Geometry MMA Seminar: Divergence on average in hyperbolic metric spaces

Speaker:  Madeline O Horton, GMU

Title: Divergence on average in hyperbolic metric spaces

Abstract:   In 1984, Sullivan proved that the Hausdorff dimension of the limit set of a geometrically finite Kleinian group acting on real hyperbolic 3-space can be completely determined by the growth rate of the group. Bishop and Jones later generalized this result to further show that the Hausdorff dimension of the conical limit set of any nonelementary Kleinian group agrees with its critical exponent, which has since paved the way for a myriad of analogous results in a variety of settings. In recent work, Riquelme and Velozo show that the Hausdorff dimension of geodesic directions that are both recurrent and diverge on average agrees with the critical exponent at infinity for any complete, pinched negative curvature Riemannian manifold. In this talk, I discuss work that extends Riquelme and Velozo's result to Gromov hyperbolic spaces. This result further serves to provide a bridge between the theory in Kleinian groups, higher rank representations, and certain subgroups of mapping class groups. This is joint with Harrison Bray, Anton Lukyanenko, and Gabriel Lumpkin.

Time:  Friday, September 25, 2026 – 1:30pm-2:30pm

Place: Exploratory Hall, Room 4208