Emerging Topics on Hypersurfaces in Contact Geometry

Organizers: Emmy Murphy, Northwestern University/IAS

Participants: Roger Casals, John Etnyre, Ko Honda, Yang Huang, Oleg Lazarev, Dishant Pancholi, Francisco Presas, Kevin Sackel

Summary: In the last two years there has been rapid progress in our understanding of hypersurfaces in high dimensional contact geometry, of two different types. One type is contact hypersurfaces: codimension 2 submanifolds which are themselves contact. A number of recent results have been established concerning the existence and non-uniqueness of such embeddings. The second type is convex hypersurfaces: codimension 1 submanifolds so that the contact structure is locally invariant in the transverse direction. An existence theorem for these was recently established by Honda-Huang, and points to potential methods of decomposing contact manifolds into understood pieces.