Optimal Transportation

The Monge-Kantorovich problem of optimal transport is to transfer mass from a given initial distribution to a prescribed target distribution in such a way that the total transport costs are minimized. This problem has originally been motivated by applications in engineering and economics. In the last decades, several unexpected connections have been discovered between optimal transport and seemingly unrelated problems in analysis, probability theory and geometry.

This course presents an overview of these developments. Some of the topics that we will discuss are
* Gradient flow methods for evolution equations
* Ricci curvature bounds for metric measure spaces
* Functional inequalities, isoperimetry, and concentration of measure

Literature:
* Filippo Santambrogio, Optimal Transport for Applied Mathematicians
* Cédric Villani, Topics in Optimal Transportation
* Cédric Villani, Optimal Transport

Target group: PhD students from all years, postdocs, anyone else who is interested

Prerequisites: A solid background in analysis.

Evaluation: pass/fail based on homework

Teaching format: Online lectures + homework
Lectures: Tue + Thu 10:15-11:30
Recitations: Tue 11:45-12:35

ECTS: 3 Year: 2020

Track segment(s):
MAT-ALG Mathematics - Algebra
MAT-ANA Mathematics - Analysis
MAT-GEO Mathematics - Geometry and Topology

Teacher(s):
Jan Maas

Teaching assistant(s):

If you want to enroll to this course, please click: REGISTER