Focused Workshop on Volume and Complexity in Non-Positive Curvature

The goal of this workshop is to investigate the connections between various measurements of complexity of lattices (in topological groups) and their co-volume. For lattices in the isometry group of the hyperbolic plane, this connection goes back to the classical Gauss-Bonnet formula — which relates the Euler characteristic of a surface to its volume. Such connections between volume and complexity have been extensively studied in the context of non-positively curved spaces, and in various settings such as Riemannian manifolds, arithmetic lattices in Lie groups, and coarse geometry. In this workshop we hope to bring together experts in these various topics with the goal of deepening our understanding of these phenomena.