Mathematics

Overview:
The course will be about recent advances on analysis over metric measure spaces with particular focus on thosewith Ricci curvature bounded from below. We will start from the definition of Sobolev space over a metric measure space and discuss:
- differential calculus on m.m.s.
- heat flow on m.m.s.
- definition of distributional Laplacian and Laplacian comparison estimates - some geometric properties of spaces with Ricci curvature bounded from below.