Differential Geometry Seminar
Organizers:
Jialong Deng, Akito Futaki
Speaker:
Rohil Prasad (Berkeley)
Time:
Tues., 21:00-22:00
Oct. 22, 2024
Online:
Zoom Meeting ID: 271 534 5558
Passcode: YMSC
Title:
Low-action pseudoholomorphic curves and invariant sets
Abstract:
Punctured pseudoholomorphic curves have been a key tool in Hamiltonian dynamics since a breakthrough 1993 paper by Hofer. I'll describe a new compactness theorem for sequences of punctured pseudoholomorphic curves that holds without the traditional technical assumption of "bounded Hofer energy". In the limit, one extracts a family of compact invariant subsets that are invariant under the Hamiltonian flow. This has various dynamical applications. I will briefly mention these applications, but I will mostly focus on the geometric analysis behind the compactness theorem. Most of the talk is based on joint work with Dan Cristofaro-Gardiner.