Publications and Projects

This site was last updated on Tuesday, April 29th, 2008.

Please click on the highlighted text in order to download a given paper in PostScript format (although a couple of the more recent ones are in PDF!), or to view information concerning a publication.

If would like to receive preprints/reprints in another format, please send me an e-mail, and I'll be happy to oblige.

Articles

"Properties of certain random trees," with S.R. Kaplan, preprint, submitted to Studia Sci. Math. Hungar.

"The average connectivity of expander graphs," preprint, submitted to J. Combin. Math. Combin. Comput.

"Decremental tag systems and random trees," with J. Knox and M. McClure, to appear in Complex Systems, 2008.

"Asymptotic connectivity of infinite graphs," to appear in Discrete Math., 2008.

"BS(1,2) and a construction of Magnus," Comm. Algebra 35 (2007) no. 12, 4088-4095.

"Rewriting systems and orderings on Artin monoids," with T. Smith, Internat. J. Algebra Comput. 17 (2007) no. 1, 61-75.

"Some new biautomatic Coxeter groups," J. Algebra 296 (2006) 339-347.

"Automorphisms of Coxeter groups," Trans. Amer. Math. Soc. 358 (2006) no. 4, 1781-1796.

"Reflection independence in even Coxeter groups," with M. Mihalik, Geom. Ded. 110 (2005) no. 1, 63-80.

"Strongly rigid even Coxeter groups," Topology Proceedings 28 (2004) no. 1, 19-54.

"A new class of rigid Coxeter groups," Internat. J. Algebra Comput. 13 (2003) no. 1, 87-94.

"Cancellative residuated lattices," with J. Cole, N. Galatos, P. Jipsen, and C. Tsinakis, Algebra Universalis 50 (2003) 83-106.

Ph.D. Dissertation

"Even rigidity in Coxeter groups," 2002. (As submitted to Vanderbilt University, March, 2002.)

Other Publications

The Isomorphism Problem in Coxeter groups (lecture notes volume for Imperial College Press, London, and World Scientific Publishing Co., Singapore), 2005. Please feel free to e-mail me if you're interested in obtaining a submission version in Postscript or PDF format. Due to space restrictions, I'm no longer posting the file on this website. There is, however, a swanky cover design worked up by the folks at WSPC, and visible at the right; click to enlarge it, and to see a rather informal testimonial, captured on April 9th, 2005!

From here to infinity: a foundation for calculus, with J. Alan Alewine, Derek Bruff, James A. Cole, Nikolaos Galatos, Erica L. C. King, Jo Ann W. Staples, Sarah Ann Stewart. Thomson Learning Custom Publishing, 2001. /

Ongoing Projects (very out-of-date! Soon to be renovated...)

I'm still thinking about the following: what can we say about the primality or compositeness of numbers of the form (2 * 3 * 5 * ... * p ) + 1? The answer so far is, "not much." But we're working on that.
I'm also still puzzling out questions of orderability, trying to push orderability (or non-orderability) results to more general Artin and Artin-like groups. Yet to be commenced is research into a generalization of Bowditch's results on the unique product property in groups acting on R-trees. (See the above preprints for some results stemming from this work on orderability.)
The ends of lattices are still on my mind. I hope to take a closer look at these, a propos the Sageev half-space construction, once I get a little time this coming summer.
I have an idea as to how one can use turning angles in two-dimensional CAT(0) cell complexes in order to get at orderability of groups acting nicely on such complexes (this goes back to the analysis of certain subsemigroups of the given group...ah, but I have said too much already!).
The wolf, the goat, and the cabbage: what in the heck does this have to do with network design applications, if anything? And could it possibly have anything to do with the connectivity of a random graph, or even the large-scale geometry of a group?
A big umbrella project I've been working on for quite a while now deals with the "connectivity at infinity" of an arbitrary graph: what can be said about this measure, and how does it relate to the (large-scale) geometry of the graph?