CMSA

The Andersen-Kashaev volume conjecture for FAMED geometric triangulations
2025-03-24 15:00 - 16:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Ka Ho Wong (Yale)
Title: The Andersen-Kashaev volume conjecture for FAMED geometric triangulations
Abstract: In the early 2010s, Andersen and Kashaev defined a TQFT based on quantum Teichmuller theory. In particular, they define a partition function for every ordered ideal triangulation of hyperbolic knot complement in $mathbb{S}^3$ equipped with an angle structure. The Andersen-Kashaev volume conjecture suggests that the partition function can be expressed in terms of a Jones function of the knot which, in its semi-classical limit, decay exponentially with decay rate the hyperbolic volume of the knot complement. In this talk, we will introduce a purely combinatorial condition on triangulations which, together with the geometricity of the triangulations, imply the Andersen-Kashaev volume conjecture and its generalization. This talk is based on the joint work with Fathi Ben Aribi.

Program on Classical, quantum, and probabilistic integrable systems - novel interactions and applications
2025-03-24 09:00 - 2025-05-24 17:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Program on Classical, quantum, and probabilistic integrable systems – novel interactions and applications
Dates: March 24–May 24, 2025
Location: CMSA, 20 Garden Street, Cambridge MA 02138
Exactly solvable models have played pivotal roles in mathematics and physics throughout their history. The program is dedicated to exploring and developing a more recent wave of their influence in stochastic models together with accompanying combinatorial, classical, and quantum integrable systems. Topics will include:

Colored and uncolored interacting particle systems with associated vertex models and line ensembles
Yang-Baxter integrability and its applications in algebraic combinatorics, quantum systems, and conformal field theory
Quantum stochastic models, quantum exclusion processes, and free probability
Emerging new aspects of classical and quantum integrable systems – hydrodynamics, large deviations of stochastic models, and random surface models

Organizers:

Amol Aggarwal, Columbia University & Clay Mathematics Institute
Guillaume Barraquand, École normale supérieure, Paris
Alexei Borodin, MIT
Ivan Corwin, Columbia University
Pierre Le Doussal, École normale supérieure, Paris
Michael Wheeler, University of Melbourne

Participants

Denis Bernard, Ecole Normale Supérieure Paris
Alexey Bufetov, University of Leipzig
Pasquale Calabrese, SISSA Trieste
Sylvie Corteel, UC Berkeley
Cesar Cuenca, Ohio State University
Jan De Gier, University of Melbourne
Andrea De Luca, CNRS, Cergy Paris University
Benjamin Doyon, King’s College London
Patrik Ferrari, University of Bonn
Vadim Gorin, UC Berkeley
Tamara Grava, SISSA
Jimmy He, Ohio State University
Jiaoyang Huang, University of Pennsylvania
Kurt Johansson, KTH Stockholm
Richard Kenyon, Yale
Alexandre Krajenbrink, Cambridge Quantum Computing & Quantinuum
Atsuo Kuniba, University of Tokyo
Matteo Mucciconi, National University of Singapore
Greta Panova, University of Southern California
Leonid Petrov, University of Virginia
Sylvain Prolhac, Université Paul Sabatier, Toulouse
Tomaž Prosen, University of Ljubljana
Tomohiro Sasamoto, Tokyo Institute of Technology
Herbert Spohn, Technical University of Munich
Li-Cheng Tsai, University of Utah

Schedule
Week 1
Monday, March 24th
11:00am – 12:00pm Room G-10, Lecture 1 of 4: Denis Bernard, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs
12:00 – 2:00pm Common Room: Program Lunch
4:00 – 4:30pm Common Room: CMSA colloquium tea
4:30 – 5:30pm Common Room, CMSA colloquium: Amol Aggarwal, Columbia University: The Toda Lattice as a Soliton Gas

Tuesday, March 25th
3:30 – 4:00pm Common Room: Program tea
4:00 – 5:00pm Room G-10, Seminar: Patrik Ferrari, Universität Bonn: Decoupling and decay of two-point functions in a two-species TASEP

Wednesday, March 26th
11:00am – 12:00pm Room G-10, Lecture 1 of 3: Atsuo Kuniba, University of Tokyo: Multispecies ASEP and t-PushTASEP on a ring and a strange five vertex model
3:00 – 4:00pm Room G-10, Lecture 2 of 4: Denis Bernard, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs
4:30 – 5:30pm Common Room: Program wine and cheese reception

Thursday, March 27th
11:00am – 12:00pm Room G-10, Lecture 1 of 2: Benjamin Doyon, King’s College London: The equations of generalised hydrodynamics, and their unusual diffusve corrections
Abstract: I will discuss the hydrodynamics of one-dimensional many-body integrable models. At the Euler scale, this is given by “generalised hydrodynamics”, whose equations only depend on the asymptotic state content and the two-body scattering shift of the model. I will explain how these equations arise, and mention some of their properties: Hamiltonian structure, exact solutions, absence of shocks. At the diffusive scale, generic one-dimensional models with state-dependent currents display super-diffusion. However, integrable models are in a special class of “linearly degenerate systems”, where there is no superdiffusion, and one might expect a standard derivative expansion. I will explain how the diffusive corrections to the Euler equations are not given by a derivative expansion, but instead governed by long-range correlations coming from an Euler-scale fluctuation theory. I will give the general ideas behind this fluctuation theory, where initial fluctuations are deterministically transported by the Euler equation. I will finally provide arguments for the conjecture that, once long-range correlations are accounted for, there is no emergent stochasticity at all scales of hydrodynamics in integrable systems.
3:30 – 4:00pm Common Room: Program tea
4:00 – 5:00pm Room G-10, Seminar: Sylvie Corteel, University of California at Berkeley: Crystal Skeletons

Friday, March 28th
12:00 – 1:00 pm Common Room: Lunch with CMSA Member Seminar
2:00 – 3:00pm Room G-10, Lecture 3 of 4 : Denis Bernard, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs
3:30 – 4:00 pm Common Room: Program tea

