Geometry and Topology Seminar

A general philosophy due to Joel Fish and Helmut Hofer states that symplectic manifolds with sufficiently rich Gromov-Witten theory should contain hypersurfaces with rich dynamics. In this talk, we will discuss many recent results that represent specific instances of this philosophy. In low dimensions, where Gromov-Witten (and related Gromov-Taubes) invariants are more well understood, strong and general results like the smooth closing lemma have been proven. The higher dimensional setting is much more mysterious, and is the subject of ongoing research. This talk is based on joint work with Shira Tanny (and the work of others).