PDE/Analysis Seminar

Speaker: Simion Filip (University of Chicago) Title: Regularity of invariant measures for random dynamical systems Abstract: Suppose that a probability measure on a compact manifold 𝑀 is invariant under a collection of diffeomorphisms of 𝑀. I will explain some criteria on the measure and diffeomorphisms which ensure that the measure is a smooth volume form on 𝑀. The assumptions say, informally, that the measure is of Lebesgue class when conditioned along a random collection of (measurable) foliations by submanifolds. The results, joint with Brown, Eskin, and Rodriguez Hertz, are applicable to measures for which we can deduce additional rigidity properties (joint with the same authors). I will explain the necessary background and motivation from dynamics.