Week 2
Monday, March 31
11:00am – 12:00pm Room G-10, Lecture 2 of 2: Benjamin Doyon, King’s College London: The equations of generalised hydrodynamics, and their unusual diffusve corrections
Abstract: I will discuss the hydrodynamics of one-dimensional many-body integrable models. At the Euler scale, this is given by “generalised hydrodynamics”, whose equations only depend on the asymptotic state content and the two-body scattering shift of the model. I will explain how these equations arise, and mention some of their properties: Hamiltonian structure, exact solutions, absence of shocks. At the diffusive scale, generic one-dimensional models with state-dependent currents display super-diffusion. However, integrable models are in a special class of “linearly degenerate systems”, where there is no superdiffusion, and one might expect a standard derivative expansion. I will explain how the diffusive corrections to the Euler equations are not given by a derivative expansion, but instead governed by long-range correlations coming from an Euler-scale fluctuation theory. I will give the general ideas behind this fluctuation theory, where initial fluctuations are deterministically transported by the Euler equation. I will finally provide arguments for the conjecture that, once long-range correlations are accounted for, there is no emergent stochasticity at all scales of hydrodynamics in integrable systems.
12:00 – 2:00pm Common Room: Program Lunch
2:00 – 3:00pm Room G-10, Lecture 2 of 3: Atsuo Kuniba, University of Tokyo: Solutions of tetrahedron and 3D reflection equations from quantum cluster algebras

Abstract: Tetrahedron and 3D equations are three-dimensional generalizations of the Yang-Baxter and the reflection equations. I will explain how quantum cluster algebras lead to solutions that generalize and unify many known solutions.

3:30 – 4:00pm Program tea

Tuesday, April 1
11:00am – 12:00pm Room G-10, Lecture 1 of 2: Kurt Johansson, KTH Stockholm: Extremal particles in uniform random Gelfand-Tsetlin patterns
Abstract: I will report on joint work with Elnur Emrah on edge fluctuations in uniform random interlacing patterns with fixed top configuration. The goal is to describe all possible limit processes that can occur, and the conditions under which they occur.
3:30pm – 4:00pm, Common Room: Program tea

Wednesday, April 2
11:00am – 12:00pm Room G-10, Lecture 4 of 4: Denis Bernard, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs
3:00 – 4:00pm Room G-10, Lecture 3 of 3: Atsuo Kuniba, University of Tokyo: Box-ball systems
Abstract: Box-ball systems are one-dimensional integrable cellular automata introduced in 1990. This talk surveys major developments that have unfolded consistently over the decades, enriching the scope of the theory. Topics include ultradiscretization, crystal theory in quantum groups, the combinatorial and thermodynamic Bethe ansatz, as well as generalized hydrodynamics.
4:30 – 5:30pm Common Room: Program wine and cheese reception

Thursday, April 3
11:00am – 12:00pm Room G-10, Lecture 2 of 2: Kurt Johansson, KTH Stockholm: Extremal particles in uniform random Gelfand-Tsetlin patterns
Abstract: I will report on joint work with Elnur Emrah on edge fluctuations in uniform random interlacing patterns with fixed top configuration. The goal is to describe all possible limit processes that can occur, and the conditions under which they occur.
3:30pm – 4:00pm Common Room: Program tea

Friday, April 4
12:00 – 1:00pm Common Room: CMSA Member Seminar and Lunch
3:30 – 4:00pm Common Room: Program tea

Week 3
Monday, April 7
12:00 – 2:00pm Common Room: Program lunch
4:00 – 4:30pm Tea with CMSA colloquium
4:30 – 5:30pm CMSA Colloquium: Ben Webster, University of Waterloo and Perimeter Institute: 3-D Mirror Symmetry

Tuesday, April 8
11:00am – 2:00pm Room G-10, Pierre Le Doussal, École normale supérieure de Paris: Exact results for the macroscopic fluctuation theory of the 1D weakly asymmetric exclusion process.
3:30 – 4:00pm Common Room: Program tea

Wednesday, April 9
12:00 – 1:00pm Common Room, CMSA Q&A Seminar and lunch: Eric Maskin, Harvard Economics: The Mathematics of Voting
4:30 – 5:30pm Common Room: Program wine and cheese reception

Thursday, April 10
3:30 – 4:00pm Common Room: Program tea

Friday, April 11
12:00 – 1:00pm Common Room: CMSA member seminar and lunch
3:30 – 4:00pm Common Room: Program tea

Week 4
Monday, April 14
12:00 – 2:00pm Common Room: Program lunch
4:00 – 4:30pm Tea with CMSA colloquium
4:30 –5:30pm CMSA colloquium: Andrey Smirnov, University of North Carolina at Chapel Hill: Quantum K-theory at roots of unity

Tuesday, April 15
11:00 am – 12:00pm Room G-10, Ivan Corwin, Columbia University: How Yang-Baxter unravels Kardar-Parisi-Zhang
Abstract: Over the past few decades, physicists and then mathematicians have sought to uncover the (conjecturally) universal long time and large space scaling limit for the so-called Kardar-Parisi-Zhang (KPZ) class of stochastically growing interfaces in (1+1)-dimensions. Progress has been marked by several breakthroughs, starting with the identification of a few free-fermionic integrable models in this class and their single-point limiting distributions, widening the field to include non-free-fermionic integrable representatives, evaluating their asymptotics distributions at various levels of generality, constructing the conjectural full space-time scaling limit, known as the directed landscape, and checking convergence to it for a few of the free-fermion representatives.
In this talk, I will describe a method that should prove convergence for all known integrable representatives of the KPZ class to this universal scaling limit. The method has been fully realized for the Asymmetric Simple Exclusion Process and the Stochastic Six Vertex Model. It relies on the Yang-Baxter equation as its only input and unravels the rich complexity of the KPZ class and its asymptotics from first principles. This is based on a few works involving Amol Aggarwal, Alexei Borodin, Milind Hegde, Jiaoyang Huang and me.
3:30 – 4:00pm Common Room: Program tea

