Abstract:
Stochastic Partial Differential Equations (SPDE) and their applications is a relatively young field of mathematics. In the past two decades and it has, however, become one of the main research directions of Probability Theory, with rising activity across its entire spectrum. In particular, modern SPDE techniques and their combination with ideas from rough path theory led to Martin Hairer's theory of regularity structures for which he was awarded the Fields medal in 2014. Since then this theory has been significantly extended, for example, by applications to the geometrical evolution of random loops on manifolds. The field of SPDE combines the classical area of Partial Differential Equations (PDE) with modern branches of Probability Theory, in particular, Stochastic Analysis, and thus constitutes one of the most prominent contact points between Analysis and Stochastics. Besides various other connections to pure mathematics (e.g. Differential Geometry, Dynamical Systems) one
main focus of SPDE are its applications to the Sciences, in particular Physics, but also Biology and Chemistry. Another main area of applications is economics, in particular mathematical finance. The aim of the session is to give an update on recent developments on SPDE and at the same time identify new frontiers with challenging open problems for the field, with emphasis on both theory and applications.
