Five lectures on regularity structures and SPDEs

TL;DR

This paper introduces regularity structures and their application to singular stochastic partial differential equations, providing foundational knowledge through five lectures and supplementary appendices.

Contribution

It offers an accessible introduction to the theory of regularity structures and their use in analyzing complex SPDEs, filling a gap in educational resources.

Findings

Provides a comprehensive overview of regularity structures

Includes technical results and contextual insights in appendices

Serves as an educational resource for SPDE analysis

Abstract

This set of five lectures provides an introduction to regularity structures and their use for the study of singular stochastic partial differential equations. Two appendices provide some additional informations that enter in the main text either as some technical results or as some results that deepen the context within which we set these lectures.