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Around unbalanced optimal transport: fluid dynamic, growth model, applications.

Presented by: 
François-Xavier Vialard Université Paris-Dauphine, INRIA Paris - Rocquencourt
Date: 
Friday 17th November 2017 - 14:00 to 14:45
Venue: 
INI Seminar Room 1
Abstract: 
In this talk, we present the so-called Wasserstein-Fisher-Rao metric (also called Hellinger-Kantorovich) by its dynamical and static formulation. The link between these two formulations is made clear by generalizing the Riemannian submersion of Otto to this new setting. Then the link with the Camassa-Holm equation can be made with this metric, in the same way Brenier made it between optimal transport and incompressible Euler. Passing by, we prove that the Camassa-Holm equation is actually an incompressible Euler equation on a bigger space. We also show the use of this metric to interpret a particular Hele-Shaw model as a gradient flow. We then finish with some examples of use of this new metric as a similarity measure on diffeomorphic registration of shapes.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons