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Geometry and Topology Seminar

Friday, February 10, 2023
4:00pm to 5:00pm
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Linde Hall 187
Finite Bowen-Margulis-Sullivan measures in higher rank
Mikolaj Fraczyk, Department of Mathematics, University of Chicago,

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.

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