Cartan connections and parabolic geometries
Abstract
Klein's famous lecture proposes that to study geometry we study homogeneous spaces ie study transformation groups acting on a space. E. Cartan found a generalization now known as "Cartan geometries", these are a curved generalization of homogeneous spaces, eg Riemannian manifolds are Cartan geometries modeled on {Euclidean group}/{orthogonal group}.
Topics for my talk will be
Cartan geometries / Cartan connections
Parabolic geometries - a special class of Cartan geometries
Examples - depending on how much time but I will probably explain conformal
geometry as a parabolic geometry