Geometric Hydrodynamics: ideal fluids from a Riemannian perspective

In 1960's Arnold initiated a program whose aim was to study motions of ideal fluids in the Lagrangian setting using differential geometric tools. Subsequently, Ebin, Marsden and Omori independently proposed functional analytic frameworks in which various questions raised by Arnold's program could be addressed. Many of these questions were developed into larger research projects and have been actively pursued since then. I will discuss the background covering the early results and, time permitting, describe some of the more recent developments.