## Tuesday Seminar on Topology

Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) KOHNO Toshitake, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya Tea: 16:30 - 17:00 Common Room

### 2018/05/08

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Dan Cristofaro-Gardiner (University of California, Santa Cruz)
Beyond the Weinstein conjecture (ENGLISH)
[ Abstract ]
The Weinstein conjecture states that any Reeb vector field on a closed manifold has at least one closed orbit. The three-dimensional case of this conjecture was proved by Taubes in 2007, and Hutchings and I later showed that in this case there are always at least 2 orbits. While examples exist with exactly two orbits, one expects that this lower bound can be significantly improved with additional assumptions. For example, a theorem of Hofer, Wysocki, and Zehnder states that a generic nondegenerate Reeb vector field associated to the "standard" contact structure on $S^3$ has either 2, or infinitely many, closed orbits. We prove that any nondegenerate Reeb vector field has 2 or infinitely many closed orbits as long as the associated contact structure has torsion first Chern class. This is joint work with Mike Hutchings and Dan Pomerleano.