Tuesday, January 28, 2014 - 15:00
1 hour (actually 50 minutes)
In 1966 V. Arnold observed that solutions to the Euler equations of incompressible fluids can be viewed as geodesics of the kinetic energy metric on the group of volume-preserving diffeomorphisms. This introduced Riemannian geometric methods into the study of ideal fluids. I will first review this approach and then describe results on the structure of singularities of the associated exponential map and (time premitting) related recent developments.