Séminaire Physique mathématique ICJ

Geometric stochastic heat equations

by Yvain Bruned (University of Edinburgh)

112 (Institut Camille Jordan)


Institut Camille Jordan

Université Lyon 1, Bât. Braconnier, 21 av. Claude Bernard, 69100 Villeurbanne

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.

Organized by

Fabien Vignes-Tourneret

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