Integrable combinatorics — IMJ-PRG summer school 2026

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

Campus Jussieu (Sorbonne Université)

The Institut de Mathématiques de Jussieu—Paris Rive Gauche organizes a yearly summer school. In 2026, the topic will be 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 tentative program will consist in four mini-courses, and four introductory research talks. In addition, there will be 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 pre-registration is now open, please complete the form if you are willing to participate. Please notice that young participants asking for accomodation in Paris should fill the form before February 28th 2026.

A temporary schedule for the week is below. More details on the scientific program, final registration and other practical matters, will appear on this page in due time.

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 Welcoming

1 Symmetries of discrete and ultradiscrete integrable systems - Lecture 1

Orateur: Rei Inoue (Chiba University)

10:30 Coffee Break

2 An Integrable Systems Perspective on Symmetric Function Theory - Lecture 1

Orateur: Luigi Cantini (Cergy-Pontoise Université)

12:30 Lunch Break

3 Multiplicative statistics of Poissonized Plancherel random partitions - Invited talk 1

Orateur: Giulio Ruzza (University of Lisbon)

4 Contributed Talk

5 Contributed Talk

15:30 Coffee Break

6 Contributed Talk

7 Contributed Talk

8 Symmetries of discrete and ultradiscrete integrable systems - Exercise class

Orateur: Rei Inoue (Chiba University)

9 Drinks and poster session

mar. 16 juin

10 Symmetries of discrete and ultradiscrete integrable systems - Lecture 2

Orateur: Rei Inoue (Chiba University)

10:30 Coffee Break

11 An Integrable Systems Perspective on Symmetric Function Theory - Lecture 2

Orateur: Luigi Cantini (Cergy-Pontoise Université)

12:30 Lunch Break

12 Integrability in Schubert Calculus - Invited talk 2

Orateur: Anna Weigandt (University of Minnesota)

13 Contributed Talk

14 Contributed Talk

15:30 Coffee Break

15 Contributed Talk

16 Contributed Talk

17 An Integrable Systems Perspective on Symmetric Function Theory - Exercise class

Orateur: Luigi Cantini (Cergy-Pontoise Université)

mer. 17 juin

18 Random Tilings and Integrable Structures - Lecture 1

Orateur: Maurice Duits

10:30 Coffee Break

19 Crystals and symmetric functions - Lecture 1

Orateur: Anne Schilling

jeu. 18 juin

20 Random Tilings and Integrable Structures - Lecture 2

Orateur: Maurice Duits

10:30 Coffee Break

21 Crystals and symmetric functions - Lecture 2

Orateur: Anne Schilling

12:30 Lunch Break

22 Fock's dimer model on the Aztec diamond - Invited talk 3

Orateur: Béatrice de Tilière (Université Paris Dauphine)

23 Random Tilings and Integrable Structures - Exercices class

Orateur: Maurice Duits (KTH, Stockholm)

16:00 Coffee Break

24 Colloquium

Orateur: Philippe Di Francesco (IPhT Saclay)

ven. 19 juin

25 Crystals and symmetric functions - Exercise Class

Orateur: Anne Schilling (UC Davis)

26 Contributed Talk

27 Contributed Talk

10:30 Coffee Breaks

28 Contributed Talk

29 Contributed Talk

30 Interacting particle systems and Macdonald polynomials - Invited talk 4

Orateur: Arvind Ayyer

12:30 Closing remarks