CMSA

Member Seminar
2025-04-18 12:00 - 13:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Han Shao

Fifth Annual Yip Lecture | Scott Aaronson (UT Austin): How Much Math Is Knowable?
2025-04-17 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Speaker: Scott Aaronson, Department of Computer Science, University of Texas, Austin
Scott Aaronson is the founding director at the Quantum Information Center at the University of Texas at Austin.
Date: April 17, 2025
Time: 4:00-5:00 pm ET (Reception following in the Math Common Room)
Location: Harvard Science Center Hall A

Title: How Much Math Is Knowable?
Abstract: Theoretical computer science has over the years sought more and more refined answers to the question of which mathematical truths are knowable by finite beings like ourselves, bounded in time and space and subject to physical laws. I’ll tell a story that starts with Gödel’s Incompleteness Theorem and Turing’s discovery of uncomputability. I’ll then introduce the spectacular Busy Beaver function, which grows faster than any computable function. Work by me and Yedidia, along with recent improvements by O’Rear and Riebel, has shown that the value of BB(745) is independent of the axioms of set theory; on the other end, an international collaboration proved last year that BB(5) = 47,176,870. I’ll speculate on whether BB(6) will ever be known, by us or our AI successors. I’ll next discuss the P!=NP conjecture and what it does and doesn’t mean for the limits of machine intelligence. As my own specialty is quantum computing, I’ll summarize what we know about how scalable quantum computers, assuming we get them, will expand the boundary of what’s mathematically knowable. I’ll end by talking about hypothetical models even beyond quantum computers, which might expand the boundary of knowability still further, if one is able (for example) to jump into a black hole, create a closed timelike curve, or project oneself onto the holographic boundary of the universe.

The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

The previous Yip Lecture featured Josh Tenenbaum (MIT) who spoke on How to grow a mind from a brain: From guessing and betting to thinking and talking

CMSA Q&A Seminar: Noah Golowich
2025-04-16 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Noah Golowich (MIT)
Topic: What is length generalization in large language models?

Instantons on Taub-NUT space and Bow Construction
2025-04-15 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Anadil Saeed Rao, Northeastern University
Title: Instantons on Taub-NUT space and Bow Construction
Abstract: In this talk I will discuss Yang-Mills Instantons in a very special geometric setting: the Taub-NUT space, which itself is a Gravitational Instanton. In the first part of the talk I will review the essentials of gravitational instanton theory from the differential geometry/physics perspective and discuss the geometry of Taub-NUT space in detail. Then I will review the essentials of the ADHM-Nahm construction which describe Instantons and Monopoles in Euclidean R^4 and R^3 respectively. In the second part of my talk I will extend the ADHM-Nahm description to Instantons on Taub-NUT space and show how the ADHM-Nahm data may be presented in terms of combinatorial diagrams called Bows and their representations.

Positive mass theorem for ALE(AE) and ALF(AF) Toric 4-Manifolds
2025-04-15 11:00 - 12:00 | CMSA G102, 20 Garden Street, Cambridge, MA, 02138
General Relativity Seminar
Speaker: Aghil Alaee, Clark University
Title: Positive mass theorem for ALE(AE) and ALF(AF) Toric 4-Manifolds
Abstract: One of the fundamental conjectures in mathematical relativity is the positivity of total mass (if it is defined!) for complete non-compact Riemannian manifolds assuming appropriate lower bounds on scalar curvature. This conjecture has been proved for AE manifolds using several techniques, starting with the celebrated results of Schoen-Yau and Witten. There are counter-examples to this conjecture in the AF, ALF, and ALE cases. In this talk, we will refine this conjecture and prove it for toric 4-manifolds. The proof is robust and can be extended to higher dimensions if additional assumptions are added. This is a joint work with Marcus Khuri and Hari Kunduri.