Wednesday, April 16
11:00am – 12:00pm Room G-10, Tamara Grava, University of Bristol: Random solitons and soliton gas
Abstract: A soliton is a localised travelling wave solution of a nonlinear dispersive equation. When the equation is integrable the interaction of many solitons is elastic. We study the behaviour of a set of N solitons for the Korteweg de Vries equation in the limit N goes to infinity (soliton gas) and the interaction of the soliton gas with a distinct soliton that we call a tracer soliton. We show that the average velocity of the tracer soliton satisfies the Zakharov-El kinetic equations. We then consider a set of random N soliton solution q_N(x,t) and its limiting soliton gas q(x,t). We prove a central limit theorem for the difference q_N(x,t)-q(x,t) for values of x and t that are bounded by log(N).
12:00 – 1:00pm Common Room: CMSA Q&A seminar and lunch: Noah Golowich, MIT: What is length generalization in large language models?
4:30 – 5:30pm Common Room: Program wine and cheese reception

Thursday, April 17
11:00am – 12:00pm Room G-10, Guillaume Barraquand, École normale supérieure de Paris: Large time cumulants of the open KPZ equation
12:00 – 1:00pm Common Room: lunch with featured Yip Lecture speaker Scott Aaronson and CMSA residents
3:30pm Common Room: Program tea
4:00 – 5:00pm Science Center Hall A: Fifth Annual Yip Lecture, Scott Aaronson: How Much Math is Knowable?
5:00 – 6:00pm Math Department Common Room at the Harvard Science Center: Yip Lecture reception

Friday, April 18
12:00 – 1:00pm Common Room: CMSA Member Seminar and lunch: Han Shao, Harvard CMSA, Topic TBD
3:30 – 4:00pm Common Room: Program tea

Week 5

Monday, April 21
11:00am – 12:00pm Room G-10, Tomaz Prosen, University of Ljubljana, Lecture 1 of 3: On Integrable Quantum and Classical Circuits (with Stochastic Boundaries)
Abstract: I will introduce Yang-Baxter integrable brickwork quantum circuit models and discuss their integrability structure, specifically, the transfer matrix, conservation laws etc. A paradigmatic example, XXZ or unitary 6-vertex circuits exhibit an unusual link to KPZ scaling at the isotropic (SU(2) symmetric) point. I will establish the link to corresponding classical integrable Landau-Lifshitz circuits and discuss some aspects of transport and full counting statistics.
12:00 – 2:00pm Common Room: Program Lunch
4:00 – 4:30pm Common Room: CMSA colloquium tea
4:30 – 5:30pm Common Room, CMSA colloquium: Ila Fiete, MIT: Modeling the emergence of complex cortical structure from simple precursors in the brain: maps, hierarchies, and modules

Tuesday, April 22
11:00am – 12:00pm Room G-10, Tomohiro Sasamoto, Tokyo Institute of Technology: Large deviation of symmetric models through classical integrable systems
3:30pm Common Room: Program tea

Wednesday, April 23
11:00am – 12:00pm Room G-10, Tomaz Prosen, University of Ljubljana: On Integrable Quantum and Classical Circuits (with Stochastic Boundaries)
Abstract: I will discuss explicit matrix product solutions for quantum many-body Markov chains, defined for a Yang-Baxter integrable quantum circuit with specific stochastic Kraus processes at its boundaries. In the continuous time limit, these solutions correspond to steady states of boundary driven Lindbladian dynamics and often yield non-trivial quasi-local conservation laws of integrable spin chains. The specific case of XXZ and Hubbard chain will be discussed.
12:00 – 1:00pm Common Room: CMSA Q&A seminar and lunch: Alexei Borodin, MIT: Connections between physics and probability
4:30 – 5:30pm Common Room: Program wine and cheese reception

Thursday, April 24
11:00am – 12:00pm Room G-10, Sylvain Prolhac, Université Paul Sabatier, Toulouse: Approach to stationarity for KPZ fluctuations in finite volume
Abstract: At late times $t$, the cumulants of the height for the KPZ fixed point in finite volume behave as affine functions of time $c_k(t) = a_k t+b_k$, up to exponentially small corrections. The constant term $b_k$ is the last remaining information about the initial state observable at long enough times. Two approaches allow us to compute this constant from the totally asymmetric exclusion process, a discrete version of the KPZ fixed point. First, an iterated version of the matrix product representation for the stationary state leads, for arbitrary initial conditions, to expressions involving extreme value statistics of Brownian paths. On the other hand, Bethe ansatz leads to rather explicit expressions for simple initial conditions. Comparison between the two approaches then provides conjectures for some generating functions of Brownian paths.
3:30pm Common Room: Program tea

Friday, April 25
11:00am – 12:00pm Room G-10, Tomaz Prosen, University of Ljubljana, Lecture 3 of 3: On Integrable Quantum and Classical Circuits (with Stochastic Boundaries)
Abstract: In the last lecture I will discuss the possibility of quantum integrability of many-body quantum Markov chain generators, such as Lindbladians with bulk or boundary dissipation, and the corresponding circuit (Kraus) counterparts. The paradigmatic example is the XX model with dephasing noise which can be mapped to a Hubbard model with imaginary interaction, both in the Hamiltonian and circuit formulation.
3:30 – 4:00pm Common Room: Program tea

Week 6

Monday, April 28
11:00am – 12:00pm Room G-10, Herbert Spohn, Technische Universitaet Muenchen, Lecture 1 of 3: Integral many-body systems and GHD
12:00 – 2:00pm Common Room: Program Lunch
2:00 – 3:00 pm Room G-10, Tomohiro Sasamoto, Tokyo Institute of Technology, Exact density profile and current fluctuations in a tight-binding chain with dephasing noise
Abstract: We consider a tight-binding chain with dephasing noise, whose time evolution is described by the quantum master equation called the Gorini-Kossakowski-Sudarhan-Lindblad (GKSL) equation. By using a connection of this model to the Hubbard model with imaginary coupling [1], we study the density profile [2] and the variance of the current [3] exactly for the model on the infinite line by writing down contour integral formulas using Bethe ansatz. The talk is based on collaborations with Taiki Ishiyama and Kazuya Fujimoto.
4:00 – 4:30pm Common Room: CMSA colloquium tea
4:30 –5:30pm Room G-10, CMSA colloquium: Peter Sarnak, IAS and Princeton University, Bass-Note Spectra of locally uniform geometries

