Nikolaos Fountoulakis
Birmingham
Random graphs on spaces of negative curvature
Random geometric graphs have been well studied over the last 50 years or
so. These are graphs that are formed between points randomly allocated
on a Euclidean space and any two of them are joined if they are close
enough. However, all this theory has been developed when the underlying
space is equipped with the Euclidean metric. But, what if the underlying
space is curved? The aim of this talk is to initiate the study of such
random graphs and lead to the development of their theory. Our focus
will be on the case where the underlying space is a hyperbolic space. We
will discuss some typical structural features of these random graphs as
well as some applications, related to their potential as a model for
networks that emerge in social life or in biological sciences.