A Zimmer embedding theorem for Cartan geometries

I will present a theorem relating the automorphism group of a Cartan geometry to the group on which the geometry is modelled: roughly, the adjoint representation of the first embeds in the adjoint representation of the second. In the study of geometric structures on manifolds, Cartan geometries provide a setting well-adapted to questions about homogeneity. The theorem and many of its consequences are strongly analogous to, and improvements of, results of Zimmer: the actions are not assumed to preserve a finite measure, and large actions are shown to imply local homogeneity.