Publications and Preprints

Full list of publications.
Slides from recent talks.
Articles on the arXiv.
Reviews from MathSciNet (subscription)
Department preprint server

to appear

Combinatorial descriptions of multi-vertex 2-complexes to appear in the Illinois Journal of Mathematics (18 pages)
Windmills and extreme 2-cells (with D. Wise) to appear in the Illinois Journal of Mathematics (16 pages)

published

Constructing non-positively curved spaces and groups in Geometeric and cohomological methods in group theory, LMS Lecture Note Series 358 (2009), 162--224. Survey article.
Geometric presentations for pure braid group (with Dan Margalit) Journal of Knot Theory and Its Ramifications 18 (2009) 1--20.
Order independence in asynchronous cellular automata (with M. Macauley and H. Mortveit) Journal of Cellular Automata 3 (2008), 37--56.
Locally quasiconvex small cancellation groups (with D. Wise) Transactions of the AMS 360 (2008), 237--271.
The Euler characteristic of the Whitehead automorphism group of a free product (with C. Jensen and J. Meier) Transactions of the AMS 359 (2007), 2577--2595.
h-vectors of generalized associahedra and noncrossing partitions (with C. Athanasiadis, T. Brady and C. Watt) International Mathematics Research Notices (2006), Article ID 69705, 1--28. (electronic)
The integral cohomology of the group of loops (with C. Jensen and J. Meier) Geometry and Topology 10 (2006), 759--784.
Noncrossing partitions in surprising locations. American Mathematical Monthly 113 (2006) 598--610. (AMM version)
The length spectrum of a compact constant curvature complex is discrete (with N. Brady) Geometriae Dedicata 119 (2006) 159--167.
Non-commutative Groebner bases for the commutator ideal, (with S. Hermiller) International Journal of Algebra and Computation 16 (2006), 187--202.
Coherence, local quasiconvexity, and the perimeter of 2-complexes, (with D. Wise) GAFA 15 (2005), 859--927.
CAT(0) is algorithmic, (with M. Elder) Geometriae Dedicata 107 (2004), no. 1, 25--46.
The hypertree poset and the l²-Betti numbers of the motion group of the trivial link (with J. Meier) Mathematische Annalen 328 (2004), no. 4, 633--652.
Bounding edge degrees in triangulated 3-manifolds (with N. Brady and J. Meier) Proceedings of the AMS 132 (2004), no. 1, 291--298.
Local-to-asymptotic topology for cocompact CAT(0) complexes (with N. Brady and J. Meier) Topology and its Applications 131 (2003), no. 2, 177--188.
Combinatorial conditions that imply word-hyperbolicity for 3-manifolds (with M. Elder and J. Meier) Topology 42 (2003), no. 6, 1241--1259.
Rigidity of Coxeter groups and Artin groups (with N. Brady, B. Muehlherr, and W. Neumann) Geometriae Dedicata 94 (2002), no. 1, 91--109.
Curvature testing in 3-dimensional metric polyhedral complexes, (with M. Elder) Experimental Mathematics 11 (2002), no. 1, 143--158.
Fans and ladders in small cancellation theory, (with D. Wise) Proceedings of the LMS 84 (2002), no. 3, 599--644.
The pure symmetric automorphisms of a free group form a duality group (with N. Brady, J. Meier, and A. Miller) Journal of Algebra 246 (2001), no. 2, 881--896.
Normal forms for free aperiodic semigroups, International Journal of Algebra and Computation 11 (2001), no. 5, 581--625.
Three-generator Artin groups of large type are biautomatic (with T. Brady) J. of Pure and Applied Algebra, 151 (2000), 1--9.
General small cancellation theory, International Journal of Algebra and Computation. 10 (2000), no. 1, 1--172. The article is also availabe in several sections.
Burnside groups and small cancellation theory Groups St. Andrews 1997 in Bath, II, 538--559, London Math. Soc. Lecture Note Ser., 261, Cambridge Univ. Press, Cambridge, 1999. This is a survey article which provides an overview of the "General Small Cancellation Theory" article listed above.
Integrating Polynomials in Secant and Tangent American Mathematical Monthly 106 (1999), no. 9, 856--858.
Gaps in the categories of finite directed and finite transitive graphs (with R. Baldinger) International Journal of Algebra and Computation 8 (1998), no. 1, 35--60.

submitted

Dynamics groups of asynchronous cellular automata (with M. Macauley and H. Mortveit) (22 pages)
Braids, posets and orthoschemes (with T. Brady) (33 pages)
Triangles, squares and geodesics (with R. Levitt) (34 pages)

preprints

An introduction to Garside structures (28 pages)

software

• cat.g software to test curvature in 3-dimensions (with M. Elder)
• coxeter.g software to test curvature in Brady-Krammer complexes (with W. Choi)