Singular Stochastic PDEs - A Short introduction to the theory of Regularity Structures

I present a hands-on introduction to the theory of regularity structures by Martin Hairer. This theory provides the machinery for treating of a class of formally ill-posed stochastic partial differential equations, including the KPZ equation which models surface growth. It can be considered a deep extension of the theory of rough paths, and I will sketch out the explicit link. No prior knowledge of rough path theory is necessary. A general acquaintance with (Schwarz) distributions will be helpful.