Quantum K-theory at roots of unity
2025-04-14 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Andrey Smirnov, University of North Carolina at Chapel Hill
Title: Quantum K-theory at roots of unity
Abstract: In this talk, I will discuss a version of quantum K-theory introduced by A.Okounkov, which can be defined through quasimap counts. In this framework, the quantum K-theory ring is obtained as a specialization of the equivariant quasimap count at $q=1$, where $q$ is the equivariant parameter associated with the torus action on the source of the quasimaps. A related, but less explored, structure emerges when $q$ is specialized at the roots of unity. I will outline the key ideas behind this construction and its implications. As an application, I’ll also describe the spectrum of $p$-curvature for the quantum connection, which offers a new proof of a recent result by P.Etingof and A.Varchenko. This talk is based on joint work with P. Koroteev.

The Extended Vertex Algebra of 4d N = 2 SCFTs and their Higher Products
2025-04-14 15:00 - 16:00 | Hybrid – G10
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Mitch Weaver, KAIST
Title: The Extended Vertex Algebra of 4d N = 2 SCFTs and their Higher Products
Abstract: Every 4d N=2 superconformal field theory contains a BPS protected sub-algebra of local operators that has the structure of a vertex operator algebra (VOA). This VOA is identified by passing to the cohomology of a nilpotent supercharge, T, whose local operator cohomology is represented by twist-translated Schur operators with support in a Euclidean two-plane. When working in 4d Minkowski space, this cohomology admits a web of three extended operators (called descent operators) that are constructed from each Schur operator in the VOA, have worldvolume support in the Lorentzian two-plane that is transverse to the Euclidean plane supporting the VOA, and behave as point-like insertions in the plane of the VOA, i.e. as new chiral operators. The combined result is the extended vertex algebra (EVA): a universal extension of the VOA that canonically has the structure of a quasi-VOA, i.e. a vertex algebra (VA) with no conformal vector but which still possesses a representation of sl(2). After reviewing the VOA of Schur operators, I will explain the origin of the descent operators and present the OPEs for a subsector of the EVA in the free hyper SCFT.
Time permitting, I will also describe the construction and basic properties of a set of higher products that are associated to each descent operator. Such products function as higher dimensional versions of 2d chiral algebra λ-brackets, i.e. positive mode operators: they are defined on the EVA and map to the operators appearing in the singular terms of OPEs involving descent operators. Their existence offers a route toward sl(2) symmetry enhancement of the EVA and suggests the latter has structural properties that are common to the higher dimensional chiral algebras describing the minimal twists of 3d N = 2 and 4d N = 1 SQFTs. This talk is based on [2211.04410] and forthcoming work.

Homological Invariants in Translation-Invariant Pauli Stabilizer Codes
2025-04-11 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Bowen Yang
Title: Homological Invariants in Translation-Invariant Pauli Stabilizer Codes
Abstract: Pauli stabilizer codes serve as foundational models in quantum error correction and the study of exotic quantum phases. In this talk, we explore the application of homological methods to translationally invariant Pauli stabilizer codes with qudits of varying dimensions. We introduce a series of invariants, termed charge modules, and delve into their properties and physical interpretations. A key focus is on codes whose charge modules exhibit zero Krull dimension, a condition indicative of the mobility of excitations. Notably, we demonstrate that this condition is universally met in two-dimensional codes with a unique ground state in infinite volume, extending prior findings beyond the realm of uniform, prime qudit dimensions. For systems where all excitations are mobile, we establish the existence of p-dimensional excitations and associated (D−p−1)-form symmetries corresponding to each element of the p-th charge module. Additionally, we define a braiding pairing between charge modules in complementary degrees.

