Speaker:  Rohil Prasad (University of California Berkeley)       

Title:  Dense existence of proper compact invariant sets for torsion 3D contact forms

Abstract:  This is joint work in progress with Dan Cristofaro-Gardiner. The study of periodic orbits of Reeb flows on 3-dimensional contact manifolds has seen major progress over the past two decades. This talk, however, will be about the topological dynamics of Reeb flows beyond periodic orbits. For any contact form for a torsion contact structure on a closed 3-manifold Y, without any genericity conditions, I'll show that any point in Y is arbitrarily close to some proper compact subset of Y which is invariant under the Reeb flow. Stronger results can also be established which parallel classical theorems of Le Calvez-Yoccoz, Franks, and Salazar for homeomorphisms of the two-sphere. The proof relies on new analytical results for holomorphic curves, various properties of embedded contact homology, and the following fun fact: a connected subset of a Hausdorff space with at least two points has no isolated points.