Strong convergence of right-angled Artin groups and spectral gaps of hyperbolic 3-manifolds

Joe Thomas (Durham University) https://simons.berkeley.edu/talks/joe-thomas-durham-university-2026-10-16 Probabilistic Phenomena on Graphs, Groups, and Manifolds The strong convergence properties of group representations of fundamental groups of graphs and manifolds have recently been exploited to obtain near optimal spectral gap results for their Laplacians. Determining the existence of sequences of unitary representations that strongly converge to the regular representation for different groups is a difficult task with few concrete results. In this talk, I will discuss joint work with Michael Magee and Anna Roig-Sanchis where we prove the existence of strongly converging unitary and hyperoctahedral representations for right-angled Artin groups. These groups are fundamental in geometric group theory, and are closely related to the fundamental groups of hyperbolic 3-manifolds. I will focus on this connection and explain the spectral implications.