Geometry Seminar

In his celebrated thesis, Margulis showed how to use a mixing property of the geodesic flow to obtain several kinds of equidistribution results for negatively curved closed Riemannian manifolds. More precisely the results concern equidistribution of closed geodesics and of orbits of the fundamental group in the universal cover. Margulis' ideas have been extended to more general geometric settings, with not necessarily compact spaces, for instance by Roblin who worked on non-compact locally CAT(-1)-spaces.
In this talk, we will consider similar questions in another geometric setting: that of convex projective manifolds, i.e. quotients of a properly convex domain of a real projective space. These manifolds appear in particular in the study of some discrete subgroups of Lie groups, and equidistribution results presented here are related to equidistribution results due to Sambarino for Anosov representations.
Convex projective manifolds naturally carry a Finsler metric (the Hilbert metric) which is in general not locally CAT(0). The projective lines are geodesics for this metric, and are parametrised by a geodesic flow. The study of the dynamics of this flow that we will present is joint work with Feng Zhu. Speaker(s): Pierre-Louis Blayac (U Michigan)