Emerging Topics Working Group: Hypersurfaces in Contact Geometry

The Institute has put the following precautionary measures in place in response to the Coronavirus (COVID-19) and asks that you help keep our campus healthy while here by being intentionally hygienic in public, washing your hands frequently and thoroughly with soap and warm water, using hand sanitizer stations that are placed in each building on campus, and adopting a no-handshake policy.

Symptoms of the coronavirus are fever, cough, and shortness of breath. Even if you are sick with symptoms other than those of the coronavirus, please do not attend events on campus until after your symptoms are gone.

For the most up to date information go to: https://www.cdc.gov/coronavirus/2019-ncov/index.html

Organizers: Emmy Murphy, Northwestern University/IAS and Daniel Alvarez-Gavela, IAS/Princeton University

By invitation only

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.