Department of Mathematics

Speaker: Martin Bauer
Title: Infinte Dimensional Geometry of Manifolds of Mappings and Diffeomorphism Groups
Affiliation: Technical University of Vienna
Date: Monday, February 1, 2016
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. Arnold noted in 1966 that Euler's equations, which govern the motion of ideal, incompressible fluids, can be interpreted as geodesic equations on the group of volume preserving diffeomorphisms with respect to a suitable Riemannian metric. Similarly, Burgers' equation, the KdV and Camassa-Holm equations, and other PDEs arising in physics have been interpreted as geodesic equations on diffeomorphism groups and more general spaces of mappings.

Sobolev metrics provide a rich class of geometries on these spaces. In my talk I will discuss local and global well-posedness of the corresponding geodesic equation, study the induced geodesic distance, and present selected numerical examples from applications in shape analysis.