The 20th Takagi Lectures
November 4 (Sat), 2017 (Sat)
11:30--12:30, 15:20--16:20
Graduate School of Mathematical Sciences
The University of Tokyo, Tokyo, Japan

Renormalisation of parabolic stochastic PDEs
Martin Hairer
(Imperial College London)


We give a survey of recent result in probability theory regarding scaling limits of systems from statistical mechanics, as well as the universality of the behaviour of such systems in so-called cross-over regimes. It transpires that some of these universal objects are described by singular stochastic PDEs. We then give a survey of the recently developed theory of regularity structures which allows to build these objects and to describe some of their properties.