Ian Agol (University of Califonia at Berkeley)

The Virtual Haken Conjecture

Abstract: Waldhausen conjectured in 1968 that every aspherical 3-manifold has a finite-sheeted cover which is Haken (contains an embedded essential surface). Thurston conjectured that hyperbolic 3-manifolds have a finite-sheeted cover which fibers over the circle.

Lecture 1: An overview of 3-Manifold Topology
Date: Wednesday, October 14th, 2015
Time: 5:00pm-6:00pm
Location: Clark Hall #107
Abstract: The first lecture will be an overview of  3-manifold topology in order to explain the meaning Waldhausen's virtual Haken conjecture and Thurston's virtual fibering conjecture, and how they relate to other problems in 3-manifold theory.
 

Lecture 2: What is Geometric Group Theory?
Date: Thursday, October 15th, 2015
Time: 4:00pm-5:00pm
Location: Monroe Hall #116
Abstract: The second lecture will give some background on geometric group theory, including the topics of hyperbolic groups and CAT(0) cube complexes after Gromov, and explain how the above conjectures may be reduced to a conjecture of Dani Wise in geometric group theory.
 

Lecture 3: Geometric Group Theory and the Virtual Haken Conjecture
Date: Friday, October 16th, 2015
Time: 4:00pm-5:00pm
Location: Monroe Hall, # 116
Abstract:  The third lecture will discuss the proof of Wise's conjecture, that cubulated hyperbolic groups are virtually special. Part of this result is joint work with Daniel Groves and Jason Manning. We will attempt to make these lectures accessible to a general mathematical audience at the level of a colloquium talk.

The University of Virginia Department of Mathematics is the host for this event. Should you have any question about this event, please contact the organizer: Slava Krushkal  at krushkal@virginia.edu.