# 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.

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