3d Mirror Symmetry is 2d Mirror Symmetry
2025-04-10 10:00 - 11:00 | Virtual
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Ki Fung Chan (Chinese University of Hong Kong)
Title: 3d Mirror Symmetry is 2d Mirror Symmetry
Abstract: We introduce an approach to studying 3d mirror symmetry via 2d mirror symmetry. The main observations are: (1) 3d brane transforms are given by SYZ-type transforms; (2) the exchange of symplectic and complex structures in 2d mirror symmetry induces the exchange of Kähler and equivariant parameters in 3d mirror symmetry; and (3) the functionalities of 2d mirror symmetry control the gluing of 3d mirrors. If time permits, we will also discuss some applications to 2d mirror symmetry at the end of the talk. Joint works with Naichung Conan Leung.

Can Transformers Do Enumerative Geometry?
2025-04-09 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Baran Hashemi, Technical University of Munich
Title: Can Transformers Do Enumerative Geometry?
Abstract: How can Transformers model and learn enumerative geometry? What is a systematic procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Neural Enumerative Reasoning model for computation of ψ-class intersection numbers on the moduli space of curves. By reformulating the problem as a continuous optimization task, we compute intersection numbers across a wide value range from 10e-45 to 10e45. To capture the recursive nature inherent in these intersection numbers, we propose the Dynamic Range Activator (DRA), a new activation function that enhances the Transformer’s ability to model recursive patterns and handle severe heteroscedasticity. Given precision requirements for computing the intersections, we quantify the uncertainty of the predictions using Conformal Prediction with a dynamic sliding window adaptive to the partitions of equivalent number of marked points. Beyond simply computing intersection numbers, we explore the enumerative “world-model” of Transformers. Our interpretability analysis reveals that the network is implicitly modeling the Virasoro constraints in a purely data-driven manner. Moreover, through abductive hypothesis testing, probing, and causal inference, we uncover evidence of an emergent internal representation of the large-genus asymptotic of ψ-class intersection numbers. This opens up new possibilities in inferring asymptotic closed-form expressions directly from limited amount of data.
This talk is based on https://openreview.net/pdf?id=4X9RpKH4Ls.

CMSA Q&A Seminar: Eric Maskin
2025-04-09 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Eric Maskin, Harvard University
Topic: The Mathematics of Voting

CMSA/Tsinghua Math-Science Literature Lecture: Scott Sheffield (MIT): Yang-Mills theory and random surfaces
2025-04-08 09:00 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA/Tsinghua Math-Science Literature Lecture
Date: April 8, 2025
Time: 9:00 – 10:30 am ET
Location: CMSA G10, 20 Garden Street, Cambridge MA & via Zoom
Speaker: Scott Sheffield (MIT)
Title: Yang-Mills theory and random surfaces
Abstract: The Clay Institute famously offered one million dollars to anyone who could mathematically construct and understand a certain continuum version of “Yang-Mills gauge theory.” This theory is the basis of the standard model of physics, and the heart of the problem is to understand the so-called “Wilson loop expectations.” Following recent work with Sky Cao and Minjae Park, I will explain how the “Wilson loop expectations” in a lattice Yang-Mills model are equivalent to “insertion costs” of loops in a related random-closed-surface-ensemble model. In a sense, these results allow us to convert one famously hard problem into another presumably hard problem. But the new problem is all about random surfaces and random permutations, and it has a lot of relationships with and similarities to other problems we understand (think domino tilings, random planar maps, Young tableaux and symmetric group representation theory, and the Weingarten calculus). It gives us some intuition for *why* certain things should be true like the “area law” or “exponential correlation decay” (what physicists call “quark confinement” or “mass gap”) even if we can’t prove all of them yet.

Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

3-d Mirror Symmetry
2025-04-07 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Ben Webster, University of Waterloo & Perimeter Institute
Title: 3-d Mirror Symmetry
Abstract: I’ll give an introduction (or update, for those who’ve been introduced) to 3d mirror symmetry from the perspective of a mathematician.

