The first part is devoted to Monge and Kantorovitch problems, discussing the existence and the properties of the optimal plan. The second part introduces the Wasserstein distance on measures and develops applications of optimal transport to PDEs, functiona ...
The goal of this course is to introduce the student to the basic notion of analysis on metric (measure) spaces, quasiconformal mappings, potential theory on metric spaces, etc. The subjects covered will vary each year. ...
The subject deals with differential geometry and its relation to global analysis, partial differential equations, geometric measure theory and variational principles to name a few. ...
The course provides an introduction to the study of curves and surfaces in Euclidean spaces. We will learn how we can apply ideas from differential and integral calculus and linear algebra in order to "measure shapes". ...