05-16&23【Oliver Edtmair】物质科研楼C1124 Geometry&Topology Seminar系列讲座


报告题目:Systoles of convex energy hypersurfaces

报告人Oliver Edtmair (加利福尼亚大学伯克利分校)

时间:2024年5月16日,23日 10:00-11:00


Part 1: Hofer-Wysocki-Zehnder proved that every strictly convex energy hypersurface in R^4 possesses a disk-like global surface of section. They asked whether a systole, i.e. a periodic orbit of least action, must span such a disk-like global surface of section. In my talk, I will give an affirmative answer to this question, based on joint work in progress with Abbondandolo and Kang. I will explain how this result can be used to obtain a sharp symplectic embedding result for convex domains in R^4. Moreover, I will explain how this relates to the strong Viberbo conjecture on the equivalence of normalized symplectic capacities.

Part 2: Continue part 1 of the talk. In particular, I will elaborate on Clarke duality and pseudoholomorphic planes