Optimal Transportation and Extremal Doubly Stochastic Measures
by
Robert J. McCann
University of Toronto
Coauthors: Najma Ahmad (CIBC), Pierre-Andre Chiappori (Columbia University), Hwa Kil Kim (Georgia Institute of Technology), Lars Nesheim (University College of London)

Despite years of study, surprisingly little is understood about the optimal transportation of a mass distribution from one manifold to another, where optimality is measured against a cost function on the product space.

This talk will be an introduction to the optimal transportation, its relation to Birkhoff's problem of characterizing of extremality among doubly stochastic measures, and recent progress linking the two. It culminates in the presentation of a criterion for uniqueness of solutions which subsumes all previous criteria, yet which is among the very first to apply to smooth costs on compact manifolds, and only then when the topology is simple. A few open problems will also be mentioned.

Date received: March 17, 2009