Geometric Analysis and Topology Seminar

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Beyond Arnold's geodesic framework of an ideal hydrodynamics

Speaker: Boris Khesin, University of Toronto

Location: Warren Weaver Hall 512

Date: Friday, February 27, 2026, 11 a.m.

Synopsis:

In 1966 V.Arnold suggested a group-theoretic approach to ideal hydrodynamics via the geodesic flow of the right-invariant energy metric on the group of volume-preserving diffeomorphisms of the flow domain. We describe several recent ramifications of this approach related to compressible fluids, optimal mass transport, as well as Newton's equations on diffeomorphism groups and smooth probability densities. It turns out that various important PDEs of hydrodynamical origin can be described in this geometric framework in a natural way. This is a joint work with G.Misiolek and K.Modin.