AQFT Lecture Series | David Ben-Zvi
2024-02-09 14:00 - 15:00, 2024-02-09 15:30 - 16:30 (America/New_York) | 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.

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.

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.

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).

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.

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?

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.

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.

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.

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.

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?

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

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

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.

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.

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.

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?

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’?

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.

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.

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.

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.

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.

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.

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
2024-03-18 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.

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.

CMSA Q&A Seminar 3/19/2024
2024-03-19 12:30 - 13:30 | 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?

AQFT Lecture Series
2024-03-20 11:00 - 12:15 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Stephen D. Miller (Rutgers University)
Title: What 4-graviton scattering amplitudes had to say about the unitary dual
Abstract: I’ll give an update on the problem of describing all unitary representations of a Lie group, including joint work with Michael Green and Pierre Vanhove that used intuition from string theory to show the unitarity of the “next to minimal” representation of E8, and more recent work with Joe Hundley and Jeff Adams, Marc van Leeuwen, and David Vogan.
