In the upcoming spring term, I will give a course on Riemannian geometry of diffeomorphism groups (80833), as part of Kazhdan Sunday seminars. It will take place on Sundays, 12–14, starting next week (March 14), via zoom (link: https://huji.zoom.us/j/88976026563?pwd=WEw3OHpOUUtBNFlQUUk2UGdteXNRZz09). After Passover, it may continue in class (Ross 70A), with a live broadcast.
The course will cover the following topics:
1. Introduction to infinite dimensional Riemannian geometry — what extends from "standard" Riemannian geometry and what does not.
2. Spaces and metrics of interest — relation between geodesic equations on diffeomorphism groups and hydrodynamics.
3. Metric properties of diffeomorphism groups — vanishing distance phenomenon, diameter, metric completeness.
4. Geodesic equations — short time existence, regularity of geodesics (following Ebin–Marsden), geodesic completeness.
I will assume some basic knowledge in functional analysis and (finite dimensional) Riemannian geometry (in the level of the basic notions courses of our department).
If you are interested in joining the mailing list of the course (for announcements, notes, etc.), please fill in your email address in the following google form:
Hope to see you next week,