Beyond Arnold's geodesic framework of an ideal hydrodynamics

In the talk we discuss ramifications of Arnold's
group-theoretic approach to ideal hydrodynamics as the geodesic flow
for a right-invariant metric on the group of volume-preserving
diffeomorphisms. We show that problems of optimal mass transport are
in a sense dual to the Euler hydrodynamics. Moreover, many equations
of mathematical physics, such as the motion of vortex sheets or fluids
with moving boundary, have Lie groupoid, rather than Lie group,
symmetries (this is a joint work with Anton Izosimov).