Bogdan Nica
Indiana University - Purdue University Indianapolis, USA

Consider an infinite, finitely generated group. A natural operator, acting on complex-valued functions on the group, is the averaging operator defined by a finite subset. What can be said about its norm(s)? I will discuss this question in a geometric situation: the subset is a sphere or a ball, and the ambient group is hyperbolic (in the sense of Gromov).