Ian Agol

The 2009 Clay Research Award was made to Ian Agol, Danny Calegari and David Gabai for their solutions of the Marden tameness conjecture, and, by implication through the work of Thurstan and Canary, of the Ahlfors measure conjecture.

The tameness conjecture asserts that a hyperbolic 3-manifold with finitely-generated fundamental group is homeomorphic to the interior of a compact 3-manifold (possibly with boundary). The Ahlfors conjecture asserts that the limit set of a finitely generated Kleinian group (i.e. the minimal invariant set on the Riemann sphere, which is the boundary at infinity of hyperbolic 3-space) has either full or zero measure, and in the former case the action of the group on it is ergodic.