Suzanne Schlich

The aim of this talk is to give a brief overview of Gromov hyperbolic spaces, also known as δ-hyperbolic spaces. In the 1980s, Gromov introduced a notion of hyperbolicity for metric spaces, generalizing large-scale properties of both the hyperbolic plane and metric trees (among others). We will give various characterizations of hyperbolic metric spaces in order to describe their geometry, in particular the geometry of their triangles. Some typical hyperbolic phenomena will be discussed, such as divergence of geodesics, approximation by trees and isoperimetric inequalities. Finally (if time permits?), we will explain what meaning can be given to the statement "almost all groups are hyperbolic".
The only prerequisite for this talk is the definition of a metric space !