Geometric stochastic PDEs – We review Parisi and Wu’s stochastic quantisation procedure and apply it to the non-linear sigma model as well as the Yang-Mills model. We then review a number of recent results on the resulting equations. In particular, this sheds some new light on an old controversy regarding the interpretation of path integrals.

Introduction to regularity structures 1 – In these two lectures, I will give an introduction to the main concepts behind the theory of regularity structures which allows to give meaning to many stochastic PDEs that were previously thought to be ill posed. This combines some of the insights and tools from (perturbative) QFT with classical PDE theory.

Introduction to regularity structures 2 – In these two lectures, I will give an introduction to the main concepts behind the theory of regularity structures which allows to give meaning to many stochastic PDEs that were previously thought to be ill posed. This combines some of the insights and tools from (perturbative) QFT with classical PDE theory.