Quantum Field Theory and Physical Mathematics
2025-04-07 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Matthew Yu (Oxford)
Title: A new tangential structure for type IIA string theory
Abstract: The Green-Schwarz anomaly cancellation condition says that the target space of heterotic string theory must come with a string structure for the theory to be consistent. In this talk we discuss a new tangential structure called string^h, first introduced by Devalapurkar, as a spin^c analogue of string. Approximating the correct tangential structure of string theory has many implications, primarily is the Swampland program via the cobordism conjecture of Mcnamara and Vafa. We will show that the spectrum of string^h has the notable property that it orients tmf_1(n), just like how the spectrum of string orients tmf, by the work of Ando-Hopkins-Rezk. Finally we will show that the anomaly condition of the partition function of M-theory, studied by Diaconescu-Moore-Witten is implied by a string^h structure on the target space of type IIA, in parallel to the Green-Schwarz anomaly for heterotic string theory, and discuss applications for anomaly cancellation.

Learning diffusion models in high-dimensions
2025-04-04 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Hugo Cui
Title: Learning diffusion models in high-dimensions
Abstract: We consider the problem of learning a generative model parametrized by a two-layer auto-encoder, and trained with online stochastic gradient descent, to sample from a high-dimensional data distribution with an underlying low-dimensional structure. We provide a tight asymptotic characterization of low-dimensional projections of the resulting generated density, and evidence how mode(l) collapse can arise. On the other hand, we discuss how in a case where the architectural bias is suited to the target density, these simple models can efficiently learn to sample from a binary Gaussian mixture target distribution.

Current Developments in Mathematics 2025
2025-04-04 09:00 - 2025-04-05 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
When: April 4, 2025 – April 5, 2025

Where: Science Center Hall C
Address: 1 Oxford Street, Cambridge, MA 02138, United States

Speaker: Michael Chapman – NYU | Pazit Haim-Kislev – Institute for Advanced Study | Jianfeng Lin – Tsinghua University | Laura Monk – University of Bristol | Ramon van Handel – Princeton University

IN-PERSON REGISTRATION
Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register and send a letter to cdm@math.harvard.edu.
A letter indicating your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research.
Detailed schedule of lectures and events coming soon.
Organizers: David Jerison, Paul Seidel, Nike Sun (MIT); Denis Auroux, Mark Kisin, Lauren Williams, Horng-Tzer Yau, Shing-Tung Yau (Harvard).
Sponsored by the National Science Foundation (pending), Harvard University Mathematics, and the Massachusetts Institute of Technology.
Harvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is, on the basis of sex, sexual orientation, or gender identity, excluded from participation in, denied the benefits of, or subjected to discrimination in any University program or activity. More information can be found here.

Current Developments in Mathematics 2025

(Strictly) Non-minimal Elliptic Threefolds and the Distance Conjecture
2025-04-03 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Rafael Álvarez García (Harvard University)
Title: (Strictly) Non-minimal Elliptic Threefolds and the Distance Conjecture
Abstract: We analyze infinite-distance limits in the complex structure moduli space of six-dimensional F-theory, providing an algebro-geometric classification and a physical interpretation. From the point of view of the Swampland Program, the motivation is to understand the fate of open-moduli infinite-distance limits in relation with the Distance Conjecture. From an F-theory perspective, the infinite-distance limits correspond to degenerations of elliptic threefolds leading to non-minimal singularities in codimension one and higher. We show how such non-crepant singularities can be removed by a systematic sequence of blow-ups of the bases of the infinite-distance degenerations, making their central fibers a union of log Calabi-Yau spaces glued together along their boundaries. We interpret said central fibers as either the endpoints of decompactification limits with six-dimensional defects or as emergent string limits, providing further evidence for the Emergent String Conjecture. Degenerations leading to strictly non-minimal singularities can correspond both to finite-distance and infinite-distance limits in the open moduli space. We analyze the chain of modifications and base changes necessary to unambiguously determine the fate of such families of F-theory models.

