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.