Groups and Dynamics Seminar

Understanding the size of the first non-zero eigenvalue of the Laplacian on a closed hyperbolic manifold provides a plethora of information about the geometry of the manifold. In this talk, I will discuss some joint work with Will Hide (Oxford) and Davide Macera (Bonn) where we obtain near-optimal spectral gaps for randomly constructed hyperbolic surfaces. Our proof uses a fusion between trace formula techniques and ideas from recent developments in strong convergence of random matrices. Time permitting, I will also discuss some joint work with Michael Magee (Durham) and Anna Roig-Sanchis (Nice) on the strong convergence of 3-manifold groups and their implications on spectral gaps for random bundles associated to hyperbolic 3 manifolds.