Diagrammatic methods for stochastic estimates in regularity structures

These lectures will explain how multiscale methods developed for analysis of Feynman diagrams can be extended to prove stochastic estimates on renormalised products that are a crucial input for the theory of regularity structures.

I will not assume any knowledge of Feynman diagrams or renormalisation in these lectures and aim to clearly describe the power-counting that appears in the analysis of these diagrams.

Time permitting, I will discuss how these diagrammatic methods also allow the renormalization of the Sine-Gordon model in the subcritical regime.