Willa Cather Professor of Mathematics Fellow of the American Mathematical Society Department of Mathematics University of Nebraska Lincoln, NE 68588-0130 USA hermiller at unl dot edu

CV

Research area and links

Publications

Teaching

Research area and links

• Research interests:
  • Topics list:
    • Geometric and combinatorial group theory, including algorithmic properties (rewriting systems, automaticity, almost convexity, etc.), asymptotic properties (growth functions, isoperimetric/diametric/tame filling functions), and homological properties (finiteness conditions, finite derivation type).
    • Connections between group theory and low dimensional topology
    • Non-commutative and commutative Groebner bases (i.e. rewriting systems for algebras).
  • Description: Group theory is the study of symmetries of objects. The "word problem", originally stated by M. Dehn in 1911, asks if there is an algorithm which can determine whether or not performing a sequence of rigid motions of an object (for examples, reflections and rotations) results in returning the object to its original position. Solvability of the word problem and related algorithmic problems is of central interest in geometric group theory. For the cases in which a problem is solvable, it is also important to understand the complexity of the possible solutions. Computer science tools from formal language theory are often valuable in this complexity analysis.
    The goal of much of my research is two-fold, both to find large classes of groups for which algorithmic problems have particularly tractable solutions, and to understand what algebraic, asymptotic, geometric, or topological properties of a group are implied by such algorithms.

• Editorial board member:
  • Journal of Algebra, 2019 -
  • Communications in Algebra, 2010-2020

• Links to research conferences 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.

• Links to Ph.D. advisees who have graduated:
  • Aurora DeBellevue
  • Ash DeClerk, at North Dakota State University
  • Andrew Quaisley, self-employed (AI Safety Researcher supported by a grant from Open Philanthropy)
  • Katie Tucker, at Northrop Grumman
  • Maranda Tomlinson, at the Center for Communications Research, Princeton
  • Nick Owad, at Hood College
  • Anisah Nu'Man, at Spelman College
  • Scott Dyer, self-employed
  • Melanie DeVries, at MetaCommunications
  • Ashley Johnson, at the University of North Alabama
  • David McCune, at William Jewell College
  • Justin James, at Minnesota State University Moorhead
  • Steve Lindblad, at Hewitt Associates

• Groups-Semigroups-Topology seminar at UNL

• Links to other pages surveying related research areas: Geometric group theory, Combinatorial group theory, Low dimensional topology