Timothy Moy

For my thesis I worked on the problem of G₂ contact geometry, an exotic structure that emerges from the theory of parabolic geometries. The field of parabolic geometries explores the interface between differential geometry and representation theory.

My supervisors are Michael Eastwood and Thomas Leistner. 

You can hear about some of the work done in my thesis, in particular the link between two contact geometries in five dimensions, Legendrean contact geometry and G₂ contact geometry, in a talk by Michael Eastwood for the 90th birthday conference of Sir Roger Penrose, based on joint work with Paweł Nurowski and myself. 

I gave a talk for the University of Adelaide Differential Geometry Seminar on Legendrean contact geometry. These are contact manifolds with an additional splitting of the contact distribution into Lagrangian subbundles. Unlike contact manifolds by themselves, these structures have local invariants. In particular I explained how, in five dimensions, one can construct a canonical vector bundle and connection which is flat if and only if the space is locally isomorphic, in an appropriate sense (preserving a contact structure and splitting), to the space of lines inside hyperplanes inside 4-dimensional Euclidean space. You can read the abstract and view the slides.