MENU

You are here

Home

Geometric Measure Theory

Measure theory on Polish spaces

Polish spaces, i.e. topological spaces that are metrizable by a complete and separable metric, are a quite general and ubiquitous framework one might end up working on and well-known to be nice settings where to study measure theory. The course aims at giving an overview of this aspect. Among other things we will study duality theory between measures and functions, weak convergence, the disintegration theorem and Kolmogorov’s product theorem.

Nonsmooth differential geometry

In the first part we will show that on general metric measure spaces, a `Sobolev-like’ first-order differentiation theory is possible, with objects like differential forms and vector fields well defined. 
 
In the second part we will study spaces with Ricci curvature bounded from below, and see that on them the curvature bound makes it possible a second-order calculus, so that, among others, Hessian and covariant derivative are both well defined.

Sign in