On (Non-Traditional) Costs and Potentials

We will discuss new proofs and results in the theory of costs and transportation. We will discuss function classes and transforms induced by costs, associated subgradients and optimal transportation. An emphasis shall be made on non-traditional costs which assume infinite values (that is, with prohibited moves), less amenable to classical techniques, and specifically on the polar cost which induces the polarity transform and the class of geometric convex functions on $\R^n$.