Christopher Svedberg: Cartan Geometry

The seminar start with introducing Klein geometry which is just another word for homogeneous geometry. This is necessary for the main topic of this seminar which is the introduction of Cartan geometry. By using differential geometry, Cartan geometry generalizes Klein's Erlangen program. Among the variants of Cartan geometry we find for instance Riemannian and conformal geometry. The corner stone of Cartan geometry is a clever use of Lie groups/Lie algebras. Finally, I will give a brief account of the applications of Cartan geometry to the theory of general relativity.