Convexity Seminar
Cost theory and geometric dualities
Speaker: Shay Sadovsky, Courant Institute, New York University
Location: Warren Weaver Hall 1314
Date: Thursday, March 6, 2025, 1 p.m.
Synopsis:
In the classical theory of optimal transport, the Legendre duality arises naturally, e.g. in Kantorovich’s duality theorem, and its image is the class of convex functions. Extending this idea to a general cost function naturally leads to a broader notion of functional cost-duality and the associated class of c-functions.
Similarly, in the setting of sets, the polar transform provides an analogous notion of duality, mapping to the class of convex sets. In this talk, I will present the notion of cost-dualities for sets. We will see that such cost-dualities actually give rise to all order-reversing involutions on sets. Finally, I will connect the notion of c-duality to general families of geometric and functional inequalities, and present some new inequalities which are obtained with this approach.