Research and Papers

I study Cartan geometries, which formalize the idea of curving a (G,X) manifold, a manifold locally modeled on a homogeneous space X for a group G. This research area a a descendent of Klein's Erlangen program, which aims to understand geometric structures in terms of the symmetry groups acting on them. I am particularly interested in parabolic Cartan geometries, where many of the developments in Cartan geometry have been concentrated. Important examples include conformal, projective and CR geometries. I am also interested in Lichnerowicz-type conjectures for these geometries, which state that a manifold with geometric data whose automorphism groups do not preserve a certain underlying structure must be locally isomorphic to the homogeneous model space for that geometry.