Integrable combinatorics — IMJ-PRG summer school 2026

15 juin 2026, 08:30 → 19 juin 2026, 13:00 Europe/Paris

Amphi 15 (Campus Jussieu, Sorbonne Université)

The Institut de Mathématiques de Jussieu—Paris Rive Gauche organizes a yearly summer school. In 2026, the topic is Integrable Combinatorics.

The field of integrable combinatorics seeks to understand certain universal phenomena through exactly soluble systems or physical models, thanks to properties of algebraic origin, coming in particular from representation theory. This school will give an introduction to methods for finding and analyzing such integrable models, as well as to purely combinatorial approaches.  We will illustrate how to solve various problems, mainly of exact or asymptotic enumeration, via a range of techniques borrowed from enumerative combinatorics, algebraic combinatorics and statistical physics.

The program consists in four mini-courses, and four introductory research talks. In addition, there are a limited number of contributed talks and a poster session to give to the participants the opportunity to present their works.

The mini-courses will be given by :

• Luigi Cantini (CY Cergy Paris University) - "An Integrable Systems Perspective on Symmetric Function Theory"
• Maurice Duits (KTH Stockholm) - "Random Tilings and Integrable Structures"
• Rei Inoue (Chiba University) - "Symmetries of discrete and ultradiscrete integrable systems"
• Anne Schilling (UC Davis) - "Crystals and symmetric functions"

The introductory research talks will be given by :

• Arvind Ayyer (IISc Bangalore) - "Interacting particle systems and Macdonald polynomials"
• Béatrice de Tilière (Université Paris-Dauphine PSL) - "Fock's dimer model on the Aztec diamond"
• Giulio Ruzza (University of Lisbon) - "Multiplicative statistics of Poissonized Plancherel random partitions"
• Anna Weigandt (University of Minnesota) - "Integrability in Schubert Calculus" 

A Colloquium will be given by Philippe Di Francesco (University of Illinois Urbana-Champaign and IPhT, CEA Paris-Saclay) on Thursday afternoon at 16h30.

The schedule for the week is below. All talks will take place in amphi 15, visible on this map of the campus (enter from place Jussieu). You may download the current version of the book of abstracts.

Local organizers : 

• Kahina Bencheikh
• Jérémie Bouttier                           
• Sylvie Corteel 
• Sofia Tarricone 
• Guillaume Barraquand
• Thomas Lejeune
• Maena Quemener
• Minghzi Zhang

 

Sponsors : IMJ-PRG, Sorbonne Université, CNRS, Faculté des Sciences Université Paris Cité, European Mathematical Society, Laboratoire Ypatia des Sciences Mathématiques, Télécom SudParis - SAMOVAR, LPENS, Annales Henri Poincaré, LPSM, UFR 929 de Mathématiques de Sorbonne Université, PIICQ, GDR EFI.

 

Book of Abstracts Summer School IMJ-PRG 2026.pdf

lun. 15 juin

08:30 → 09:00 Welcoming

09:00 → 10:30 Symmetries of discrete and ultradiscrete integrable systems - Lecture 1

Orateur: Rei Inoue (Chiba University)

10:30 → 11:00 Coffee Break

11:00 → 12:30 Random Tilings and Integrable Structures - Lecture 1

Orateur: Maurice Duits (KTH, Stockholm)

12:30 → 14:00 Lunch Break

14:00 → 15:00 Interacting particle systems and Macdonald polynomials - Invited talk 1

Orateur: Arvind Ayyer (IIS Bangalore)

15:00 → 15:15 Arctic curves of the Aztec diamond and related models - Contributed talk 1

Orateur: Mateusz Piorkowski (KTH, Stockholm)

15:15 → 15:30 Tensor decomposition of Demazure crystals - Contributed talk 2

Orateur: Divya Setia (Institute of Mathematics, Polish Academy of Sciences)

15:30 → 16:00 Coffee Break

16:00 → 16:15 Integrability in discrete random matrix theory - Contributed talk 3

Orateur: Roger Van Peski (Columbia University)

