Yann Brenier (yann.brenier@universite-paris-saclay.fr)
Luca Nenna (luca.nenna@universite-paris-saclay.fr)
Registration to the class is mandatory
IMPORTANT: the next lectures will take place in room 2L8!
Optimal transport is a powerful mathematical theory at the interface between optimization and probability theory with far reaching applications. It defines a natural tool to study probability distributions in the many situations where they appear: mathematical physics, data science, partial differential equations, statistics or shape processing. In this course we will present the classical theory of optimal transport, efficient algorithms to compute it and applications.
Pre-requisites: Notions on measure theory, weak convergence, and convex analysis. Some basic knowledge of Python.
Language: The class will be taught in French or English, depending on attendance.
Organisation: Lectures will take place on Wednesday afternoon from 2pm to 5pm at the Institut de mathématique d’Orsay (IMO) building 307 on the campus of Orsay, Room 2L8.
Evaluation: written exam + homework
Homework: Here you can find the homework to get some extra points for the final evaluation. The short report must be submit to luca.nenna@universite-paris-saclay.fr by March 25 at 6 a.m. (New York time).
| Date | Lecturer | Topic | Lecture notes |
|---|---|---|---|
| 16/02/2022 | LN | Primal and dual formulations | Lecture 1 |
| 23/02/2022 | LN | Entropic Optimal Transport | Lecture 2, Slide |
| 02/03/2022 | LN | Functionals over $\mathcal P(\Omega)$ | Lecture 3 |
| 09/03/2022 | LN | Applications (Wasserstein Geodesics and MFGs) | Lecture 4 slide |
| 16/03/2022 | YB | Eulerian Approach I | Lecture 5 and 6 |
| 23/03/2022 | YB | Eulerian Approach II | |
| 30/03/2022 | EXAM |
where YB:=Yann Brenier and LN:=Luca Nenna.
Here you can find some lecture notes in French by Nathael Gozlan, Paul-Marie Samson and Pierre-André Zitt.
Annals: Exam 2014