical local Langlands correspondence.
Abstract: I will discuss a conjectural categorical form of the local Langlands correspondence for p-adic groups and establish the tame part of such correspondence (currently for unramified groups with connected center, and for Q_l-coefficients). I will also explain how to extract a (n enhanced) discrete Langlands parameter for depth zero supercuspidal representations from the categorical equivalence.

AQFT Lecture Series
2024-03-15 14:15 - 15:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Tasho Kaletha (University of Michigan)
Title: Covers of reductive groups and functoriality
Abstract: When studying problems arising from Langlands’ functoriality principle, one often encounters groups that are extensions of complex reductive groups by Galois groups, but that do not necessarily satisfy all properties to be L-groups of reductive groups. We will show, in the case of a local base field F, that such group can be understood as L-groups of covers of reductive groups. This generalizes to the case of arbitrary local fields work of Adams–Vogan for real groups. These covers, for a fixed connected reductive group G, can be understood either as arising from a certain “universal” cover of the topological group G(F) by a certain “fundamental” group tildepi_1(G). We will present two concrete applications of this, one that gives a characterization of the local Langlands correspondence for supercuspidal L-parameters when p is sufficiently large, and one to the construction of transfer factors in the theory of endoscopy.

AQFT Lecture Series
2024-03-15 11:45 - 12:45 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Baiying Liu (Purdue)
Title: Recent progress on certain problems related to local Arthur packets of classical groups
Abstract: In this talk, I will introduce recent progress on certain problems related to local Arthur packets of classical groups. First, I will introduce a joint work with Freydoon Shahidi towards Jiang’s conjecture on the wave front sets of representations in local Arthur packets of classical groups, which is a natural generalization of Shahidi’s conjecture, confirming the relation between the structure of wave front sets and the local Arthur parameters. Then, I will introduce a joint work with Alexander Hazeltine and Chi-Heng Lo on the intersection problem of local Arthur packets for symplectic and split odd special orthogonal groups, with applications to the Enhanced Shahidi’s conjecture, the closure relation conjecture, and the conjectures of Clozel on unramified representations and on unramified components of automorphic representations. This intersection problem also has been worked out independently at the same time by Hiraku Atobe. In a recent joint work with Alexander Hazeltine, Chi-Heng Lo, and Freydoon Shahidi, we made an upper bound conjecture on wavefront sets of admissible representations of connected reductive groups. In the last part of my talk, I will introduce our recent progress towards this conjecture.

Monopoles, scattering, generalized symmetries
2024-03-15 10:00 - 11:30 | Virtual
Quantum Matter in Mathematics and Physics Seminar
Speaker: Diego Delmastro (Simons Center for Geometry and Physics)
Title: Monopoles, scattering, generalized symmetries

Abstract: Gauge theory is a very mature subject by now. Surprisingly, some of its symmetries have only been properly understood in the last couple of years. Specifically, such theories typically have a very rich set of symmetries, involving modern notions such as higher-form symmetries, higher-group symmetries, and categorical symmetries. A proper understanding of these generalized symmetries is not really crucial if we are interested in scattering processes involvingfundamental particles only, but it does become quite essential if we want to add monopoles into the mix. In this talk I will review where these generalized symmetries come from, and how they impose constraints on scattering amplitudes of elementary particles against heavy monopoles. This will allow us to resolve a decades-old puzzle concerning such processes, where incoming electrons appear to become fractional particles after the scattering event.

Cluster state as a noninvertible SPT phase
2024-03-13 10:00 - 12:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Shu-Heng Shao (SUNY Stony Brook)
Title: Cluster state as a noninvertible SPT phase

Abstract: We will point out a non-invertible symmetry of the ordinary 1+1d Z2xZ2 cluster Hamiltonian. Therefore, the cluster state can be viewed as a non-invertible SPT phase under this fusion category symmetry, which is Rep(D8). We furthermore find two new stabilizer states that are distinct from the cluster state as Rep(D8) SPT phases, but identical as Z2xZ2 SPT phases. Finally, we discuss the degenerate edge modes at the interfaces between these three Rep(D8) SPT phases.

AQFT Lecture Series
2024-03-08 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Dihua Jiang (U Minnesota)
Title: Shalika Periods: Functoriality and Arithmetic
Abstract: Shalika periods of automorphic forms were first used by H. Jacquet and J. Shalika (1990) in their construction of global zeta integrals for exterior square L-functions of GL(2n). They were also used by S. Friedberg and H. Jacquet (1993) in their construction of global zeta integrals for the standard L-functions with connections to the linear periods. A. Ash and D. Ginzburg (1994) used them in their study of p-adic L-functions of GL(2n). In this talk, we will first review the implication of the Shalika periods to the Langlands functoriality and the connections with automorphic descents and theta correspondence. Then we turn to my recent work joint with B. Sun and F. Tian on an application of Shalika periods to algebraicity of critical L-values of cuspidal automorphic of GL(2n) of symplectic type.

