Geometry, topology, and effective rigidity of hyperbolic 3-manifolds

Contact: Aru Ray

In the 1970s, Bill Thurston proposed a program to understand 3-manifolds from a geometric perspective as a way to address outstanding topological questions. After Perelman, we know most 3-manifolds are hyperbolic, but the existence of such a geometric structure leaves a great deal of geometric information about the structure unclear. In this talk I will describe a broad effort to classify three-manifolds geometrically in terms of topological data and its implications for the larger question of how to extract geometric information directly from topological and combinatorial data specifying a 3-manifold.

This talk will be expository and aimed at a general geometry & topology audience.