In this course I plan to give an introduction to optimal transport: I'll first introduce the optimal transport problem and explain how to solve it in some important cases of interest. Then I'll show a series of applications to geometry and to gradient flows.
The aim of the course is to provide a self contained introduction to optimal transport. The students are expected to know the basic concepts of measure theory. Although not strictly required, some basic knowledge of Riemannian geometry may be useful.
Topics in Optimal Transportation (Graduate Studies in Mathematics, Vol. 58), by Cédric Villani
Optimal Transport for Applied Mathematicians (Calculus of Variations, PDEs, and Modeling), by Filippo Santambrogio
Optimal transport and curvature, available at Link
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)