**April 29 – May 17, 2019**

**Organizers: Jacques Hurtubise (McGill), Nicolai Reshetikhin (Berkeley), Lauren K. Williams (Berkeley)**

The theory of integrable systems, with its origins in symmetries, has intricate ties to a wide variety of areas of mathematics. Sometimes the ties are straightforward, but in many cases, the links are more complicated, and indeed somewhat difficult to make explicit. Some of these interfaces, between integrability, geometry, representation theory, and probability theory will be dominating subjects during the conference and satellite activities. Themes to be covered include the role of cluster algebras and cluster varieties in the description of moduli spaces, the links between integrable systems and representation theory appearing in such areas as quantum groups and quantization of moduli spaces, and the fascinating interfaces of probability theory, combinatorics and integrable systems appearing in several processes linked to statistical mechanical models.

The event will take place over three weeks.

During the first week of activities, April 29 – May 3, introductory lectures for graduate students will take place. It will consist of four four-hour series of lectures:

Gaétan Borot (MPIM)

“Geometric and topological recursion”

Mikhael Gekhtman (Notre Dame)

“Cluster Integrable Systems”

Nicolai Reshetikhin (Berkeley)

“An overview of the construction of integrable systems based on factorizable Poisson Lie groups”

Hugh Thomas (UQAM)

“Introduction to cluster algebras”

A conference will take place during the second week, May 6-10.

**Invited Speakers:**

Jorgen Andersen (Aarhus), Marco Bertola (Concordia), Alexander Bobenko (Berlin)(*), Alexander Borodin (MIT), Luigi Cantini (Cergy), Filippo Colomo (INSM, Firenze), Sylvie Corteel (Paris-Diderot), Ivan Corwin (Columbia), Rukmini Dey (ICTS- Bangalore), Philippe di Francesco (Illinois)(*), Laszlo Feher (Szeged and Budapest), Vladimir Fock (Strasbourg), Vadim Gorin (MIT)(*), John Harnad (CRM, Concordia), Rinat Kedem (Illinois), Richard Kenyon (Brown), Boris Khesin (Toronto), Alisa Knizel (Columbia), Dmitri Korotkin (Concordia), Osya Mandelshtam (Brown) (*), Marta Mazzocco (Loughborough), Alexander Okounkov (Columbia)(*), Vladimir Rubtsov (Angers)(*), Gus Schrader (Columbia), Vasilisa Schramchenko (Sherbrooke), Alexander Shapiro (Berkeley)(*), Andrey Smirnov (Berkeley)(*), Andrea Sportiello (Paris-Nord), Véronique Terras (Paris-Sud), Taras Skrypnyk (Milan), Jasper Stokman (Amsterdam)(*), Harold Williams (Davis), Pavel Winternitz (CRM, Montréal), Milen Yakimov (Louisiana State)

(*) To be confirmed

During the third week, May 13-17, research discussions and seminars will continue together with follow-up lectures for graduate students.