Tuesday, April 29
11:00 am – 12:00pm Room G-10, Pasquale Calabrese, SISSA Trieste, Lecture 1 of 3: Quantum Mpemba effect
2:00 – 3:00 pm Room G-10, Greta Panova, University of Southern California, Grothendieck shenanigans: permutons from pipe dreams via integrable probability
Abstract: Pipe dreams are tiling models originally introduced to study objects related to the Schubert calculus and K-theory of the Grassmannian. They can also be viewed as ensembles of random lattice walks with various interaction constraints. In our quest to understand what the maximal and typical algebraic objects look like, we revealed some interesting permutons. The proofs use the theory of the Totally Asymmetric Simple Exclusion Process (TASEP). Deeper connections with domino tilings of the Aztec diamond and its frozen boundary allow us to describe the extreme cases of the original algebraic problem. This is based on joint work with A. H. Morales, L. Petrov, D. Yeliussizov.
3:30 – 4:00pm Common Room: Program tea

Wednesday, April 30
11:00am – 12:00pm Herbert Spohn, Technische Universitaet Muenchen, Lecture 2 of 3: Integral many-body systems and GHD
12:00 – 1:00pm (tentative) Common Room: CMSA Q&A seminar and lunch
3:00 – 4pm Room G-10, Pasquale Calabrese, SISSA Trieste, Entanglement evolution and quasiparticle picture 1
4:30 – 5:30pm Common Room: Program wine and cheese reception

Thursday, May 1
11:00am – 12:00pm Room G-10, Herbert Spohn, Technische Universitaet Muenchen, Lecture 3 of 3: Integral many-body systems and GHD
2:00 – 3:00 pm Room G-10, Li-Cheng Tsai, University of Utah, Stochastic heat flow by moments
Abstract: The Stochastic Heat Flow (SHF) is the scaling limit of the directed polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE), at the critical dimension of two and near the critical temperature. The finite-dimensional distributions of the SHF was obtained by Caravenna, Sun, and Zygouras (2023) by proving that the discrete polymers converge to a universal (model-independent) limit. In this talk, I will report a new approach based on axioms. We formulate the SHF as a two-parameter continuous measure-valued process that satisfies a set of axioms, and prove the uniqueness in law under these axioms. The key feature of the axioms concerns the matching of the first four moments. As an application, we prove the convergence of the noise-mollified SHE to the SHF, which only requires moment estimates.
3:30pm Common Room: Program tea

Friday, May 2
11:00am – 12:00pm Room G-10, Pasquale Calabrese, SISSA Trieste, Lecture 3 of 3: Entanglement evolution and quasiparticle picture 2
12:00 – 1:00pm Common Room, CMSA Member seminar and lunch
2:00 – 3:00 pm Room G-10, Leonid Petrov, University of Virginia: Random Fibonacci Words
Abstract: Fibonacci words are words of 1’s and 2’s, graded by the total sum of the digits. They form a differential poset YF which is an estranged cousin of the Young lattice powering irreducible representations of the symmetric group. We introduce families of “coherent” measures on YF depending on many parameters, which come from the theory of clone Schur functions (Okada 1994). We characterize parameter sequences ensuring positivity of the measures, and we describe the large-scale behavior of some ensembles of random Fibonacci words. The subject has connections to total positivity of tridiagonal matrices, Stieltjes moment sequences, orthogonal polynomials from the (q-)Askey scheme, and residual allocation (stick-breaking) models. Based on a joint work with Jeanne Scott.
3:30 – 4:00pm Common Room: Program tea

Week 7

Monday, May 5
11:00am – 12:00pm Room G-10, Jan De Gier, University of Melbourne, Lecture 1 of 3: Pfaffian point process for TASEP on the half line
12:00 – 2:00pm Common Room: Program Lunch
2:00 – 3:00 pm Jiaoyang Huang, University of Pennsylvania: Ramanujan Property and Edge Universality of Random Regular Graphs
Abstract: Extremal eigenvalues of graphs are of particular interest in theoretical computer science and combinatorics. Specifically, the spectral gap—the difference between the largest and second-largest eigenvalues—measures the expansion properties of a graph. In this talk, I will focus on random d-regular graphs.I will begin by providing background on the eigenvalues of random d-regular graphs and their connections to random matrix theory. In the second part of the talk, I will discuss our recent results on eigenvalue rigidity and edge universality for these graphs. Eigenvalue rigidity asserts that, with high probability, each eigenvalue concentrates around its classical location as predicted by the Kesten-McKay distribution. Edge universality states that the second-largest eigenvalue and the smallest eigenvalue of random d-regular graphs converge to the Tracy-Widom distribution from the Gaussian Orthogonal Ensemble. Consequently, approximately 69% of d-regular graphs are Ramanujan graphs. This work is based on joint work with Theo McKenzie and Horng-Tzer Yau.

