Henry Wilton

I am a Scott Russell Johnson Senior Research Fellow in Mathematics at Caltech. You can find me in Sloan 272. My principal areas of research include limit groups and the logic of free and hyperbolic groups, separability and profinite completions, the fundamental groups of 3-manifolds and other areas of geometric group theory.

All my articles, notes and slides are in pdf format, so you can view them using Acrobat Reader.

Teaching

In the Fall 2009 term I will teach Math 109A—Introduction to Geometry and Topology.

In the Spring 2009 semester at the University of Texas at Austin, I taught a graduate course in Geometric Group Theory. We focussed on residual finiteness and word-hyperbolic groups. The students wrote up notes on this blog. I intend to clean this up sometime soon. Material from other courses that I have taught before is available here.

Papers

Here is a list of my publications on MathSciNet.

My thesis concerned limit groups and subgroup separability.

Preprints

Here is an ArXiv search for me.

• Polygonal words in free groups (with Sang-hyun Kim). Preprint (2009).
• Conjugacy separability of 1-acylindrical graphs of free groups (with Owen Cotton-Barratt). Preprint (2009).
• Some virtually special hyperbolic 3-manifold groups (with Eric Chesebro and Jason DeBlois). Preprint (2009).
• On surface subgroups of doubles of free groups (with Cameron Gordon). Preprint (2009).
• Profinite properties of graph manifolds (with Pavel Zalesskii). Preprint (2008).

Notes

• My Part III essay on The Geometrization Conjecture
• The Rips Machine
• In the autumn of 2007 I visited the MSRI for their Geometric Group Theory programme. Lars Louder and I took notes on Zlil Sela's course on definable sets in free groups. In their current, incomplete state they can be found here.

Talks

This is a list of some talks that I've given. Some of them have accompanying notes or slides, of variable quality. E-mails pointing out typos and other errors are appreciated.

• Introductory talk (Workshop on limit groups and their generalisations, University of Southampton, July 2009)
• A topological approach to conjugacy separability (Topology Seminar, UT Austin, September 2008)
• Enumerating limit groups (Non-positive curvature and the elementary theory of free groups, Anogia, Greece, June 2008)
• A structure theory for limit groups and Positive-genus towers (Geometry, Topology and Dynamics Seminar, UIC, April 2008)
• Computing solutions to systems of equations over free and hyperbolic groups (Groups and Dynamics Seminar, Texas A&M, March 2008)
• Computing solutions to systems of equations over free and hyperbolic groups (AMS Sectional Meeting, Baton Rouge, March 2008)
• Residually free 3-manifolds (Topology Seminar, Rice, March 2008)
• Residually free 3-manifolds (Topology Seminar, UT Austin, February 2008)
• Enumerating limit groups (Post-doc seminar, MSRI, Berkeley, September 2008)
• Subgroup separability in residually free groups (Introduction to Geometric Group Theory, MSRI, Berkeley, August 2008), visible online here
• Hall's Theorem for limit groups (Caen, July 2007)
• Hall's Theorem for limit groups (Paris-Sud 11, Orsay, July 2007)
• Limit groups, LERF and local retractions (Geometry & Topology Seminar, Caltech, February 2007)
• Limit groups are LERF (Topology Seminar, UT Austin, October 2006)
• Some residual properties of groups (AMS Sectional Meeting, University of Utah, October 2006)
• Some residual properties of groups (Amitsur Algebra Colloquium, Hebrew University of Jerusalem, April 2006)
• Limit groups, measure equivalence and subgroup separability (Geometry, Integrable Systems and Topology, University of Glasgow, January 2006)
• Subgroup separability and limit groups (London Algebra Colloquium, November 2005)
• At the Geometric Topology conference at Będlewo in July 2005, Lars Louder and I gave a series of recitations to accompany Mladen Bestvina's workshop on limit groups. Here are the slightly illegible handwritten notes from recitations I and III. (Będlewo, July 2005)
• An Introduction to Limit Groups (Series for Telgiggy, Imperial College, London, January 2005)

I also have notes/slides for graduate talks on An Introduction to Geometrization, Group actions on trees, Algebraic geometry over groups, Bass-Serre theory and Hyperbolic spaces, R-trees and outer automorphisms.

Other mathematicians etc.

These are links to the web pages of some other mathematicians: my mathematical family, colleagues, collaborators, housemates etc.

• My thesis supervisor, Martin Bridson, University of Oxford
• My doctorbruder, Michael Tweedale, University of Bristol
• Eric Chesebro, University of Montana
• Owen Cotton-Barratt, University of Oxford
• Jason DeBlois, University of Illinois at Chicago
• Pavel Zalesskii, University of Brasilia
• Sam Kim, UT Austin
• Alan Reid, UT Austin
• Daniel "Danny" Groves, UIC
• Ben Klaff, UIC
• David "Ben" McReynolds, University of Chicago
• Claire Postlethwaite is an applied mathematician in Auckland.
• Tim Storer is a philosopher.