Title: Cartan geometries

Abstract: Cartan geometries provide a description of manifolds that carry
certain types of geometric structures as "curved analogs" of homogeneous spaces. My talk will start by
outlining this concept and its role in connecting classical geometry, in particular Klein's
Erlangen program, to differential geometry. Next, I will briefly discuss examples for which the concept is of
interest. Finally, I will sketch an application of this point of view to the study of automorphism
groups of geometric structures.