|Dept.||University of British Columbia, Canada|
Optimal transportation theory studies phenomena where mass distributions are matched in an ecient way, with respect to a given transportation cost. In the most standard case, optimal transport maps are given by the gradient of convex functions that solve the Monge-Ampere equation.
(1) In the First lecture, we explain some of the most basic concepts and techniques for regularity theory of the Monge-Ampere equation.
(2) In the second lecture, we discuss a few recent results.