# MIGSAA Mini-Course: Singular SPDEs and Regularity Structures

## Organisation

The course will take place 26th - 30th June 2018 in David Hume Tower lecture theatre C.

The course is open to all PhD students (MIGSAA, UoE, HW & external). Please fill in the Doodle poll to help us order roughly right amount of coffee.

## Timetable

Times Tue-Thu Tuesday Wednesday Thursday Times Fri Friday
09:00-11:00 Lecture HW Lecture MG Lecture HW 09:00-10:30 Final HW
11:00-11:30 Coffee Coffee Coffee 10:30-11:00 Coffee
11:30-12:30 Exercises HW Exercises MG Exercises HW 11:00-12:30 Final MG
12:30-14:00 Lunch Lunch Lunch
14:00-16:00 Lecture MG Lecture HW Lecture MG
16:00-16:30 Coffee Coffee Coffee
16:30-17:30 Exercises MG Exercises HW Exercises MG

## Introduction to regularity structures - Analysis

### Mate Gerencser (IST, Austria):

We give a detailed overview of the analytic side of the theory of regularity structures. For singular SPDEs to be well-posed, a new family of function spaces is introduced, and their calculus is discussed. These tools allow one to solve abstract counterparts of a large class of singular equations in these new function spaces. A crucial analytic insight lies in a new viewpoint on the notion of regularity', through which very rough functions, or even distributions, can be regarded as smooth'.

## Introduction to regularity structures - Probability

### Hendrik Weber (Warwick):

The theory of regularity structures provides a systematic way to define and construct solutions to a large class of classically ill-posed stochastic PDE. Solving an equation within this theory amounts to two steps: The construction of a finite number of approximate solutions - the probabilistic or perturbative step - and the analysis of the full problem in the analytic step. In these lectures I will demonstrate the probabilistic step and show how to construct the approximate solutions. This will include a reminder on some known facts from stochastic Analysis as well as some algebraic tricks that allow to efficiently organise very complicated expressions.

### Funding

The course is supported by the Maxwell Institute Graduate School in Analysis and its Applications.