Combings, Local-to-Global Properties and Divergence

Explore a 50-minute lecture by Cornelia Drutu examining the intersection of geometric and coarsely analytic approaches to group theory. Delve into how groups interact with their boundaries and asymptotic cones, with particular focus on concepts encoding non-positive curvature such as combings and globalizations of local properties. Learn about recent advances in coarse invariants like divergence functions, including the discovery that under mild non-positive curvature conditions, certain dichotomies emerge—for instance, either no asymptotic cone has cut points or all asymptotic cones have cut points, and divergence functions are either linear or superlinear. The lecture draws from joint research with Davide Spriano and Stefanie Zbinden, presented at the Hausdorff Center for Mathematics.