Title: Calibrations in Riemannian and pseudo-Riemannian geometry and their relation to optimal transport problems.
<br><br>
Abstract: The optimal transportation problem can be formulated as a volume-critical submanifold problem.  We will discuss calibrations in both Riemannian and pseudo-Riemannian settings, and mention some recent results and open problems related to special Lagrangian submanifolds.  The analogy between solutions of optimal transportation problems and special Lagrangian submanifolds of Calabi-Yau manifolds is quite strong: The celebrated McLean theorem which holds for the latter can be adapted to the former case where it produces some interesting "local" solutions to the optimal transport problem.