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SUMMARY:Around unbalanced optimal transport: fluid dynamic\, growth model\
 , applications. - François-Xavier Vialard (Université Paris-Dauphine\; I
 NRIA Paris - Rocquencourt)
DTSTART:20171117T140000Z
DTEND:20171117T144500Z
UID:TALK95209@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk\, we present the so-called Wasserstein-Fisher-Rao
  metric (also called Hellinger-Kantorovich) by its dynamical and static fo
 rmulation.  The link between these two formulations is made clear by gener
 alizing the Riemannian submersion of Otto to this new setting. Then the li
 nk with the Camassa-Holm equation can be made with this metric\, in the sa
 me way Brenier made it between optimal transport and incompressible Euler.
   Passing by\, we prove that the Camassa-Holm equation is actually an inco
 mpressible 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 t
 hen finish with some examples of use of this new metric as a similarity me
 asure on diffeomorphic registration of shapes.
LOCATION:Seminar Room 1\, Newton Institute
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