Convex Hypersurfaces and Robust Heterodimensional Dynamics

A hypersurface in a contact manifold comes equipped with a natural dynamical system, called the characteristic foliation. Special cases include the suspension flow of a contactomorphism and the Liouville flow on a Liouville manifold. In this talk, I will discuss recent work resolving some longstanding questions about the topology of hypersurfaces in contact manifolds, by studying the dynamics of characteristic foliations via methods from partially hyperbolic dynamics. This talk covers joint work with Michael Huang (USC), Dishant Pancholi (Chennai) and Yasha Eliashberg (Stanford).