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.