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.
Objective
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.
Literature
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
Performance assessment
Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course