Riemannian Exponential Map on the Group of Volume-Preserving Diffeomorphisms

Symplectic Dynamics Seminar
Topic:Riemannian Exponential Map on the Group of Volume-Preserving Diffeomorphisms
Speaker:Gerard Misiolek
Affiliation:University of Notre Dame; Member, School of Mathemtics
Date:Wednesday, October 19
Time/Room:4:00pm - 5:00pm/S-101
Video Link:https://video.ias.edu/symplectic/misiolek

In 1966 V. Arnold showed how solutions of the Euler equations of hydrodynamics can be viewed as geodesics in the group of volume-preserving diffeomorphisms. This provided a motivation to study the geometry of this group equipped with the $L^2$ metric. I will describe some recent work on the structure of singularities of the associated exponential map and related results.