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Explore the Hamiltonian geometry of fluids in this 55-minute colloquium talk by Boris Khesin, presented at the Colloque des sciences mathématiques du Québec (CSMQ) on January 12, 2024. Delve into the group-theoretic approach to ideal hydrodynamics proposed by V. Arnold in the 1960s, which utilizes the geodesic flow of the right-invariant energy metric on the group of volume-preserving diffeomorphisms. Discover recent developments in this field, including applications to compressible fluids, optimal mass transport, and Newton's equations on diffeomorphism groups and smooth probability densities. Learn how various important partial differential equations of hydrodynamical origin can be naturally described within this geometric framework, providing a comprehensive understanding of fluid dynamics from a mathematical perspective.
