Alfred Galichon
Title: Topics in Equilibrium Transportation

Motivated by problems from Economics, I  will present a general framework for "Equilibrium Transportation", which embeds the Monge-Kantorovich "Optimal Transportation" theory, but is more general, and more natural in some applications. In the discrete case, this framework allows for a unified description of Gale and Shapley's stable marriage problem, as well as Koopmans and Beckmann's optimal assignment problem. I will sketch the link with "Galois connections" and recent results by Trudinger on the local theory of prescribed Jacobian equations. I will then turn to computational issues, and will present an extension of Sinkhorn's algorithm that allows for efficient approximate computation of these problems. Finally, I will discuss statistical estimation of these models and give properties of the Maximum Likelihood Estimator.