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Special Colloquium
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Matt Jacobs, ZOOM: The power of duality in optimal transport
Thursday, January 14, 2021, 03:00pm - 04:00pm
Variational problems involving optimal transport play an important role in PDEs and a growing number of applied fields. In this talk, I will discuss some recent theoretical and numerical results on these problems. The unifying idea behind these results is to approach the problem via convex duality. Exploiting the interplay between primal and dual variables, we obtain a novel L^1 contraction property for the optimizers. Notably, the proof only requires the existence of optimal transport maps. As a result, we are able to avoid imposing the much more stringent conditions required for their regularity. In addition, the dual problem is very numerically tractable. This allows us to obtain state-of-the-art simulations of Wasserstein gradient flows including difficult cases like incompressible flows. This talk is a combination of joint work with Inwon Kim, Flavien Leger, Jiajun Tong, and Wonjun Lee.
Location: ZOOM

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