This talk will give an outline of a proof of the Ending Laminations Theorem direct from Teichmuller geodesics [2]. As with the Minsky-Brock-Canary proof, the broad strategy uses Minsky's approach, developed over the last decade and more, of constructing a geometric model for given ending lamination data, and proving that any hyperbolic manifold with this ending lamination data is Lipschitz equivalent to the model. But there are two main differences. The first is that the geometric model is constructed direct from Teichmuller geodesics, and the theory used is a theory of Teichmuller geodesics developed for a different purpose in [1]. The second is that the proof is more directly related to results that Minsky developed for the case of combinatorial bounded geometry, and mimics a proof in the bounded geometry case.

[1] Rees, M., Views of Parameter Space: Topographer and Resident.

Asterisque 288, 1983

[2] Rees, M., The Ending Laminations Theorem direct from Teichmuller

geodesics, http://www.liv.ac.uk/~maryrees/maryrees.homepage.html