Professor Department of Mathematics University of Nebraska Lincoln, NE 68588-0130 USA Avery Hall 304 Phone: (402) 472-7238 Fax: (402) 472-8466 smh at math dot unl dot edu

Research area and links

Publications

Research area and links

• Research interests:
  • Geometric group theory, including algorithmic properties (rewriting systems, automaticity, almost convexity, etc.), asymptotic properties (isoperimetric/diametric/tame filling functions), and homological properties (finiteness conditions, finite derivation type).
  • Non-commutative and commutative Groebner bases (i.e. rewriting systems for algebras).
• Groups-Semigroups-Topology seminar at UNL.
• Past conferences that I co-organized:
  • Special Session on Algorithmic and Geometric Properties of Groups and Semigroups, AMS Fall 2011 Central Section Meeting, Lincoln, NE, October 14-16, 2011.
  • Approaches to Group Theory: Using Algebraic, Analytic, and Geometric Tools in the Study of Groups, Ithaca, NY, October 9-11, 2010.
  • International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory, Lincoln, NE, May 17-21, 2009.
  • Special Session on Geometric Methods in Group Theory and Semigroup Theory, AMS Fall 2005 Central Section Meeting, Lincoln, NE, October 21-23, 2005.
  • International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory, Lincoln, NE, May 15-19, 2000.
  • Workshop on Groebner bases and rewriting techniques, Rewriting Techniques and Applications subconference of 1999 Federated Logic Conference, Trento, Italy, June 30-July 1, 1999.
  • Rewriting Techniques and Noncommutative Groebner Bases, Twenty-Second Holiday Symposium Las Cruces, NM, January 3-7, 1997.
• Past Ph.D. students:
  • Steve Lindblad, now at Hewitt Associates
  • Justin James, now at Minnesota State University Moorhead
  • David McCune, now at William Jewell College
• Links: Geometric group theory, Combinatorial group theory, Low dimensional topology

Publications

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

• 4-moves and the Dabkowski-Sahi invariant for knots, with M. Brittenham and R. Todd, arXiv:1209.6240.
• Conjugacy growth series and languages in groups, with L. Ciobanu, arXiv:1205.3857.
• Stackable groups, tame filling invariants, and algorithmic properties of groups, with M. Brittenham, arXiv:1109.6309.
• 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.
• 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.

Expository, education, and editorial publications

• 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.
• 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.
• 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.
• 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.