# C^\infty closing lemma for three-dimensional Reeb flows via embedded contact homology

Thursday, February 16, 2017 -

10:00am to 11:00am

I will explain an application of embedded contact homology (ECH) to Reeb dynamics. Specifically, I prove so-called $C^\infty$ closing lemma for Reeb flows on closed contact three-manifolds. The key ingredient of the proof is a result by Cristofaro-Gardiner, Hutchings and Ramos, which claims that the asymptotics of ECH spectral invariants recover the volume of a contact manifold. Applications to closed geodesics on Riemannian two-manifolds and Hamiltonian diffeomorphisms of symplectic two-manifolds (joint work with M.Asaoka) will be also presented.

Speaker:

Kei Irie

Kyoto University, Japan

Event Location:

IAS - West Building Lecture Hall