Title: Heat asymptotics in sub-Riemannian geometry

Abstract: In the mid 50’s De Giorgi used the heat equation to introduce his seminal notion of perimeter of a measurable set. In the mid 90’s M. Ledoux provided a beautiful proof of the isoperimetric inequality, completely based on the heat equation. In this talk I will present some recent developments in sub-Riemannian geometry, based on some new and unexpected properties of the heat equation . The presentation will be completely self-contained.