Critical exponents for Poincaré profiles and conformal dimension

Abstract: Benjamini, Schramm and Timár quantified how well-connected an infinite graph is in terms of its "separation profile", where one considers the cut size of finite subgraphs. There is an "L^p" version of this that uses Poincaré inequalities to measure the connectivity of finite subgraphs. These "p-Poincaré profiles" were used in previous work with Hume and Tessera to show a variety of non-embedding results between groups. I'll mainly talk about current work with Hume where we further study the connection between these profiles and the conformal dimension of the boundary at infinity of certain Gromov hyperbolic groups.

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar