Information geometry of diffeomorphism groups

Klas Modin (Chalmers U of Technology, Gothenburg)

Feb 06. 2025, 14:00 — 15:00

The study of diffeomorphism groups and their applications to problems in analysis and geometry has a long history. Geometric hydrodynamics, pioneered by V. Arnold in the 1960s, considers an ideal fluid flow as the geodesic motion on the infinite-dimensional group of volume-preserving diffeomorphisms of a flow domain in the energy metric. A similar consideration on the space of densities led to a geometric description of the optimal mass transport and the Kantorovich-Wasserstein metric. Likewise, the information geometry associated with the Fisher-Rao metric and Hellinger distance has an equally beautiful infinite-dimensional geometry and can be regarded as a higher Sobolev analogue of optimal transportation.

In this mini-course, I shall describe various Riemannian metrics on diffeomorphism groups and describe the connection to information geometry. The material is based on a forthcoming essay with B. Khesin and G. Misiolek, which shall make up the course literature.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Infinite-dimensional Geometry: Theory and Applications (Thematic Programme)
Organizer(s):
Tomasz Goliński (U of Białystok)
Gabriel Larotonda (U of Buenos Aires)
Alice Barbara Tumpach (WPI, Vienna)
Cornelia Vizman (WU of Timisoara)