Geometry and Topology Seminar

Let M be a negatively curved closed manifold. The Bowen Margulis Sullivan (BMS) measure on M can be understood as the unique probability measure on the unit tangent bundle of M which maximizes the entropy of the geodesic flow. The construction of BMS measures can be extended to locally symmetric spaces. where they proved to be a useful tool in the study of discrete subgroups of semi-simple Lie groups. I will talk about a joint work with Min Ju Lee where we show that a higher rank locally symmetric space admits a finite BMS measure if and only if it is finite volume. This leads to a new criterion detecting lattices among the discrete subgroups of higher rank Lie groups.