Fields Colloquium

In this talk, we will consider optimal transport on Lorentzian manifolds, where the cost is induced by the action of a charged test particle in a background electromagnetic field given by an exact two-form. As in the case of the Lorentzian distance cost (McCann ‘20, Cavalletti–Mondino ‘24, Braun–McCann ‘24), displacement convexity of entropy along $L^1$ displacement interpolations can be characterized by a timelike lower bound on a modified Ricci curvature that incorporates the field. We will then look at electromagnetic fields in Minkowski spacetime and see how some properties of the field can be read off from displacement convexity. Joint work with Davide Manini.