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Geometric stochastic heat equations

Date: Thursday, April 18, 2019 14:45 - 15:45
Speaker: Yvain Bruned (University of Edinburgh)
Location: Erwin Schrödinger Institute in Vienna
Series: Mathematics and CS Seminar
Host: Jan Maas

Abstract:

We will explain how to solve a class of one-dimensional stochastic PDEs driven by space-time white noise using the theory of Regularity Structures invented by Martin Hairer. This class of equations is invariant under the action of the diffeomorphism group and covers many singular stochastic PDEs as the stochastic heat equation, rough Burgers equations and the KPZ equation. The main point is to find solutions satisfying different symmetry properties as the invariance under the action of diffeomorphisms and Itô's isometry.  This is a joint work with Franck Gabriel, Martin Hairer and Lorenzo Zambotti.

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