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

Schedule and teaching

Research area and links

Publications

Fall 2009 schedule and teaching

• Mathematics 221H: TR 9:30-10:45 AvH 118
• Mathematics 221: TR 12:30-1:45 Teac 205
• Advising: R 2:30-4:00, ? ??-?? AvH 304
• FDT working group: M 12:00-2:00, F 2:00-3:00 AvH 304
• Sparse working group: F 11:00-1:00 AvH 304
• ADVANCE Recruit-NE: T 2:00-3:30 Admin 208
• Office hours: M 2:30-4:20, T 11:00-11:50 AvH 304
• Groups-Semigroups-Topology Seminar: T 4:00-5:30, AvH 351
• Commutative Algebra Seminar: W 3:30-4:20, R 2:30-3:20, AvH 351
• Mathematics Colloquium: F 4:00-5:00, AvH 115

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Research area and links

• Research interests:
  • Geometric group theory, including asymptotic properties (isoperimetric functions, tameness functions associated to combings), homological properties (finite derivation type), and word problem solvability (almost convexity, automaticity, rewriting systems, etc.).
  • Non-commutative and commutative Groebner bases (i.e. rewriting systems for algebras).
• Past conferences that I co-organized:
  • 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.
• Groups-Semigroups-Topology seminar at UNL.
• Recent Ph.D. students:
  • Steve Lindblad, Hewitt Associates
  • Justin James, Minnesota State University Moorhead
• 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.

• Tame combing and almost convexity conditions, with S. Cleary, M. Stein, J. Taback, submitted for publication.
• Decision problems for inverse monoids presented by a single sparse relator, with S. Lindblad, J. Meakin, submitted for publication.
• 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

• 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, 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.