The BMS professors Martin Hairer (Courant Institute, NYU and Warwick) and
Jonathan Mattingly (Duke) are offering a lecture series on

Ergodic theorems for infinite dimensional Markov processes

The aim of these lectures is to present a number of recent results on
the long-time behaviour of Markov processes in infinite-dimensional
spaces, with a focus on stochastic PDEs. We will start by giving a short
introduction to the theory of stochastic evolution equations, followed
by an introduction to ergodic theory for Markov processes. This will
allow us to build some intuition on the problems at hand, as well as
an understanding of the challenges that need to be tackled. The introduction
will be relatively self- contained, aimed at students with knowledge of
basic graduate analysis and some introduction to probability theory. We will
then present a general theory that gives a framework in which many questions
of interest can be solved.

The second half of the course will show how to apply the general theory
to a large class of stochastic PDEs and stochastic delay equations.
The central question will be "what is different in infinite dimensions?" and
how can we overcome the added difficulties. One of the main achievements
presented there will be an infinite-dimensional generalisation of
Hörmander's celebrated "sums of squares" theorem. Along the way will touch
on topics from Malliavin calculus and stochastic analysis.

Schedule of the course