Colloquium| Institute of Mathematical Sciences
Time：14:00-15:00, November 7 Thursday
Location：Room S408, IMS
Speaker: Elia Bruè, Scuola Normale Superiore
Abstract: The theory of flows associated to non-smooth vector fields, pioneered by DiPerna-Lions and Ambrosio, has a broad range of applications to different fields of mathematics. The aim of this talk is to present a recent and new application of this theory to the field of non-smooth geometry.
More precisely, I will outline a new regularity result for Lagrangian flows of Sobolev vector fields, where the regularity is understood with respect to a newly defined quasi-metric built from the Green function of the Laplacian. As an application I will prove that non-smooth spaces with Ricci bounded below have constant dimension. This result generalizes a celebrated theorem of Colding and Naber for Ricci limit spaces.
This talk is based on a work in collaboration with Daniele Semola.