University of Toronto
                Fields Analysis Working Group Seminar
                   Tuesday 11. August, 12:10-1:00pm
                             Fields 210


Speaker: Max-Konstantin von Renesse (Technische Universitaet Berlin)

Title: An optimal transport perspective on the Schroedinger equation

We show that the Schroedinger equation is a lift of Newton's 2nd law of motion to the space of probability measures, on which derivatives are taken w.r.t. the Wasserstein Riemannian metric.  Here the potential is the is sum of the total classical potential energy of the extended system, plus its Fisher information.  The precise relationship is established via a well known (`Madelung') transform which is shown to be a symplectic submersion of the standard symplectic structure of complex valued functions into the canonical symplectic space over the Wasserstein Riemannian manifold.