Prof. Mladen Bestvina

Title: Asymptotic Dimension

Abstract: Asymptotic dimension is an analog of topological dimension in the large-scale context of geometric group theory. This talk will introduce asymptotic dimension, and describe some of its basic properties. One of the important aspects of the theory is to establish that several finitely generated groups arising naturally in a geometric context, e.g. Gromov-hyperbolic groups, non-uniform lattices in Lie groups, etc., have finite asymptotic dimension. In particular, this proves the Novikov conjecture for such groups. Towards the end, we shall discuss asymptotic dimension of mapping class groups and the outer automorphism group of free groups.