Learning Dynamical Transport without Data
2025-04-02 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Michael Albergo (Harvard)
Title: Learning Dynamical Transport without Data
Abstract: Algorithms based on dynamical transport of measure, such as score-based diffusion models, have resulted in great progress in the field of generative modeling. However, these algorithms rely on access to an abundance of data from the target distribution. A complementary problem to this is learning to generate samples from a target distribution when only given query access to the unnormalized log-likelihood or energy function associated to it, with myriad application in statistical physics, chemistry, and Bayesian inference. I will present an algorithm based on dynamical transport to sample from a target distribution in this context, which can be seen as an augmentation of annealed importance sampling and sequential Monte Carlo. Time permitting, I will also discuss how to generalize these ideas to dynamics of discrete distributions. This is joint work with Eric Vanden-Eijnden, Peter Holderrieth, and Tommi Jaakkola.

Introduction to the probabilistic approach to Louville theory III
2025-04-01 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Bowen Yang, CMSA
Title: Introduction to the probabilistic approach to Louville theory III
Abstract: I will continue with the construction of Liouville CFT from probabilistic methods, following a review by Guillarmou, Kupiainen, and Rhodes (arXiv:2403.12780). The talk will emphasize technical aspects of Gaussian free fields (GFF) and contrast them with Brownian motion. The references is arXiv:2004.04720

Low-regularity Local Well-posedness of the Elastic Wave System
2025-04-01 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Sifan Yu, National University of Singapore
Title: Low-regularity Local Well-posedness of the Elastic Wave System
Abstract: In this talk, I will present a recent work on the elastic wave system in three spatial dimensions. For admissible harmonic elastic materials, we prove a low-regularity local well-posedness result for the corresponding elastic wave equations. For such materials, we can split the dynamics into the “divergence-part” and the “curl-part,” and each part satisfies a distinct coupled quasilinear wave system with respect to different acoustical metrics. Our main result is that the Sobolev norm H^{3+} of the “divergence-part” (the “faster-wave part”) and the H^{4+} of the “curl-part” (the “slower-wave part”) can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption H^{3+} is optimal for the “divergence-part.” This is a joint work with Xinliang An and Haoyang Chen.

Homotopical Methods for Free and Interacting Fermionic SPTs
2025-03-31 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Cameron Krulewski, MIT
Title: Homotopical Methods for Free and Interacting Fermionic SPTs
Abstract: We develop and compute homotopical “free-to-interacting maps” to compare classifications of fermionic symmetry-protected topological phases (SPTs), determining when such phases are stable under interactions or, alternatively, interaction-enabled. Generalizing work of Freed-Hopkins, we construct maps from K-theory to Anderson-dual spin bordism in two new situations: for weak phases, which are SPTs protected by discrete translation symmetry, and for the “Bott spiral” studied by Queiroz-Khalaf-Stern, who observed that the tenfold way classification of free theories breaks down to a large 2-torsion interacting classification. Along the way, we employ T-duality, generalizations of the spin orientation of KO-theory, and the Adams spectral sequence.
This talk is based on joint work with Omar Antolín Camarena, Arun Debray, Natalia Pacheco-Tallaj, Daniel Sheinbaum, and Luuk Stehouwer.

The Competition Complexity of Dynamic Pricing
2025-03-28 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Tomer Ezra
Title: The Competition Complexity of Dynamic Pricing
Abstract: One of the most fundamental questions in mechanism design is the tradeoff between simplicity and optimality. A canonical example of this tradeoff is competition complexity in auctions, which quantifies how many additional bidders are needed for a simple mechanism to (approximately) match the revenue of the optimal mechanism.
In this talk, we analyze the competition complexity of dynamic pricing in the setting of selling a single item. We establish tight asymptotic guarantees for various scenarios, including when bidder values are i.i.d., independent, or correlated. Our results characterize the performance of different classes of dynamic pricing algorithms and provide insights into their effectiveness under varying market conditions.

