Tuesday, January 24, 2023 11am to 12pm
About this Event
Jan Peszek, University of Warsaw
Abstract: In 2001 F. Otto discovered a (nowadays well-known) relationship between the continuity equation and gradient flows with respect to the 2-Wasserstein metric. This connection provides a convenient description of many new and classical models and PDEs including Keller-Segel and Fokker-Planck as well as models of first-order collective dynamics.
I am going to present a recent work (joint with David Poyato), wherein we introduce the so-called fibered 2-Wasserstein metric (which admits only transportation along fibers controlled by a prescribed probabilistic distribution) and explore its applicability in gradient flows. Based on such a metric, we develop the notion of heterogeneous gradient flows, and prove that they are equivalent to solutions of parameterized continuity equations. Lastly, I will present a collection of applications ranging from mixtures of fluids, to multispecies models of collective dynamics, and to (the essential) applications in alignment models.
This program is open to all eligible individuals. USC operates all of its programs and activities consistent with the university’s Notice of Non-Discrimination. Eligibility is not determined based on race, sex, ethnicity, sexual orientation or any other prohibited factor.
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