Introduction to geometric hydrodynamics I

Abstract: The aim of the lectures is to explain Arnold’s discovery from 1966 that solutions to Euler’s equations for the motion of an incompressible fluid correspond to geodesics on the infinite-dimensional Riemannian manifold of volume preserving diffeomorphisms. In many ways, this discovery is the foundation for the field of geometric hydrodynamics, which today encompasses much more than just Euler’s equations, with deep connections to many other fields such as optimal transport, shape analysis, and information theory.

differential geometryprobability

Audience: advanced learners

Young Researchers between Geometry and Stochastic Analysis 2021