Speaker: Denis Osin

Abstract:
To each metric space of finite asymptotic dimension, one associates a collection of invariants called type functions. These functions are closely related to the Hilbert space compression rate of the group, dimension of asymptotic cones, and other asymptotic invariants. The aim of this talk is to discuss some results about type functions of connected Lie groups, lattices, and relatively hyperbolic groups. We also study the question which functions can be realized as type functions of finitely generated groups.