4:00 – 4:30pm Common Room: CMSA colloquium tea
4:30 –5:30pm Common Room, CMSA colloquium: Ariel Procaccia, Harvard University, Thinking Outside the Ballot Box

Tuesday, May 6
11:00 am – 12:00pm Room G-10, Jan De Gier, University of Melbourne, Lecture 2 of 3: Pfaffian point process for TASEP on the half line
2:00 – 3:00 Richard Kenyon, Yale University, Multinomial dimers and 3d limit shapes
Abstract: The “multinomial dimer model” on a graph G is the dimer model on the N-fold blow up of G (the graph obtained by replacing each vertex with N vertices and each edge with a complete bipartite graph K_{N,N}). In the large N limit this model is tractable for general graphs: we find formulas for the partition function and limit shapes in some natural settings, including a three-dimensional version of the Aztec Diamond. This is joint work with Catherine Wolfram (Yale).
3:30 – 4:00pm Common Room: Program tea

Wednesday, May 7
3:00 – 4pm Room G-10, Jan De Gier, University of Melbourne, Lecture 3 of 3: Pfaffian point process for TASEP on the half line
4:30 – 5:30pm Common Room: Program wine and cheese reception

Thursday, May 8:
2:00 – 3:00 pm Room G-10, Andrea De Luca, CNRS Cergy Paris University, Monitored quantum systems, product of random matrices and permutations
3:30pm Common Room: Program tea

Friday, May 9:
12:00 – 1:00pm Common Room: CMSA Member Seminar and lunch, Sergiy Verstyuk, Harvard CMSA, Title TBD
2:00 – 3:00 pm Room G-10, Cesar Cuenca, Ohio State University, Random partitions at high temperature
Abstract: By using Fourier transforms based on Jack symmetric polynomials, we study discrete particle ensembles x_1>x_2>…>x_N with the inverse temperature beta in the regime where beta tends to zero, as the number of particles tends to infinity. We prove the LLN and characterize the limiting measure in terms of a moment problem. For fixed-time distributions of special Markov chains, the limiting measures can be expressed in terms of the eigenvalues of certain Jacobi operators.
3:30 – 4:00pm Common Room: Program tea

Week 8

Monday, May 12
11:00am – 12:00pm Room G-10, Jimmy He, Ohio State University, Symmetries of periodic and free boundary measures on partitions
Abstract: The periodic and free boundary q-Whittaker measures are probability measures on partitions defined in terms of q-Whittaker functions and an additional parameter $u$ controlling the behavior of the system at the boundary. I will explain a hidden distributional symmetry of this model which exchanges the $u$ and $q$ parameters, as well as related results on Hall-Littlewood measures. As a special case, we recover identities of Imamura–Mucciconi–Sasamoto. This is joint work with Michael Wheeler.
12:00 – 2:00pm Common Room: Program Lunch
4:00 – 4:30pm Common Room: CMSA colloquium tea
4:30 – 5:30pm Common Room, CMSA colloquium: Anna Seigal, Harvard University, Factorizations for data analysis

Tuesday, May 13
3:30pm Common Room: Program tea

Wednesday, May 14
12:00 – 1:00pm Common Room: CMSA Conference Reports seminar and lunch: Hugo Cui, Harvard CMSA, reporting on the Perimeter Institute Theory+AI Workshop
3:00 – 4:00pm Room G-10, Alexandre Krajenbrink, Cambridge Quantum Computing and Quantinuum, Unveiling the classical integrable structure of the weak noise theory of the KPZ class: example of the matrix Log–Gamma polymer and the q-TASEP
4:30 – 5:30pm Common Room: Program wine and cheese reception

Thursday, May 15
11:00am – 12:00pm Room G-10: Roger Van Peski, Columbia University, Integrability in discrete random matrix theory

Abstract: Integrable structure has been well-used in classical random matrix theory, and recently is also enjoying application in the parallel world of discrete random matrices (over integers, p-adic integers, and finite fields). In this talk I will try to cover—at least briefly—the following:

Some favorite probabilistic results (convergence of discrete random matrix local limits to a new integrable interacting particle system, the ‘reflecting Poisson sea’),
Some exact formulas with Hall-Littlewood polynomials that make these results possible, and
Some intriguing newer formulas (joint with Jiahe Shen) for Hermitian and antisymmetric p-adic matrices, which naturally feature ‘formal’ Hall-Littlewood processes with negative t parameter.

2:00 – 3:00 pm Room G-10, Matteo Mucciconi, National University Singapore, Orthogonality of spin q-Whittaker polynomials
Abstract: Spin q-Whittaker polynomials are a family of symmetric polynomials that can be defined as partition functions of a solvable lattice model. Their study reveals that they possess mysterious properties such as additional “unorthodox” symmetries, eigenrelations with respect to difference operators and a self orthogonality that I will prove in the talk. A particular case of these results include a novel orthogonality for the Grothendieck polynomials from K-theory of Grassmannian. I will also discuss applications to exact solutions of directed random polymer models with Beta weights.
3:30pm Common Room: Program tea

Friday, May 16
12:00 – 1:00pm Common Room: CMSA Member Seminar and lunch: Samy Jelassi, Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining
3:30 – 4:00pm Common Room: Program tea

Videos are available on the Youtube Playlist.

Verlinde's formula in logarithmic conformal field theory
2025-03-17 16:40 - 17:40 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Thomas Creutzig (University of Alberta)
Title: Verlinde’s formula in logarithmic conformal field theory
Abstract: Two-dimensional conformal field theories lead to rich mathematical structure. For example its chiral algebra is a vertex algebra and the axioms of rational conformal field theory define modular tensor categories. A highlight of this development was Verlinde’s formula of rational conformal field theory, a formula that computes tensor product rules from modular data of characters.
Nowadays one is interested in logarithmic conformal field theories, in particular the underlying representation categories of the vertex algebras are not semi-simple and usually also not finte. Modular data and Verlinde’s formula become quite a mystery and I will explain how to resolve it.

Freedman CMSA Seminar: Michael Freedman (CMSA) & Elia Portnoy (MIT)
2025-03-12 15:00 - 17:00 | Hybrid – G10
Freedman CMSA Seminar
Speaker: Michael Freedman, Harvard CMSA (3:00–4:00 pm ET)
Title: How many links can you fit in a box?
Abstract: I’ll discuss a “made up” problem on the interface of topology and packing, which may well be classified as “recreational math”. Here is the first question suppose you have a unit box, how many unlinked (split) copies of the Hopf link (c_1,i,c_2,i) and be embedded so that for each copy the two components c_1,i and c_2,i maintain a distance of at least some fixed epsilon >0. Is this number even finite?

