Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond

Abstract

We present recent results on counting and distribution of circles in a given circle packing invariant under a geometrically finite Kleinian group and discuss how the dynamics of flows on geometrically finite hyperbolic $3$ manifolds are related. Our results apply to Apollonian circle packings, Sierpinski curves, Schottky dances, etc.Comment: To appear in the Proceedings of ICM, 201