Summary of research results in these publications

Articles

Papers are available as pdf files. Note that these are the preprint versions, and they differ in varying amounts from the published versions and arxiv versions at the references listed below.

• Automaticity for graphs of groups, with D.F. Holt, S. Rees, and T. Susse, arXiv:1905.05943; to appear in Groups, Geom., Dyn.
• Determining solubility for finitely generated subgroups of PL homeomorphisms, with C. Bleak and T. Brough, arXiv:1507.06908; to appear in Trans. Amer. Math. Soc.
• Autostackability of Thompson's group F, with N. Corwin, G. Golan, A. Johnson, and Z. Sunic, J. Algebra 545 (2020), 111-134.
• A counterexample to the Bernhard-Jablan Unknotting Conjecture, with M. Brittenham, Experiment. Math. (2019), DOI: 10.1080/10586458.2019.1580633.
• Geometry of the word problem for 3-manifold groups, with M. Brittenham and T. Susse, J. Algebra 499 (2018), 111-150.
• HNN extensions and stackable groups, with C. Martinez-Perez, Groups, Geom., Dyn. 12 Issue 3, (2018), 1123-1158.
• No positive cone in a free product is regular, with Z. Sunic, Internat. J. Algebra Comput. 27 (2017), 1113-1120.
• Conjugacy languages in groups, with L. Ciobanu, D.F. Holt, and S. Rees, Israel J. Math. 211 (2016), 311-347.
• Homology and closure properties of autostackable groups, with M. Brittenham and A. Johnson, J. Algebra 452 (2016), 596-617.
• Tame filling invariants for groups, with M. Brittenham, Internat. J. Algebra Comput. 25 (2015), 813-854.
• A uniform model for almost convexity and rewriting systems, with M. Brittenham, J. Group Theory 18 (2015), 805-828.
• Algorithms and topology for Cayley graphs of groups, with M. Brittenham and D.F. Holt, J. Algebra 415 (2014), 112-136.
• Conjugacy growth series and languages in groups, with L. Ciobanu, Trans. Amer. Math. Soc. 366 (2014), 2803-2825.
• 4-moves and the Dabkowski-Sahi invariant for knots, with M. Brittenham and R. Todd, J. Knot Theory Ramifications 22 (2013), 1350069.1-20.
• Tame combing and almost convexity conditions, with S. Cleary, M. Stein, J. Taback, Math. Z. 269 (2011), 879-915.
• Decision problems for inverse monoids presented by a single sparse relator, with S. Lindblad, J. Meakin, Semigroup Forum 81 (2010), 128-144.
• Groups whose geodesics are locally testable, with D. F. Holt and S. Rees, Internat. J. Algebra Comput. 18 (2008), 911-923.
• A characterization of virtually free groups, with R. H. Gilman, D. F. Holt, and S. Rees, Arch. Math. 89 (2007), 289-295.
• Poly-free constructions for right-angled Artin groups, with Z. Sunic, J.Group Theory 10 (2007), 117-138.
• Star-free geodesic languages for groups, with D. F. Holt and S. Rees, Internat. J. Algebra Comput.17 (2007), 329-345.
• Noncommutative Gröbner bases for the commutator ideal, with J. P. McCammond, Internat. J. Algebra Comput. 16 (2006), 187-202.
• Computations with Frobenius powers, with I. Swanson, Experiment. Math. 14 (2005), 161-173.
• Minimal almost convexity, with M. Elder, J. Group Theory 8 (2005), 239-266.
• Homological finite derivation type, with J. M. Alonso, Internat. J. Algebra Comput. 13 (2003), 341-359.
• Isoperimetric inequalities for soluble groups, with J. R. J. Groves, Geom. Dedicata 88 (2001), 239-254.
• Measuring the tameness of almost convex groups, with J. Meier, Trans. Amer. Math. Soc. 353 (2001), 943-962.
• Monomial orderings, rewriting systems, and Gröbner bases for the commutator ideal of a free algebra, with X. H. Kramer and R. C. Laubenbacher, J. Symbolic Comput. 27 (1999), 133-141.
• Rewriting systems and geometric three-manifolds, with M. Shapiro, Geom. Dedicata 76 (1999), 211-228.
• Artin groups, rewriting systems and three-manifolds, with J. Meier, J. Pure Appl. Algebra 136 (1999), 141-156.
• Tutorial on string rewriting systems and extensions of Gröbner bases, Proceedings of the Federated Logic Conference '99 Workshop on Gröbner Bases and Rewriting Techniques, 1999.
• Tame combings, almost convexity and rewriting systems for groups, with J. Meier, Math. Z. 225 (1997), 263-276.
• Algorithms and geometry for graph products of groups, with J. Meier, J. Algebra 171 (1995), 230-257.
• Rewriting systems for Coxeter groups, J. Pure Appl. Algebra 92 (1994), 137-148.
• Electronic structure of polyhedral alkanes, with C. A. Scamehorn and R. M. Pitzer, J. Chemical Physics 84 (1986), 833-837.
• A regression model for forecasting microwave radio fading at Palmetto, GA, with J. A. Schiavone, IEEE Trans. Antennas and Propagation AP-34 (1986), 936-942.
• A family of random number routines, with H. B. Thompson, J. Comput. Math. Science Teaching 4 no.4 (1985), 57-60.
• Computer managed problem drill: The program PROBLEM, with H. B. Thompson, J. Comput. Math. Science Teaching 2 no.1 (1982), 25-30.

Conference Proceedings

• Proceedings of the International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory 2009, co-edited with C. Bleak, T. Jajcayova and S. Margolis, Internat. J. Algebra Comput. 21 (2011), no. 1-2.
• Proceedings of the International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory 2000, co-edited with J. Meakin and M. Sapir, Internat. J. Algebra Comput. 12 (2002), no. 1-2.