## April 1 – 26, 2019 » Topological and Rigorous Computational Methods for High Dimensional Dynamics

**Organizers: Jean-Philippe Lessard (McGill), Konstantin Mischaikow (Rutgers), Jan Bouwe van den Berg (VU Amsterdam)**

The focus of this program is on identifying explicit dynamical structures in nonlinear systems that are high dimensional, poorly resolved, or both. In these problems, computational mathematics is often the only feasible way forward.

The first featured workshop explores the computational challenges of rigorously identifying and extracting fundamental dynamical features such as equilibria, periodic orbits, connecting orbits and invariant manifolds in infinite-dimensional dynamical systems. The second featured workshop investigates the development of computational algebraic topological tools for studying multiparameter, nonlinear systems where the nonlinearities are poorly defined.

The main aim is to identify, characterize, and predict nonlinear dynamics from high-dimensional time series data sets. Each workshop is preceded by a hands-on tutorial aimed at graduate students, postdocs and early- to mid-career mathematicians.

## 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, 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.

## 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.