Topology and geometry of ends of hyperbolic 3-manifolds

Abstract: The classification of non-compact hyperbolic 3-manifolds with finitely-generated fundamental groups depends on an understanding of the topology and asymptotic geometry of their ends. A number of advances in recent years have made this classification possible, and more. I will discuss the background and features of this theory, and its applications to a fuller understanding of the ways in which these manifolds (compact and non-compact) cover and approximate each other.