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Welcome Seminar - Beibei Liu

beibei
September 4, 2025
3:00 pm - 4:00 pm
Scott Labs E001

Beibei Liu
The Ohio State University

Title
Brownian motion and orbit counting of Kleinian groups

Abstract
Kleinian groups are discrete isometry subgroup of hyperbolic spaces. The action on the spaces is quite related to the geometry and dynamics of the quotient manifolds. I will introduce Kleinian groups of divergence type, which is equipped with nice dynamical features. Furthermore, if the group is a subgroup of a lattice, we show that the divergence type implies that random walks on the Schreier graph associated with the group is recurrent. The main ingredient is a connections among orbit counting of the group action on hyperbolic spaces, the volume growth rate of the quotient manifolds, and the growth rate of the Schreier graph.

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