Introduction to stochastic PDEs

Stochastic PDEs form a relatively recent area of mathematics that combines many different fields, including PDE theory, stochastic analysis, ergodic theory, functional analysis, etc. This course is an introduction to the area with the aim of being able to appreciate some 21st century developments towards the end of the course. We will mainly focus on the development of a rather general solution theory for linear and semilinear stochastic PDEs, including stochastically forced heat, Navier-Stokes, and reaction-diffusion equations.

Some of the tools developed in this course, in particular infinite-dimensional measure theory and linear semigroup theory, are of much broader interest.