Geometry and Topology Seminar

The Weinstein conjecture states that on any closed manifold, a "Reeb" vector field must have at least one closed orbit. The three dimensional version of this conjecture was proved several years ago by Taubes. I will explain recent joint work with Michael Hutchings and Vinicius Ramos showing that a Reeb vector field on a closed three-manifold always has at least two closed orbits. The proof involves a recently discovered relation between the volume of any contact three-manifold and the length of certain finite sets of Reeb orbits. Part of the talk will involve an introduction to a kind of Floer homology for contact three-manifolds, called Embedded Contact Homology.