Alessio Porretta's course in 2015

Alessio Porretta (Università di Roma Tor Vergata) gave a 10-week course at the IHP (11 rue Pierre et Marie Curie - Paris 5ème) in March and April 2015.

It dealt with " Some PDE methods in mean field games theory".

 

Lectures on:

- March 9th 2015: Room 314 from 10h00 to 12h00
- March 12th, 2015: Room 314 from 10h00 to 12h00
- March 23rd, 2015: Room 314 from 10h00 to 12h00
- March, 26th, 2015: Room 314 from 10h00 to 12h00
- March 30th, 2015: Room 314 from 10h00 to 12h00
- April 2nd, 2015: Room 201 from 10:00 to 12h00
- April 7th, 2015: Room 314 from 10h00 to 12h00
- April 9th, 2015: Room 314 from 10h00 to 12h00
- April 13th, 2015: Room 314 from 10h00 to 12h00
- April 16th, 2015: Room 201 from 10:00 to 12h00


Abstract:

Mean field games theory was initiated by J.-M. Lasry and P.-L. Lions since 2006 in order to describe control processes with large number of agents (say, a population of identical individuals) whose strategy is influenced by the overall distribution of the agents. The macroscopic description, suggested as an asymptotic regime of Nash equilibria of N-players games when N goes to infinity, is given in terms of a new system of PDEs, where a backward Hamilton-Jacobi-Bellman equation (describing the individual strategy) is coupled with a forward Kolmogorov-Fokker-Planck equation (describing the evolution of the distribution law). The goal of this course is to present several problems and methods recently developed in the study of those systems, addressing questions such as the long time behavior and its connection with the turnpike property of controlled systems, the optimal transport of the distribution law, the well-posedness of weak theories and other possible related directions of research.

Lecture #1 - 09/03/2015

Lecture #2 - 12/03/2015

Lecture #3 - 23/03/2015

Lecture #4 - 26/03/2015

Lecture #5 - 30/03/2015

Summary of unrecorded lesson

Lecture #6 - 02/04/2015

Lecture #7 - 07/04/2015

Lecture #8 - 09/04/2015

Lecture #9 - 13/04/2015

Lecture #10 - 16/04/2015