Quasisymmetry, quasiconformality and conformal dimension in metric spaces
by
Jeremy Tyson
University of Illinois

The past decade has seen dramatic progress in the study of first-order geometric analysis in metric measure spaces of bounded geometry. Rigidity and classification problems in the theory of hyperbolic groups are a significant and ongoing source of motivation. In this talk, I will survey some recent advances from the viewpoint of nonsmooth metric analysis, including the equivalence of the principal definitions of quasiconformality and quasisymmetry, and the theory of conformal dimensions of metric spaces with application to Cannon's conjecture.

Date received: March 5, 2006