This course is intended as a gentle introduction to the problem of optimal mass transport. This problem asks for the most efficient way to move one distribution of mass to another distribution, relative to a given cost function.
The theory of optimal mass transport has had a long history dating back to Monge in the 18th century and has led to a wealth of applications to other fields in recent years. Topics addressed in the course include:
1. Monge's formulation of the Optimal Mass Transport problem
2. The Kantorovich problem
3. Kantorovich-Rubinstein duality
4. Existence of optimal transport maps: Brenier's theorem
5. Transport problems with linear cost
6. The Wasserstein distance and its properties
7. Applications to isoperimetric inequalities
Prerequisite: a basic understanding of measure theory, for example from the course Mesure et Intégration (MA.3400/4400).
- Enseignant·e: Stefan Wenger