September 10 – 28, 2018 » 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.

September 17 – October 14, 2018 » Algebra and combinatorics at LaCIM, a conference for the 50th anniversary of the CRM

Organizers: François Bergeron (UQAM),Srecko Brlek (UQAM), Christophe Hohlweg (UQAM)

Scientific Committee

• François Bergeron (UQAM);
• Valérie Berthé (Université Paris-Diderot);
• Srecko Brlek (UQAM);
• Laurent Habsieger (Université Claude Bernard, Lyon);
• Sylvie Hamel (UdeM)
• Christophe Hohlweg (UQAM);
• Jean-Christophe Novelli (Université Paris-Est);
• Nathan Reading (North Carolina State University);
• Lauren Williams (UC Berkeley).

escription: On the occasion of CRM’s 50th anniversary in 2018, the Laboratoire de Combinatoire et d’Informatique Mathématique (LaCIM) organizes a month of scientific activities to discuss the state-of-the-art and manifold interconnections between the lively topics that have long been at the core of research at LaCIM: algebraic combinatorics, combinatorial representation theory, Coxeter groups theory, combinatorics of words, discrete geometry, enumerative combinatorics, mathematical computer science and their applications. The scientific activities will be articulated around the confirmed participations of Mireille Bousquet-Mélou and Ezra Miller; together with a week-long international conference to be held from the 24th to the 28th of September 2018. This conference will be organized as follows:

* two days session dedicated to subjects related to ties between algebra and combinatorics;
* two days session dedicated to subjects related to ties between combinatorics, theoretical computer science, and statistical physics.

The bridge between the two sessions will be a special event on Wednesday 26th, aiming at underlying 30 years of partnership of LaCIM and CRM through 4 conferences given by:

* Mireille Bousquet-Mélou,
* Ezra Miller,

and by LaCIM’s past and current holders of the Canadian Research Chair, “Algebra, Combinatorics and Mathematical Computer Science”

* Christophe Reutenauer and
* Hugh Thomas.

August 1 – 31, 2019 » Quiver Varieties and Representation Theory

Organizers: Joel Kamnitzer (Toronto), Hugh Thomas (UQAM)

The representation theory of quivers (and related preprojective algebras) has been studied by researchers from algebra, while the geometry of quiver varieties has been studied by researchers in geometric representation theory.  This activity will bring together members of these two communities to exchange recent progress and to stimulate further research and collaboration.  Among other topics, we will discuss quantization of quiver varieties, Coulomb branch constructions using quiver varieties, tilting theory for preprojective algebras, and categorification of cluster algebras.