Symmetry in quantum field theory
2024-03-08 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Dan Freed (Harvard Mathematics and CMSA)
Title: Symmetry in quantum field theory
Abstract: In joint work with Greg Moore and Constantin Teleman we show how ideas and techniques in topological field theory apply to the study of symmetry in quantum field theory. I will discuss how this came about, beginning with some discussion of symmetry in mathematics more generally, and give some examples.

A model for studying the sign problem on quantum computers: Z(3) gauge theory with three fermion flavors in 1+1 dimensions
2024-03-08 09:00 - 10:00 | Virtual
Quantum Matter in Mathematics and Physics Seminar
Speaker: Semeon Valgushev (Iowa State University)
Title: A model for studying the sign problem on quantum computers: Z(3) gauge theory with three fermion flavors in 1+1 dimensions
Abstract: Many properties of quantum field theories can be understood with the help of classical numerical methods. Yet there are several outstanding problems — most remarkably the behaviour of nuclear matter at finite density and out-of-equilibrium real-time dynamics — that require the use of quantum algorithms. We present a simple yet physically rich toy model of QCD/nuclear matter at finite density, termed “QZD”, where Z stands for Z(3) gauge theory coupled to Nf = 3 fermion flavors, suitable for simulation on near-term quantum devices. We study it using tensor networks and find that in weak coupling the spectrum is that of the expected mesons and baryons, although the corrections in weak coupling are nontrivial. In strong coupling, besides the usual baryon, the singlet meson is a baryon anti-baryon state. For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively.

AQFT Lecture Series
2024-03-07 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: John Francis (Northwestern)
Title: Integrating braided categories over 3-manifolds
Abstract: I’ll describe a form of factorization homology, which gives an invariant of framed 3-manifolds given as input a rigid braided-monoidal category with duals. More generally, the construction gives an invariant of framed n-manifolds from an E_{n-1}-monoidal category with duals. This construction relies on a form of the tangle hypothesis, that a dualizable object in an E_{n-1}-monoidal category uniquely determines a functor from the category of tangles in n-space. This is joint work with David Ayala.

AQFT Lecture Series
2024-03-07 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: An Huang (Brandeis)
Title: Tate’s thesis and p-adic strings
Abstract: I shall explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis, which in particular, gives rise to an attempt of physically deriving quadratic reciprocity. I shall then propose a genus one p-adic string worldsheet action, where the key is an explicit definition of a p-adic Laplacian operator on a Tate curve, and the computation of its Green’s function. I shall also mention a very recent attempt of developing a Lorentzian version of the p-adic worldsheet action.

Geometric construction of toric NCRs
2024-03-07 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Jesse Huang, University of Alberta
Title: Geometric construction of toric NCRs
Abstract: The Rouquier dimension of a toric variety is recently shown to be achieved by the Frobenius pushforward of O via coherent-constructible correspondence. From the perspective of noncommutative geometry, this result leads to a geometric construction of toric NCR of the invariant ring of the Cox ring with respect to a multi-grading which also gives the information about its global dimension. From the perspective of mirror symmetry, the same construction provides a universal “wall skeleton” capturing VGIT wall-crossings, which contains a window for each chamber as a full subcategory. From the perspective of commutative algebra, the same construction indicates the existence of virtual resolutions of the multigraded diagonal bimodule, which agrees with a recent result of Hanlon-Hicks-Larzarev constructing one such resolution explicitly. In this talk, I will survey these perspectives. The talk is based on joint works with P. Zhou, joint works with D. Favero, and work in progress with D. Favero.

LILO: Learning Interpretable Libraries by Compressing and Documenting Code
2024-03-06 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Gabe Grand, MIT CSAIL and Dept. of EE&CS
Title: LILO: Learning Interpretable Libraries by Compressing and Documenting Code
Abstract: While large language models (LLMs) now excel at code generation, a key aspect of software development is the art of refactoring: consolidating code into libraries of reusable and readable programs. In this paper, we introduce LILO, a neurosymbolic framework that iteratively synthesizes, compresses, and documents code to build libraries tailored to particular problem domains. LILO combines LLM-guided program synthesis with recent algorithmic advances in automated refactoring from Stitch: a symbolic compression system that efficiently identifies optimal lambda abstractions across large code corpora. To make these abstractions interpretable, we introduce an auto-documentation (AutoDoc) procedure that infers natural language names and docstrings based on contextual examples of usage. In addition to improving human readability, we find that AutoDoc boosts performance by helping LILO’s synthesizer to interpret and deploy learned abstractions. We evaluate LILO on three inductive program synthesis benchmarks for string editing, scene reasoning, and graphics composition. Compared to existing neural and symbolic methods – including the state-of-the-art library learning algorithm DreamCoder – LILO solves more complex tasks and learns richer libraries that are grounded in linguistic knowledge.

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

Speaker: Yannai Gonczarowski, Harvard University

Question: What do people mean when they say ‘the intersection between theoretical computer science and economic theory’?

CMSA Q&A Seminar 3/5/2024
2024-03-05 12:30 - 13:30 | 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.
