CMSA

Program on Classical, quantum, and probabilistic integrable systems - novel interactions and applications
2025-03-24 09:00 - 2025-05-24 17:00 (America/New_York) | 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.
