# Mathematics Colloquia and Seminars

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### Two or infinity

**Geometry/Topology**

Speaker: | Dan Cristofaro-Gardiner, UC Santa Cruz |

Location: | 3106 MSB |

Start time: | Tue, Dec 3 2019, 1:30PM |

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 C. Taubes in 2007. I will discuss joint work showing that for a wide class of Reeb vector fields on closed three-manifolds, there are either two, or infinitely many, distinct closed orbits. I will also say a few words about how one might extend this result to all Reeb vector fields on closed three-manifolds.