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Research

My research is in Combinatorial and Geometric Group Theory, with a particular focus on the automorphism groups of groups and algorithms in group theory. You can find preprints, seminar slides and other things related to my research below. If you would like a copy of one of these papers, send me an email and I will be happy to oblige.

External grants received

Recipient of a Collaboration Grant for Mathematicians from the Simons Foundation for a project entitled "Languages and Geometry of Automorphisms of Groups''. This grant carries a value of $35,000 over the period September 2014 through August 2019.

Contributions to expository texts

Author of the chapter "Coxeter Groups" in Office Hours with a Geometric Group Theorist, eds. Matt Clay and Dan Margalit, Princeton University Press, 2017, ISBN 9780691158662. A description of this text is available on the publisher's website.

Papers appearing in peer-reviewed forums (journals and proceedings)

Recognizing Right-Angled Coxeter Groups Using Involutions. With Charles Cunningham, Andy Eisenberg and Kim Ruane.
Pacific J. Math., 284-1 (2016), pp. 41-77; MR3530862
CAT(0) Extensions of Right-angled Coxeter Groups. With Charles Cunningham, Andy Eisenberg and Kim Ruane.
Topology Proc., 48 (2016), pp 277-287. (This paper was e-published on December 3, 2015.); MR3431824
On Groups Presented by Monadic Rewriting Systems with Generators of Finite Order
Bull. Aust. Math. Soc., 91 (2015), no. 3, pp 426-434; MR3338967
The Bieri-Neumann-Strebel Invariant of the Pure Symmetric Automorphisms of a Right-Angled Artin Group. With Nic Koban.
Illinois J. Math., 58 (2014), no. 1, pp 27-41; MR3331840
The Symmetries of McCullough-Miller Space
Algebra Discrete Math., 14 (2012), no. 2, pp. 239-266; MR3099973
On the Derived Length of Coxeter groups. With Peter A. Brooksbank.
Comm. Algebra, 40 (2012), no. 3, 1142-1150; MR2899931
On the Automorphisms of a Graph Product of Abelian Groups. With Mauricio Gutierrez and Kim Ruane.
Groups Geom. Dyn. 6 (2012), no. 1, pp. 125-153; MR2888948
Normal Forms for Automorphisms of Universal Coxeter Groups and Palindromic Automorphisms of Free Groups. With Kim Ruane.
Internat. J. Algebra Comput. 20 (2010), no. 8, pp. 1063-1086; MR2747416
The Automorphism Group of the Free Group of Rank Two is a CAT(0) Group. With Kim Ruane and Genevieve S. Walsh.
Michigan Math. J. 59 (2010), 297-302; MR2677622
Rigidity of Graph Products of Abelian Groups. With Mauricio Gutierrez.
Bull. Aust. Math. Soc. 77 (2008), no. 2, 187-196; MR2428781
Andrews-Curtis Groups and the Andrews-Curtis Conjecture
J. Group Theory 10 (2007), no. 3, 373-387; MR2320974
The Manifestation of Group Ends in the Todd-Coxeter Coset Enumeration Procedure
Internat. J. Algebra Comput. 17 (2007), no. 1, 203-220; MR2300414
Palindromic Primitives and Palindromic Bases in the Free Group of Rank Two
J. Algebra 304 (2006), no. 1, 359-366; MR2256396

Preprints submitted for publication

Under revision

Detecting the Growth of Free-group Automorphisms by their Action on the Homology of Subgroups of Finite Index
Following the advice of the editor and referee, this paper has been undergoing a major rewrite. It will be available again soon.

D.Phil. Thesis

The Topology of Finite Graphs, Recognition and the Growth of Free-group Automorphisms
My thesis was supervised by Martin Bridson and Danny Groves and Marc Lackenby. It was submitted at the University of Oxford, 2004.

Miscellaneous

Some 'C' code for playing with primitive elements
This program allows the user to enter words in {x, y, X, Y}* and then tests to see if the word is a reduced primitive in F(x, y). The algorithm for testing cyclically reduced primitive elements is very fast (linear in length of input) and follows from Osborne and Zieshang (Invent. Math, 1981). Of course, Whitehead's Algorithm is also very fast and works for higher rank free groups, but this is easy to do by hand and fun to play with.