2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217178This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.To appear in workshop proceedings for "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces". Comments welcomeDifferential GeometryGeometric TopologyArithmetic lattices and weak spectral geometrytext