# Ian Agol - Virginia Mathematics Lectures - October 14-16, 2015

#### Event start date: Wednesday, October 14, 2015

##### The Virtual Haken Conjecture
• Lecture 1: An overview of 3-Manifold Topology
• Lecture 2: What is Geometric Group Theory?
• Lecture 3: Geometric Group Theory and 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

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?

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

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.

Virginia Mathematics Lectures archive

Date published: Wednesday, October 14, 2015