Length and volume in symplectic geometry

Members' Seminar
Topic:Length and volume in symplectic geometry
Speaker:Daniel Cristofaro-Gardiner
Affiliation:University of California, Santa Cruz; von Neumann Fellow
Date:Monday, October 21
Time/Room:2:00pm - 3:00pm/Simonyi Hall 101
Video Link:https://video.ias.edu/members/2019/1021-DanielCristofaro-Gardiner

Symplectic capacities are measurements of symplectic size.  They are often defined as the lengths of certain periodic trajectories of dynamical systems, and so they connect symplectic embedding problems with dynamics.  I will explain joint work showing how to recover the volume of many symplectic 4-manifolds from the asymptotics of a family of symplectic capacities, called "ECH" capacities.   I will then explain how this asymptotic formula was used by Asaoka and Irie to prove the following dynamical result: for a C^{\infty} generic diffeomorphism of S^2 preserving an area form, the union of periodic points is dense