Geodesics and Laplace spectrum on 3D contact sub-Riemannian manifolds: the Reeb flow

Joint work with Luc Hillairet (Orléans) and Emmanuel Trélat (Paris). A 3D closed manifold with a contact distribution and a metric on it carries a canonical contact form. The associated Reeb flow plays a central role for the asymptotics of the geodesics and for the spectral asymptotics of the Laplace operator. I plan to describe it using some Birkhoff normal forms.