March 12 – 16, 2018 » Workshop in Geometric Analysis and Nirenberg Lectures by Eugenia Malinnikova

Workshop organizers: Pengfei Guan (McGill), Alina Stancu (Concordia), Jérôme Vétois (McGill)

Geometric analysis has seen several major developments in recent years. Some of the most spectacular breakthroughs were made in the last decade and include Perelman’s work on Hamilton’s Ricci flow and his resolution of the Poincaré conjecture and Thurston’s geometrization conjecture; Brendle’s resolution of the Lawson conjecture; the Differentiable Sphere theorem by Schoen and Brendle; and Marques and Neves’ resolution of the Willmore conjecture. It is an ideal time to bring together mathematicians in this area to learn more about the achievements of others, foster collaboration, and enable new breakthroughs.

The workshop will focus on prominent current areas of geometric analysis including, but not limited to, geometric evolution equations, minimal surfaces, conformal geometry, complex structures and Kähler geometry, and applications to relativity. An important theme in this area has been the development and use of sophisticated techniques from the theory of partial differential equations to study natural equations that arise in geometry.

CRM Nirenberg Lectures organizers: Pengfei Guan (McGill), Dima Jakobson (McGill), Iosif Polterovich (Montréal), Alina Stancu (Concordia)

The CRM Nirenberg Lectures in Geometric Analysis have taken place every year since 2014. The series is named in honour of Louis Nirenberg, one of the most prominent geometric analysts of our time. The 2018 lectures will be delivered by Professor Eugenia Malinnikova from the Norwegian University of Science and Technology in Trondheim. Malinnikova’s contributions include a groundbreaking joint work with A. Logunov on the nodal geometry of Laplace eigenfunctions, that has led to a proof of two major conjectures in the field due to Shing-Tung Yau and Nikolai Nadirashvili. The research achievements of Eugenia Malinnikova have been recognized by the 2017 Clay Research Award and an invitation to speak at the 2018 ICM in Rio de Janeiro.

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.

June 1 – 30, 2019 » Homological Algebra, Microlocal Analysis and Symplectic Geometry

Organizers: Emmanuel Giroux (UMI CNRS-CRM & ENS Lyon), Stéphane Guillermou (Grenoble Alpes) 

The purpose of this scientific program will be to present and discuss the recent developments in applications of the microlocal analysis of sheaves to symplectic geometry. We will especially focus on the work of Dmitry Tamarkin, the scholar-in-residence for this program, who will lecture on his microlocal category and its relationships with the Fukaya category. The first week of the program will be devoted to introductory lectures in order to provide young participants with the necessary background. In the subsequent two weeks, Dmitry Tamarkin will present his work in the morning sessions, and more discussions on the contents of his lectures will be scheduled in the afternoon sessions. Finally, a workshop will be organized in the last week of the program.

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.

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.