Higher-dimensional contact topology

Applications are closed
for this workshop

Higher-dimensional contact topology

April 15 to April 19, 2024

at the

American Institute of Mathematics, Pasadena, California

organized by

Roger Casals, Yakov Eliashberg, Ko Honda, and Gordana Matic

This workshop, sponsored by AIM and the NSF, will focus on the development of higher-dimensional contact topology, with a focus on convex hypersurface theory and contact submanifolds. We will bring a diverse group of experts, spanning a variety of career stages, and represent the different research interests from the international community of researchers in contact topology.

The first aim of the workshop is to develop and apply convex hypersurface theory so as to discover new results in higher-dimensional contact topology. This is motivated by recent works which open the floor to tackling problems in higher-dimensional contact topology that previously seemed inaccessible. Many geometric objects in lower-dimensional convex surfaces, such as divides and bypasses, can be effectively manipulated so as to classify (germs of) contact structures near a convex surface. Part of the workshop shall focus on establishing these results in higher dimensions and discovering how to manipulate convex hypersurfaces. In particular, this also involves the study of the dynamics of the involved vector fields. In particular, this includes:

  1. Develop the relationship between Convex Hypersurface Theory and the problem of Weinstein fillability of contact manifolds, and determine ways in which Convex Hypersurface Theory can be used for the classification of contact structures in higher-dimensional contact manifolds.
  2. Develop and apply parametric Convex Hypersurface Theory and study of the dynamics of Liouville vector fields in higher dimensions.
The second aim of this workshop is to broaden and deepen the study of higher-dimensional contact submanifolds, the natural higher-dimensional counter-part to transverse knots. Following recent developments, the first steps for a rich theory of contact divisors (codimension-2 contact submanifolds) have now been established. In particular, existence is now understood, as it is the fact that the same smooth isotopy class can be often represented by different (even infinitely many) contact isotopy classes. This opens a long series of interesting questions, many of which we believe can be addressed using currently available methods, or by suitably developing some of the recent ideas in the field further. In particular, we hope to:

  1. Develop new constructions for contact submanifolds which are smoothly isotopic but not contact isotopic, as well as methods to distinguish them.
  2. Study the applications of bypasses in higher dimensions.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org

Plain text announcement or brief announcement.