Integrability and Combinatorics at Finite Temperature

Joy Lukman

  • 7 Jun 2021 - 25 Jun 2021
    8:00 am - 5:00 pm

Dan Betea (KU Leuven)
Greta Panova (University of Southern California)
Leonid Petrov (University of Virginia)
Tomohiro Sasamoto (Tokyo Institute of Technology)
Michael Wheeler (University of Melbourne)

Program Description:
The overall goal of the program is to advance the methods of integrability and combinatorics towards structural and asymptotic results across a wide range of finite temperature models of statistical physics. Here the notion of “finite temperature” might have different meanings in different situations, and a complete understanding of the range of finite temperature models and related asymptotic phenomena is a work in progress. The potential impact of the program is based on previous very successful treatment in the past 20 years of “infinite temperature” models (based on, e.g., sums of independent random variables) in classical and modern probability theory, and of “zero temperature” models (e.g. last passage percolation). The latter were analyzed using the methods of integrability and combinatorics, and currently these methods are being extended by a number of groups towards more complicated “finite temperature” settings, in order to capture new universal phenomena. Our aim is to bring together members of these groups, and produce further advances in this direction. It is expected that new finite-temperature universal phenomena will apply to a wide range of real-world settings, such as to the structure of ice and other condensed matter models, magnetism, quantum spin systems, thermodynamics, and polymers.

The program will run for three weeks. with different focus on each week:
Week 1. Focus on combinatorics of zero- and finite-temperature exactly solvable models. Tutorial lectures on symmetric and non-symmetric functions in connection with particle systems and other models.
Week 2. Focus on quantum integrability and asymptotics. Tutorial lectures on Bethe ansatz, duality, quantum groups, representation theory, statistical mechanics.
Week 3. Focus on integrable probability, analytic methods, and asymptotics. Tutorial lectures on random matrices, random partitions, random polymers, and particle systems.

Program Structure:
Below is the draft of Program Structure. Please click to enlarge.
Note: actual times may differ slightly and things may change as the workshop approaches


  • Deadline: 31 March 2021
  • Registration is by invitation only

MATRIX Wine and Cheese Afternoon 8 June 2021
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.