16:15 → 16:30 On the convoy of the ASEP speed process - Contributed talk 4

Orateur: Yuan Tian (Max Planck Institute for Mathematics in the Sciences)

16:30 → 17:30 Symmetries of discrete and ultradiscrete integrable systems - Exercise class

Orateur: Rei Inoue (Chiba University)

17:30 → 19:00 Drinks and poster session

mar. 16 juin

09:00 → 10:30 Symmetries of discrete and ultradiscrete integrable systems - Lecture 2

Orateur: Rei Inoue (Chiba University)

10:30 → 11:00 Coffee Break

11:00 → 12:30 Random Tilings and Integrable Structures - Lecture 2

Orateur: Maurice Duits (KTH, Stockholm)

12:30 → 14:00 Lunch Break

14:00 → 15:00 Integrability in Schubert Calculus - Invited talk 2

Orateur: Anna Weigandt (University of Minnesota)

15:00 → 15:15 Stationary inverse-Wishart polymers - Contributed talk 5

Orateur: Zikun Ouyang (CEREMADE & LPENS)

15:15 → 15:30 Gaudin model, oscillating Young tableaux and cactus group - Contributed talk 6

Orateur: Anfisa Gurenkova (Skoltech, HSE)

15:30 → 16:00 Coffee Break

16:00 → 16:15 Lattice Models, Representation Theory, and Whittaker Functions - Contributed talk 7

Orateur: Claire Frechette (Umeå University)

16:15 → 16:30 Marking in doubly periodic dimer models - Contributed talk 8

Orateur: Nedialko Bradinoff (KTH, Stockholm)

16:30 → 17:30 Random Tilings and Integrable Structures - Exercices class

Orateur: Maurice Duits (KTH, Stockholm)

mer. 17 juin

09:00 → 10:30 An Integrable Systems Perspective on Symmetric Function Theory - Lecture 1

Orateur: Luigi Cantini (Cergy-Pontoise Université)

10:30 → 11:00 Coffee Break

11:00 → 12:30 Crystals and symmetric functions - Lecture 1

Orateur: Anne Schilling (UC Davis)

jeu. 18 juin

09:00 → 10:30 An Integrable Systems Perspective on Symmetric Function Theory - Lecture 2

Orateur: Luigi Cantini (Cergy-Pontoise Université)

10:30 → 11:00 Coffee Break

11:00 → 12:30 Crystals and symmetric functions - Lecture 2

Orateur: Anne Schilling (UC Davis)

12:30 → 14:00 Lunch Break

14:00 → 15:00 Fock's dimer model on the Aztec diamond - Invited talk 3

Orateur: Béatrice de Tilière (Université Paris Dauphine)

15:00 → 16:00 Crystals and symmetric functions - Exercise Class

Orateur: Anne Schilling (UC Davis)

16:00 → 16:30 Coffee Break

16:30 → 17:30 Colloquium

Orateur: Philippe Di Francesco (IPhT Saclay and University of Illinois Urbana-Champaign)

ven. 19 juin

09:00 → 10:00 An Integrable Systems Perspective on Symmetric Function Theory - Exercise class

Orateur: Luigi Cantini (Cergy-Pontoise Université)

10:00 → 10:15 On the Schubert support of Grothendieck polynomials - Contributed talk 9

Orateur: Judy Hsin-Hui Chiang (University of Minnesota Twin Cities)

10:15 → 10:30 q-s Catalan Numbers and Constrained Exclusion Processe - Contributed talk 10

Orateur: Ali Zahra (LPCT, Université de Lorraine, Nancy)

10:30 → 11:00 Coffee Breaks

11:00 → 11:15 Domino tilings of the Aztec diamond in random environment - Contributed talk 11

Orateur: Zografos Panagiotis (Leipzig University)

11:15 → 11:30 About Aztec houses - Contributed talk 12

Orateur: Charly Nys (IRMP, UCLouvain)

11:30 → 12:30 Multiplicative statistics of Poissonized Plancherel random partitions - Invited talk 4

Orateur: Giulio Ruzza (University of Lisbon)

12:30 → 13:00 Closing remarks