An Introduction to Singular Stochastic PDEs via Regularity Structures
Abstract
Next lectures
14.10.2024, 10:00 (E1 05 (Leibniz-Saal))
In the past decade, following breakthrough works by Hairer and by Gubinelli, Imkeller and Perkowski, there has been rapid progress in obtaining a notion of solution for singular SPDEs; which are roughly speaking PDEs with a random forcing of low enough regularity that the PDE is not classically well-posed in any space of distributions and instead requires the use of probabilistic data for a suitable "renormalisation".
In a series of challenging works lying at the intersection of analysis, probability and algebra, Hairer's theory of regularity structures has been extended to a systematic machinery treating general "subcritical" (or "super-renormalisable") semilinear singular SPDEs. The purpose of this course is to give a more digestible introduction to Hairer's approach. In early lectures, in order to expose the ideas leading to the general machinery, we will develop a small parameter solution theory for some relatively simple singular SPDEs. The topics of later lectures will be fixed according to audience interest.
Keywords
SPDE, Renormalisation, Regularity Structures
Prerequisites
A basic knowledge of spaces of test functions and distributions (as in e.g. Rudin's Functional Analysis Chapter 6).