Speaker: Elia Portnoy, MIT (4:00–5:00 pm ET)
Title: An explicit packing of links in a box and some progress in quantitative embeddings
Abstract: Following Freedman’s talk, I’ll begin by showing how to pack a large number of links in a box with certain geometric and topological constraints (joint with Fedya Manin). If time permits, I’ll also discuss some progress and open questions for the following quantitative embedding problem: given a simplicial complex X, what is the smallest size of a map from X to R^n so that the preimage of each unit ball intersects a small constant number of simplices?

Discovery in Mathematics with Automated Conjecturing
2025-03-12 14:00 - 15:00 | Hybrid – G10
New Technologies in Mathematics Seminar
Speaker: Randy Davila, RelationalAI and Rice University
Title: Discovery in Mathematics with Automated Conjecturing
Abstract: Automated conjecturing is a form of artificial intelligence that applies heuristic-driven methods to mathematical discovery. Since the late 1980s, systems such as Fajtlowicz’s Graffiti, DeLaViña’s Graffiti.pc, and TxGraffiti have collectively contributed to over 130 publications in mathematical journals. In this talk, we outline the evolution of automated conjecturing, focusing on TxGraffiti, a program that employs linear optimization methods and several distinct heuristics to generate mathematically meaningful conjectures. We will then introduce GraphMind, a dueling framework where the Optimist proposes conjectures while the Pessimist seeks counterexamples, fostering a feedback loop that strengthens automated reasoning. Finally, we will present GraffitiAI, a Python package that extends automated conjecturing across various mathematical domains.
Bio: Randy R. Davila is a Lecturer in the Department of Computational Applied Mathematics & Operations Research at Rice University and a Library Engineer at RelationalAI, specializing in relational knowledge graph systems for intelligent data management. He earned his PhD in Mathematics from the University of Johannesburg in 2019, with research focused on graph theory and combinatorial optimization. His work explores artificial intelligence in mathematical conjecture generation, graph theory, and neural network applications to combinatorial problems. As the creator of TxGraffiti, he has developed AI-driven systems that have contributed to numerous mathematical publications. His recent projects include GraphMind, a dueling agent-based framework that pairs conjecture generation with counterexample discovery, and GraffitiAI, a Python package for automated conjecturing across mathematical disciplines.

CMSA Q&A Seminar: Dan Freed
2025-03-12 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Dan Freed, Harvard University
Topic: What are spectra (in homotopy theory)?

Introduction to the probabilistic approach to Louville theory
2025-03-11 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Leon Liu, Harvard
Title: Introduction to the probabilistic approach to Louville theory
Abstract: I will give an introduction to the probabilistic approach to Louville theory, following Hairer’s notes.

Positive scalar curvature with point singularities
2025-03-11 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Rudolf Zeidler, Mathematical Institute, University of Münster
Title: Positive scalar curvature with point singularities
Abstract: I will explain a certain topological construction of positive scalar curvature metrics with uniformly Euclidean ($L^infty$) point singularities. This provides counterexamples to a conjecture of Schoen. It also shows that there are metrics with uniformly Euclidean point singularities which cannot be smoothed via a geometric flow while simultaneously preserving non-negativity of the scalar curvature. Based on recent joint work with Simone Cecchini and Georg Frenck.

Comments on Non-Invertible Symmetries in K3 CFTs and the Conway Moonshine Module
2025-03-10 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Sarah Harrison, Northeastern
Title: Comments on Non-Invertible Symmetries in K3 CFTs and the Conway Moonshine Module
Abstract: There is an established connection between discrete symmetry groups of K3 non-linear sigma models and a distinguished N=1 chiral SCFT called the Conway moonshine module. More specifically, all symmetry groups of K3 NLSMs preserving the N=4 superconformal algebra can be obtained as subgroups of “Conway zero”, the group of symmetries of the Conway module, and their explicit action on the BPS spectrum can (almost always) be obtained via traces in the Conway module. A natural question is whether this relation extends to fusion category symmetry of these theories. I will discuss positive evidence in this direction, by exploring examples of non-invertible topological defect lines in K3 NLSMs and the Conway module. This is based on work in progress with R. Angius, S. Giaccari, and R. Volpato.

A Tetrahedral Approach to Calabi-Yau Geometry
2025-03-07 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Charles Doran, CMSA
Title: A Tetrahedral Approach to Calabi-Yau Geometry
Abstract: We will open with a quick introduction to the what and why of Calabi-Yau geometry. Following this, we will consider the problem of deforming tetrahedra while preserving the areas of their faces, following our noses to discover a beautiful path to elliptic curves, K3 surfaces, and beyond. Time permitting, we will also discuss motivations and applications across physics. The talk should be broadly accessible.

Physical Yukawa Couplings in Heterotic String Compactifications
2025-03-06 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Giorgi Butbaia, University of New Hampshire
Title: Physical Yukawa Couplings in Heterotic String Compactifications
Abstract: Calabi-Yau compactifications of the $E_8times E_8$ heterotic string provide a promising route to recovering the four-dimensional particle physics described by the Standard Model. While the topology of the Calabi-Yau space determines the overall matter content in the low-energy effective field theory, further details of the compactification geometry are needed to calculate the normalized physical couplings and masses of elementary particles. In this talk, we present novel numerical techniques for computing physically normalized Yukawa couplings in a number of heterotic models in the standard embedding using machine learning. We observe that the results produced using these techniques are in excellent agreement with the expected values.

Machine Learning G2 Geometry
2025-03-05 14:00 - 15:00 | Hybrid
New Technologies in Mathematics Seminar
Speaker: Elli Heyes, Imperial College
Title: Machine Learning G2 Geometry
Abstract: Compact Ricci-flat Calabi-Yau and holonomy G2 manifolds appear in string and M-theory respectively as descriptions of the extra spatial dimensions that arise in the theories. Since 2017 machine-learning techniques have been applied extensively to study Calabi-Yau manifolds but until 2024 no similar work had been carried out on holonomy G2 manifolds. In this talk, I will firstly show how topological properties of these manifolds can be learnt using neural networks. I will then discuss how one could try to numerically learn metrics on compact holonomy G2 manifolds using machine-learning and why these approximations would be useful in M-theory.

