# abstract

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