What is... a hyperbolic space?

Vortrag von Davide Spriano

Datum: 28.11.17  Zeit: 17.15 - 18.30  Raum:

The definition of a Gromov hyperbolic space, although very accessible, carries deep consequences. Indeed, after Gromov's seminal paper "Hyperbolic Groups", the study of hyperbolic groups and spaces (and further generalizations) has become a more and more active area of research in mathematics. A hyperbolic space is a geodesic metric space that has some additional condition on the behavior of geodesics. Roughly speaking, two geodesic are either very close, or diverge. The case of parallel geodesic at arbitrarily large distance (as in the Euclidean plane) is missing. The main goal of this talk is to present the definition of a hyperbolic space and to use it to prove some basic results. If time allows, we will give an overview on some generalizations of hyperbolicity by presenting some examples of spaces that exhibit behaviors that are "weakly hyperbolic".