Abstract: Curt McMullen's work involves two beautiful and closely related subjects: the theory of Kleinian groups and hyperbolic 3-manifolds, and the study of iterates of holomorphic functions of \C^ ("complex dynamics"). In the 1980's, Dennis Sullivan proposed a dictionary by means of which one can try to understand complex dynamics in terms of powerful analytic and geometric techniques in Kleinian groups (eg. quasiconformal mappings) and vice versa. I will discuss this dictionary, mention some of McMullen's contributions and show some pictures. This is the first in a series of three colloquia which will introduce some of the work of 1998 Fields Medal winners Curtis T. McMullen, W. Timothy Gowers and Richard Borcherds respectively. Each talk will be geared to a general mathematical audience and all are invited to attend.
