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# Professor Pego (Carnegie Mellon University), Mathematics Colloquium

## December 7, 2017 @ 4:00 pm - 5:00 pm

**Title:** *Least action, incompressible flow, and optimal transport*

**Abstract:** We describe a striking connection between Arnold’s least-action principle for incompressible Euler flows and geodesic paths for Wasserstein distance. The least-action problem for geodesic distance on the `manifold’ of fluid-blob shapes exhibits instability due to microdroplet formation. A connection with fluid mixture models via a variant of Brenier’s relaxed least-action principle for generalized Euler flows will be outlined also.

This is joint work with Jian-Guo Liu and Dejan Slepcev.