MIGSAA Mini-Course: Singular SPDEs and Regularity Structures


Istvan Gyongy and David Siska

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.


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.


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