Stochastic Partial Differential Equations

Stochastic partial differential equations (SPDEs) have been an increasingly active field of research since the late 1960s. As illustrated by Martin Hairer’s Fields Medal, obtained in 2014 for developing the theory of regularity structures, SPDEs have now become a central field in mathematics, at the intersection of probability theory and analysis of partial differential equations. SPDEs have many important applications, for instance in condensed matter physics, in chemistry, in neuroscience, in climate modelling, and in financial mathematics. Many very promising advances have been made in recent years, both on a fundamental level, such as existence results for very singular equations, and on an applied level, including quantitative results on the behaviour of solutions and numerical methods. The aim of the workshop is to gather a number of leading international experts of the field, in order to obtain an overall picture of recent progress, and to discuss open problems and future directions of research. Part of the scientific program will be dedicated to the theory of regularity structures and its applications. The program will also address applications of SPDEs to various fields such as statistical physics, neuroscience and climate models. The program will consist in about 30 talks, and we expect at least 50 participants. We also plan to support the attendance of a number of young participants (postdocs and students finishing their PhD thesis).