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Optimal transport, mean field games and gradient flows

Presented by: 
J Carrillo Imperial College London
Date: 
Wednesday 8th October 2014 - 16:30 to 17:00
Venue: 
INI Seminar Room 1
Session Title: 
Mini Workshop on Kinetic Models and Mean Field Games in Finance
Abstract: 
I will review how optimal transport can be seen as a mean field game via the Benamou-Brenier formula. Then I will show how Nash-Cournot equilibria are related to local minimizers of interaction energies or free energies penalized with the Wassertein distance. I will discuss briefly numerical schemes based on the optimal transportation viewpoint for the evolution PDEs obtained which are related to gradient flows of the free energy.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons