The University of Arizona
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Unbalanced optimal transport and its connection to the Camassa-Holm equation

Hamiltonian Systems

Unbalanced optimal transport and its connection to the Camassa-Holm equation
Series: Hamiltonian Systems
Location: ONLINE
Presenter: François-Xavier Vialard, LIGM, Université Gustave Eiffel, CNRS

In this talk, I explain the formulation of the Wasserstein-Fisher-Rao distance, introduced a few years ago as the natural extension of the Wasserstein L2 metric to the space of positive Radon measures. We present the equivalence between the dynamic formulation and a static formulation, where we relax the marginal constraints with relative entropy. Then, we will present a connection with standard optimal transport on a cone space. The second part of the talk is motivated by this optimal transport distance and we study a generalized Camassa-Holm equation, for which we study existence of minimizing generalized geodesics, a la Brenier.

The talk will be via Zoom at: https://utoronto.zoom.us/j/99576627828

Passcode: 448487