18,23 Aug 2016; IMS (UiTø), RealFag A228. 12:15-13:30.

Dennis The

Homogeneous integrable Legendrian contact structures

While all contact manifolds are locally equivalent, endowing the contact distribution with additional data often yields a rich geometric structure with non-trivial local invariants. For Legendrian contact structures, this means that the contact distribution is split into two complementary subspaces that are maximally isotropic with respect to a natural (conformal) symplectic form.

In my first talk, I'll give an overview of this geometry: motivations for its study coming from complex (CR) geometry, explaining how a large subclass of it can be equivalently viewed as a complete 2nd order PDE system, describing the fundamental curvature quantities, and the notion of duality.  This will be a general talk, requiring only basic notions from differential geometry.

In a sequel talk, I'll focus on the problem of classifying homogeneous such structures in dimension five.  In particular, I'll outline a systematic "top-down" method called "Cartan reduction" for carrying out such classifications.  (While this very general method dates back to Elie Cartan's work in the early 1900's, it is not well-known.)

This is based on joint work with Boris Doubrov and Sasha Medvedev.