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.
This colloquium is part of the Distinguished Lecture Series (DLS) organized by The (Indian) Mathematics Consortium (TMC), and co-hosted by IIT-B and ICTS-TIFR. For more information about this lecture series, and to register, please visit the homepage of the TMC DLS.