Past lectures

Abstract

Gromov hyperbolic metric spaces are spaces which appear negatively curved at large scales. These spaces have been studied extensively in the last 15 years, and have found applications in group theory, geometric topology, Kleinian group theory, and dynamics/rigidity theory. Gromov hyperbolic spaces have a naturally defined boundary (or boundary at infinity), which is a topological space endowed with additional structure („generalized quasiconformal structure“). The boundary is a fundamental tool in the subject, and is essential in most applications.

The lectures will begin by covering the basics of Gromov hyperbolic spaces, and will then focus on the topology of the boundary. The second half will be devoted to quasisymmetric/quasiconformal structure, and interplay with more analytical notions/objects such as metric measure spaces and Poincare inequalities.