Volodymyr Nekrashevych: Hyperbolic groupoids

We will define the notion of a hyperbolic groupoid (or pseudogroup) generalizing properties of the action of a Gromov hyperbolic group on its boundary. A new phenomenon, not present in the case of hyperbolic groups, is duality for hyperbolic groupoids: for every hyperbolic groupoid G there is a naturally defined groupoid G' acting on the boundary of the Cayley graph of G. The groupoid G' is also hyperbolic, and G'' is equivalent to G. Some examples, in particular coming from group actions, will be discussed.