# Category: Mathematical Physics

## September – December 2018 » Thematic Semester on Mathematical Challenges in Many-Body Physics and Quantum Information

## March 1 – 31, 2019 » New Developments in Free Probability and Applications

**Organizers: Benoît Collins (Kyoto), James Mingo (Queen’s), Roland Speicher (Saarland), Dan-Virgil Voiculescu (Berkeley)**

## April 29 – May 17, 2019 » Faces of Integrability

**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.

During the first week of activities, introductory lectures for graduate students will take place, as well as research seminars and discussions. The conference will take place during the second week. During the third week, research discussions and seminars will continue together with follow-up lectures for graduate students.

## July 1 – 31, 2019 » Expansions, Lie Algebras and Invariants

**Organizers: Anton Alekseev (Genève), Dror Bar-Natan (Toronto), Roland van der Veen (Leiden)**

Our workshop will bring together a number of experts working on “expansions” and a number of experts working on “invariants” in the hope that the two groups will learn from each other and influence each other. “Expansions” are solutions of a certain type of intricate equations within graded spaces often associated with free Lie algebras; they include Drinfel’d associators, solutions of the Kashiwara–Vergne equations, solutions of various deformation quantization problems, and more. By “invariants” we refer to quantum-algebra-inspired invariants of various objects within low-dimensional topology; these are often associated with various semi-simple Lie algebras. The two subjects were born together in the early days of quantum group theory, but have to a large extent evolved separately. We believe there is much to gain by bringing the two together again.