CMSA Q&A Seminar: Puskar Mondal
2025-03-05 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Puskar Mondal, Harvard CMSA
Topic: What is the positive energy theorem?

Large value estimates in number theory and computer science
2025-03-03 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Larry Guth, MIT
Title: Large value estimates in number theory and computer science
Abstract: A large value estimate for a matrix M is a simple type of estimate in quantitative linear algebra. Estimates of this type appear in many parts of math, both pure and applied. One example is the large value problem for Dirichlet polynomials from analytic number theory, which is related to estimates about the zeroes of the Riemann zeta function. We will also give some examples from computer science. Many large value problems are difficult. On the pure math side, the sharp conjecture about large values of Dirichlet polynomials has been open for a long time and is out of reach of current methods. On the computer science side, we don’t know any efficient algorithm to approximately solve the large value problem for a given matrix M. Many experts think that such an algorithm does not exist. In this talk we will survey how large value estimates come up, the known methods for working on them, and some of the obstacles to fully understanding them.

Quantum Field Theory and Physical Mathematics
2025-03-03 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Kai Xu, Harvard
Title: Finite Landscape of 6d N=(1,0) Supergravity
Abstract: We present a bottom-up argument showing that the number of massless fields in six-dimensional quantum gravitational theories with eight supercharges is uniformly bounded. Specifically, we show that the number of tensor multiplets is bounded by T≤193, and the rank of the gauge group is restricted to r(V)≤480. Given that F-theory compactifications on elliptic CY 3-folds are a subset, this provides a bound on the Hodge numbers of elliptic CY 3-folds: h1,1(CY3)≤491, h1,1(Base)≤194 which are saturated by special elliptic CY 3-folds. This establishes that our bounds are sharp and also provides further evidence for the string lamppost principle.

The Combinatorics of the Amplituhedron – Tiles, Tilings, and Cluster Algebras
2025-02-28 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Matteo Parisi
Title: The Combinatorics of the Amplituhedron – Tiles, Tilings, and Cluster Algebras
Abstract: The amplituhedron is the image of the positive Grassmannian—the region of the Grassmannian where all Plücker coordinates are nonnegative—under a totally positive linear map. It is a far-reaching generalization of cyclic polytopes and hyperplane arrangements, and the positive Grassmannian itself. The “volume” of the amplituhedron encodes probabilities of particle interactions in the quantum field theory N=4 super Yang-Mills, and calculating this volume involves decomposing (or tiling) the amplituhedron into smaller pieces (or tiles) and summing their volumes. This talk will delve into the rich combinatorics of these tiles and tilings, presenting recent results on some of the central conjectures in this area, including the magic number, BCFW tiling, and cluster adjacency conjectures.

2d chiral Lagrangian for asymptotic dynamics for 4d (self-dual) Einstein gravity
2025-02-27 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Wei Bu (Harvard University)
Title: 2d chiral Lagrangian for asymptotic dynamics for 4d (self-dual) Einstein gravity
Abstract: In this talk, I will present a simple chiral 2d Lagrangian living on a 2d celestial sphere on the null boundary of 4d Minkowski space and briefly mention its first principal derivation using twistor theory. This 2d theory gives the asymptotic/edge dynamics of 4d (self-dual) Einstein gravity in asymptotically flat spacetimes. For example, using simple 2d CFT computations, one could recover generators of asymptomatic symmetries. If time permits, I’ll further discuss the potential of using this theory to produce a QFT computation of the entropy of a certain asymptotically flat black hole.

Datasets for Math: From AIMO Competitions to Math Copilots for Research
2025-02-26 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Simon Frieder, Oxford
Title: Datasets for Math: From AIMO Competitions to Math Copilots for Research
Abstract: This talk begins with a brief exposition of the AI Mathematical Olympiad (AIMO) on Kaggle, now in its second iteration, outlining datasets and models available to contestants. Taking a broader perspective, I then examine 1) the overarching issues the current datasets suffer from—such as binary evaluation or constrained sets of use cases— and 2) the trajectory they set for competition-style mathematical problem-solving, which is different from mathematical research practice. I argue for a fundamental shift in dataset structure and composition, both for training and evaluation, and introduce the idea of mapping mathematical workflows to data, a key example underscoring the need for this shift. I touch upon new thinking LLMs and their role in redefining LLM math evaluation, highlighting their implications for dataset design. Finally, I propose general improvements to the current state of mathematical datasets, including mathematical adaptations of dataset documentation (e.g., datasheets).

Algebras of "symmetries" in QFT and applications to solitons (2)
2025-02-25 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Dan Freed, Harvard CMSA and Math
Title: Algebras of “symmetries” in QFT and applications to solitons (2)
https://arxiv.org/abs/2403.08883

BKL bounces outside homogeneity
2025-02-25 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Warren Li ( Princeton University)
Title: BKL bounces outside homogeneity
Abstract: In work spanning the late 20th century, physicists Belinski, Khalatnikov and Lifshitz (BKL) proposed a general ansatz for solutions to the Einstein (vacuum) equations near singularities. They suggest that the spacetime dynamics at different spatial points on the singularity decouple and are well-approximated by a system of autonomous nonlinear ODEs, whose orbits are governed by a chaotic cascade of “BKL bounces”. In this talk, we present recent work verifying BKL’s heuristics in a large class of symmetric, but spatially inhomogeneous, spacetimes. In particular, we prove decoupling even in the presence of (up to one) BKL bounce. The proof uses nonlinear ODE analysis coupled to hyperbolic energy estimates, and one hopes our methods may be applied more generally.