AlphaProof: when reinforcement learning meets formal mathematics
2025-03-27 10:00 - 11:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Thomas Hubert (Google DeepMind)
Title: AlphaProof: when reinforcement learning meets formal mathematics
Abstract: Galileo, the renowned Italian astronomer, physicist, and mathematician, famously described mathematics as the language of the universe. Progress since only confirmed his intuition as the world we live in can be described with extreme precision with just a few mathematical equations.
In the last 70 years, the rise of computers has also enriched our understanding of and revolutionized the world we live in. Mathematics tremendously benefited from this digital revolution as well: while Gauss had to compute primes by hand, computers and computation are now routinely used in research mathematics and contribute to grand problems like the Birch and Swinnerton-Dyer conjecture, one of the Millennium Prize Problems.
Today, computers are entering a new age, one in which computation can be transformed into reasoning. In this talk, I would like to discuss two such developments that will undoubtedly have an integral role to play in the future of mathematics: the concurrent rise of formal mathematics and of machine intelligence.

From quantum difference equations to Maulik-Okounkov quantum affine algebra
2025-03-27 10:00 - 11:00 | Virtual
Mathematical Physics and Algebraic Geometry Seminar
*via Zoom only*
Speaker: Tianqing Zhu (Tsinghua University)
Title: From quantum difference equations to Maulik-Okounkov quantum affine algebra
Abstract: Capping operator is one the core subject in the K-theoretic quasimap counting to quiver varieties. It has been shown by Okounkov and Smirnov that it satisfies a system of q-difference equations governed by the MO quantum affine algebras. In this talk we will show how to construct the similar quantum difference equation via the shuffle algebras. Then we will show how to use the monodromy data of these quantum difference equations to prove the isomorphism of the positive half of the MO quantum affine algebras of affine type A and the positive half of the quantum toroidal algebras. If time permits, I will also give a brief explanation on how to extend the proof to the general case.

Unstable Fluids in Expanding Cosmologies
2025-03-25 16:00 - 17:00 | Virtual
General Relativity Seminar
Speaker: Elliot Marshal, School of Mathematics at Monash University
Title: Unstable Fluids in Expanding Cosmologies
Abstract: The FLRW solution is the simplest cosmological model in general relativity, describing a fluid-filled, spatially homogeneous universe. While there is extensive literature in the physics community on cosmological models with a linear equation of state , rigorous stability results have, until recently, been limited to FLRW models with accelerated expansion and small sound speeds. In this talk, I will discuss numerical work on two types of instabilities which can occur in non-linearly perturbed FLRW models outside of this regime. The first concerns a longstanding conjecture of Alan Rendall on FLRW models with positive cosmological constant and super-radiative (K>1/3) equations of state. Our numerical work, in collaboration with F. Beyer and T.A. Oliynyk, supports Rendall’s conjecture and highlights the underlying mechanism for the instability. In the second case, I will discuss evidence that perturbations of slowly expanding (decelerated) FLRW models generically form shocks in finite time. This contrasts with known results for accelerated models where shock formation is suppressed for suitably small perturbations.

The Toda Lattice as a Soliton Gas
2025-03-24 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Amol Aggarwal, Columbia University
Title: The Toda Lattice as a Soliton Gas
Abstract: A basic tenet of integrable systems is that, under sufficiently irregular initial data, they can be thought of as dense collections of many solitons, or “soliton gases.” In this talk we focus on the Toda lattice, which is an archetypal example of an integrable Hamiltonian dynamical system. We explain how the system, under certain random initial data, can be interpreted through solitons, and provide a framework for studying how these solitons asymptotically evolve in time. The arguments use ideas from random matrix theory, particularly the analysis of Lyapunov exponents governing the decay rates of eigenvectors of random tridiagonal matrices.

The Andersen-Kashaev volume conjecture for FAMED geometric triangulations
2025-03-24 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: 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?
