Title and Abstracts: WTC 2009

Dani Wise, McGill
   Title: Groups with a quasiconvex hierarchy
Abstract: Nonpositively curved cube complexes have become increasingly central objects in combinatorial and geometric group theory. We will give a quick introduction focusing especially on their identity as "higher dimensional graphs". We will then outline how to use nonpositively curved cube complexes to resolve certain outstanding group theoretical problems. These include Baumslag's conjecture on the residual finiteness of one-relator groups with torsion, as well as the virtual-fibering problem for Haken hyperbolic 3-manifolds.

Denis Osin, Vanderbilt
   Title:
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Thomas Koberda, Harvard
   Title: Representations of mapping class groups and residual properties of 3-manifold groups.
Abstract: I will talk about homological representations of mapping class groups, namely ones which arise from actions on covering spaces. I will prove that these are asymptotically faithful and indicate how the Nielsen-Thurston classification can be obtained from these representations. I will then discuss how mapping tori of mapping classes can be used to analyze the image of these representations. As a corollary, I will exhibit a class of compact 3-manifolds whose fundamental groups are, for every prime p, virtually residually finite p.

Pallavi Dani, LSU
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Joan Licata, Stanford
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Amir Mohammadi, Chicago
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Jason Behrstock, CUNY
   Title: Quasi-isometric classification of right angled Artin groups
Abstract: Any finitely generated group can be endowed with a natural metric which is unique up to maps of bounded distortion (quasi-isometries). A fundamental question is to classify finitely generated groups up to quasi-isometry. Surprisingly, for a large family of right angled Artin groups the quasi-isometric classification can be described in terms of a concept in computer science called "bisimulation." We will describe this classification and a geometric interpretation of bisimulation. (Joint work with Walter Neumann and Tadeusz Januszkiewicz.)

Johanna Mangahas, Michigan
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