Toward constructing a large-scale quantum computer based on TQFT
2025-02-24 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Liyuan Chen ( Harvard)
Title: Toward constructing a large-scale quantum computer based on TQFT
Abstract: Topological quantum computation, motivated by topological quantum field theory (TQFT), offers a promising path toward fault-tolerant universal quantum computation. However, the practical realization of such a system remains challenging due to the difficulty of finding suitable topological materials. In this work, we provide a comprehensive blueprint for constructing a fault-tolerant universal quantum computer based on the quantum double model $mathcal{D}(S_3)$, a specific non-Abelian topological order. We implement logical computations using quantum circuits on qubits and qutrits, including a single non-Clifford gate, compatible with near-term quantum devices. This work bridges the gap between abstract mathematical frameworks and noise-resilient quantum computation on near-term devices. Our proposal offers a promising path to realize a non-Abelian anyon-based large scale quantum computer.

The geometry of pure spinor superfield formalism
2025-02-20 10:00 - 11:00 | Virtual
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Simone Noja (Heidelberg University)
Title: The geometry of pure spinor superfield formalism
Abstract: In this talk I will present a mathematical perspective on the pure spinor superfield formalism. In particular, I will discuss how field multiplets in supersymmetric theories can be constructed mathematically from geometric data associated with certain algebraic varieties—namely, the nilpotence variety of the (super)symmetry algebra of the theory. After discussing key examples, I will, time permitting, outline a possible generalization of the formalism within the framework of derived geometry.

CMSA Q&A Seminar: Phillip Matchett Wood
2025-02-19 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Phillip Matchett Wood, Harvard University
Topic: Info session on the CMSA/Mathematics Summer REU Program (Research Experience for Undergraduates)

Algebras of "symmetries" in QFT and applications to solitons (1)
2025-02-18 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Dan Freed, Harvard CMSA and Math
Title: Algebras of “symmetries” in QFT and applications to solitons (1)
https://arxiv.org/abs/2403.08883

General Relativity Seminar
2025-02-18 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Maximilian Ofner, University of Vienna
Title: Stability and Instability of Relativistic Fluids in Slowly Expanding Spacetimes
Abstract: Homogeneous and isotropic solutions to the relativistic Euler equations are known to be unstable on a Minkowski background. However, for FLRW models with a fast expansion rate, relativistic fluids stabilize. This scenario suggests a transition between stable and unstable behavior, somewhere along a family of spacetimes parametrized by their expansion rate. In this talk we will discuss this phase transition for various equations of state, focusing on the regime of linear and decelerated expansion. This is based on recent analytical results, complemented by numerical analysis.

Jack polynomials and enumeration of non-orientable maps
2025-02-14 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Houcine Ben Dali, Harvard CMSA
Title: Jack polynomials and enumeration of non-orientable maps
Abstract: A map is a graph embedded on a surface, which may be orientable or not. The representation theory of the symmetric group can be used to write the generating series of maps on orientable surfaces using Schur symmetric functions.
Several conjectures suggest that Jack polynomials—a one-parameter deformation of Schur functions—are related to the enumeration of non-orientable maps counted with a “non-orientability” weight. In this talk, I will discuss some of these conjectures and present recent progress in this direction.

2025 Ding Shum Lecture: Irit Dinur, IAS: Expanders from local to global
2025-02-13 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On February 13, 2025 the CMSA hosted the sixth annual Ding Shum Lecture, given by Irit Dinur, Institute for Advanced Study.
Location: Harvard Science Center Hall A & via Zoom Webinar
Speaker: Irit Dinur, Institute for Advanced Study

Title: Expanders from local to global
Abstract: Imagine a network—like a social network, a transportation system, or even a biological system—where every part of the network is robustly connected to the rest. Expander graphs are the mathematical idealization of such networks. They are structures where any small group of points (nodes) has many connections to the rest of the graph, ensuring that no part is isolated and information (or influence) spreads efficiently throughout.
We will begin by surveying expander graphs, their discovery and construction, and some fascinating applications such as error-correcting codes, pseudorandomness, and probabilistically checkable proofs (PCPs), highlighting their role as a foundation for many breakthroughs in theoretical computer science. Then, we will shift focus to an exciting new kind of expanders called high dimensional expanders (HDXs). While expanders are well-understood and widely applied, HDXs remain enigmatic, with potential that we are only starting to uncover. We will talk about a fascinating local to global feature that HDXs have, and some applications.

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

The Structure of the Flux Landscape
2025-02-13 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Damian Van de Heisteeg, Harvard CMSA
Title: The Structure of the Flux Landscape
Abstract: Identifying flux vacua in string theory with stabilized complex structure moduli presents a significant challenge, necessitating the minimization of a scalar potential complicated by infinitely many exponential corrections. In order to obtain exact results we connect three central topics: transcendentality or algebraicity of coupling functions, emergent symmetries, and the distribution of vacua. We demonstrate these ideas on an explicit example where we determine the landscape of exact flux vacua with a vanishing superpotential. We examine the implications of the tadpole bound, which intriguingly confines flux vacua to real values of the moduli, providing a potential avenue for addressing the strong CP problem.

Discovering Data Structures: Nearest Neighbor Search and Beyond
2025-02-12 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Omar Salemohamed, Mila
Title: Discovering Data Structures: Nearest Neighbor Search and Beyond
Abstract: As neural networks learn increasingly sophisticated tasks—from image recognition to mastering the game of Go—we ask: can deep learning discover data structures entirely from scratch? We introduce a general framework for data structure discovery, which adapts to the underlying data distribution and provides fine-grained control over query and space complexity. For nearest neighbor (NN) search, our model (re)discovers classic algorithms like binary search in one dimension and learns structures reminiscent of k-d trees and locality-sensitive hashing in higher dimensions. Additionally, the model learns useful representations of high-dimensional data such as images and exploits them to design effective data structures. Beyond NN search, we believe the framework could be a powerful tool for data structure discovery for other problems and adapt our framework to the problem of estimating frequencies over a data stream. To encourage future work in this direction, we conclude with a discussion on some of the opportunities and remaining challenges of learning data structures end-to-end.

CMSA Q&A Seminar: Javier Gomez-Serrano
2025-02-12 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Javier Gomez-Serrano, Brown University
Topic: Please tell us about the Millennium prize problem for Navier-Stokes and segue from that into ML?
