Bounded cohomology shows that lattices in higher rank Lie groups are not acylindrically hyperbolic. Nevertheless, convex cocompact subgroups of higher rank simple Lie groups can be defined and studied in analogy to the theory of Kleinian groups. We use these ideas to construct in some cases surface subgroups of cocompact lattices in higher rank Lie groups.

We exhibit some dynamical properties of the Weil Petersson geodesic flow. As an application, we obtain geometric information on random hyperbolic 3-manifolds which fibre over the circle.