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Seminar

OT Programmatic Seminar: Optimal Transport Problem For Contact Structures October 29, 2013 (03:45PM PDT - 04:45PM PDT)
Parent Program: Optimal Transport: Geometry and Dynamics
Location: MSRI: Baker Board Room
Speaker(s) Fraydoun Rezakhanlou
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In the Monge--Kantorovich transportation problem, we search for a plan that minimizes the cost of transporting mass from a set of locations  to another set of locations. According to a result of Moser, two volume forms on a compact Manifold of the same total volume are isomorphic and a solution to Monge--Kantorovich  problem offers a special solution to Moser's problem. A celebrated result of Gray asserts that if instead of volume forms we take two contact structures on a compact manifold, then they are isomorphic provided that they can be connected by a smooth arc of contact structures. In this talk, I discuss an optimal transport problem for Gray's result which has a similar flavour as Benamou-Brenier's formulation of  Monge--Kantorovich problem.

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