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MIGSAA short course in Singular SPDEs and Regularity Structures

Held in the David Hume Tower, George Square, Edinburgh, EH8 9JX, in Lecture Theatre C, from 26th  – 29th June 2018 (with Tuesday – Thursday full days and Friday half day), this event promises to be a constructive workshop for PhD students working with SPDEs.

To express your intention to attend, please use the link to the course's web page and use the doodle poll therein.

Organisers: Istvan Gyongy, David Siska

Singular SPDEs are now a rapidly expanding area of research thanks in particular to the theory of regularity structures. The aim of this mini-course is to give MIGSAA students (and other PhD students) the opportunity to better understand these recent developments.

The courses will be delivered by leading researchers in the area, both of whom are actively working with leaders in the field.

Speaker: Mate Gerencser (IST, Austria)
Title: Introduction to regularity structures - Analysis
Abstract: 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’.

Speaker: Hendrik Weber (Warwick)
Title: Introduction to regularity structures - Probability
Abstract: 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.