Convex co-compact groups and relative hyperbolicity

The notion of convex co-compact groups generalizes convex co-compact Kleinian groups from rank one Lie groups to the projective general linear groups of rank at least two. This generalization encompasses many interesting examples coming from Anosov subgroups and non-Gromov hyperbolic projective reflection groups. In this talk, we will discuss a geometric property that completely characterizes relatively hyperbolic convex co-compact groups (with respect to any finite collection of peripheral subgroups). We also characterize the Bowditch boundary of the group as a quotient of a subset of the real projective space. Our results are analogous to results on CAT(0) spaces with isolated flats. This is joint work with Andrew Zimmer.