Speaker: David Futer
Title: From Combinatorics to Geometry for Knots and 3-Manifolds
Affiliation: Michigan State University
Date: Wednesday, March 5, 2008
Place and Time: Room 102, Love Building, 3:35-4:30 pm

Abstract. Powerful theorems of Thurston, Perelman, and Mostow tell us that almost every 3-manifold admits a hyperbolic metric, and that this metric is unique. Thus, in principle, there is a 1-to-1 correspondence between a combinatorial description of a 3-manifold and its geometry. On the other hand, a concrete dictionary between combinatorial features and geometric measurements has been much harder to obtain.
I will survey some recent results that explicitly relate the combinatorics of a knot diagram to geometric features of the knot complement and related closed 3-manifolds. There are also interesting connections to the behavior of surfaces and the Jones polynomial of the knot.