Low-action pseudoholomorphic curves and invariant sets

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.