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Spaces with Ricci curvature bounded from below

Lecturer: 
Nicola Gigli
Course Type: 
PhD Course
Academic Year: 
2014-2015
Period: 
December-April
Duration: 
60 h
Description: 

Aim of the course is to be an introduction to the study of `metric measure spaces with Ricci curvature bounded from below'. Preliminaries are measure theory and some knowledge of Riemannian geometry. Then I will discuss:

- the basics of optimal transport theory
- The concept of convergence of metric-measure structures 
- Lott-Sturm-Villani approach to lower Ricci curvature bounds 
- A variant of the Lott-Sturm-Villani approach
- Sobolev functions on mm spaces
- Differential structure of mm spaces
- Some geometric properties of these spaces
 
Location: 
14th A-134, 15th A-133, 16th-A128

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