# Optimal Transport and Congestion

## Short course in the MFO seminar on Optimal Transport Theory and Hydrodynamics

This course, part of the Oberwolfach Seminar held from October 14 to
19 at MFO, contains four lectures.
### Program

1) * (15/10, morning)* ** Introduction to static OT.**

Monge and Kantorovich problems, dual problem, optimality conditions,
Brenier theorem, 1D case.

2) * (15/10, afternoon)* ** Introduction to dynamic OT.**

Wasserstein distances, curves in the Wasserstein space, geodesics,
Benamou-Brenier formaula.

3) * (16/10, morning)* ** Stationary traffic congestion.**

Beckmann problem, transport density, measures on curves. Nash and Wardrop
equilibria and traffic congestion.

4) * (16/10, morning)* ** Mean Field Games.**

Introduction to MFG and in particular variational
MFG. Duality. Optimality conditions and Lagrangian equilibria. Few
words on regularity.
.

### References:

For the two first lectures the main reference is my book
*Optimal Transport for Applied Mathematicians* (see here or here for a non-official version).
More precisely:

Lecture 1 : Chapter 1, sections 1.1 to 1.3

Lecture 2 : Chapter 5

Lecture 3 uses Chapter 4 from this book, but one can also look at this survey

The topics of
Lecture 4 are only mentioned in the book (section 8.4.4), but one can also look at this survey