Edgar A. Bering IV : Expected Behaviors of 3-Manifolds

Posted by Edgar Bering , part of the Graduate Student Colloquium.

At

May 1, 2014, 4:15 p.m.

In

SEO 636

Abstract

Recent advances in 3-manifold theory have settled the conjectural picture proposed by Bill Thurston in the 1980's, however these resolutions have a common theme: they tend not to be effective. For example, Ian Agol's resolution of the Virtual Haken Conjecture is purely existential; every 3-manifold has a finite-index cover that is ``sufficiently large'', but there are no known bounds on this index in terms of the starting manifold. In this talk we will review some of the history of the result and then discuss recent work in understanding 3-manifolds and their covers statistically, concluding with some open problems in this direction. The talk will aim to be self contained and broadly accessible.

Refreshments will be served.