Program on Classical, quantum, and probabilistic integrable systems – novel interactions and applications
March 24, 2025 @ 9:00 am - May 24, 2025 @ 5:00 pm
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
Videos are available on the Youtube Playlist.