Emily Stark
Wesleyan University
Title
Conformal dimension for boundaries of certain Coxeter groups
Abstract
Conformal dimension is a powerful analytic invariant of a metric space that captures the fractal behavior amongst deformations of the metric space. This invariant has made a significant impact on geometric group theory and the study of spaces with negative curvature. We study a family of Coxeter groups that are built of Kleinian groups and are hyperbolic relative to virtually abelian subgroups. We give bounds on the conformal dimension of the Bowditch boundary of these groups. Our results imply there are infinitely many quasi-isometry classes within the family of Coxeter groups with defining graph a complete graph and edge labels greater than or equal to three. Consequently, there are infinitely many quasi-isometry classes among hyperbolic groups with Pontryagin sphere boundary. This is joint work with Elizabeth Field, Radhika Gupta, and Robbie Lyman.
