# Author: André Montpetit

## 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.

## May 1 – 31, 2019 » Data Assimilation: Theory, Algorithms, and Applications

**Organizers: Tony Humphries (McGill), Sebastian Reich (Potsdam & Reading), Andrew Stuart (Caltech)**

The seamless integration of large data sets into computational models provides one of the central challenges for the mathematical sciences of the 21st century. When the computational model is based on dynamical systems and the data is time ordered, the process of combining data and models is called data assimilation. Historically, the field has been primarily developed by practitioners within the geophysical sciences; however, it has enormous potential in many more subject areas.

This month-long thematic activity is aimed at developing the underpinning mathematical theory of data assimilation, the process of combining data with dynamical systems to learn hidden states and unknown parameters. The activities will be guided and informed by applications coming from the physical, biomedical, social and cognitive sciences. Methodologies based around particle filtering, ensemble Kalman filtering, optimization and Bayesian inverse problems will underpin the program. Long-term visitors in all of these fields will be present, and a number of short-term visitors will attend around the four workshops devoted to underpinning methodologies, geophysical applications, biomedical applications and applications from the social and cognitive sciences.

## 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.