A tourist's guide to regularity structures and singular stochastic PDEs

TL;DR

This paper provides a comprehensive, self-contained overview of regularity structures, highlighting their core analytic and algebraic aspects and demonstrating their application to understanding singular stochastic partial differential equations.

Contribution

It offers an accessible, self-contained exposition of regularity structures and their use in analyzing singular stochastic PDEs, making advanced concepts more approachable.

Findings

Clarified the core analytic and algebraic features of regularity structures.

Demonstrated applications to singular stochastic PDEs.

Provided an accessible, self-contained treatment of the subject.

Abstract

We give an essentially self-contained treatment of the fundamental analytic and algebraic features of regularity structures and its applications to the study of singular stochastic PDEs.