Minicurso: Introduction to the theory of Regularity structures por Dirk Erhard da UFBA

The theory of Regularity structures is a framework, recently introduced by Martin Hairer, that allows to treat a priori ill-defined stochastic PDEs(singular PDE) via a renormalisation approach. Prominent examples include the KPZ equation

and the parabolic Anderson model. The aim of this lecture is two-fold. First we want to explain what we mean by renormalisation and why it is necessary and natural in some cases. Second we want to present the main ingredients of the theory of Regularity structurs and if time permits the latest developments in the field.