Applications are closed
for this workshop

Engel structures

April 17 to April 21, 2017

at the

American Institute of Mathematics, San Jose, California

organized by

Yakov Eliashberg, Dieter Kotschick, Emmy Murphy, and Thomas Vogel

This workshop, sponsored by AIM and the NSF, will be devoted to the emerging theory of Engel structures on four-manifolds, especially questions of rigidity versus flexibility, and its (potential) connections with contact topology, dynamics, and four-dimensional differential topology and gauge theory.

The main purpose of the workshop is to review some recent progress on the existence of Engel structures and to stimulate further research by bringing into focus geometrically interesting questions and by making connections to the modern theory of four-manifolds. With this goal in mind, the workshop will bring together people with different areas of expertise: those responsible for previous work on Engel structures, experts in contact topology and related topics, and experts on four-manifolds. Questions of a more dynamical flavor as well as questions pertaining to subriemannian geometry may also be discussed.

The main topics for the workshop are:

  • the exploration of all known approaches to the existence of Engel structures, including the recently discovered ones,
  • attempts to find a definition of tightness, respectively overtwistedness, for Engel structures,
  • discussion of the extension h-principle for Engel structures, respectively of new obstructions to extendability, and
  • possible connections to modern four-manifold theory (exotic smooth structures, gauge theory, Heegaard-Floer theory).

The workshop will differ from typical conferences in some regards. 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.

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