Education

• 1983 - Ph.D. in Mathematics, Southern Illinois University at Carbondale
• 1976 - M.S. in Theoretical Physics, University of Wroclaw, Wroclaw, Poland
• 1976 - ABT in Astronomy, University of Wroclaw, Wroclaw, Poland

Research Interests

• Clifford algebras and their generalizations, e.g., quantum Clifford algebras
• Mathematical structure of classical and quantum Clifford algebras including group algebra approach to Clifford algebras
• Transposition anti-automorphim of Clifford algebras
• Representations of the symmetric group in the package SymGroupAlgebra including representing S_n in a Clifford algebra Cl_n,n
• Non-commutative Groebner bases in Grassmann and Clifford algebras, see package GfG
• Groebner bases applied to solving engineering problems, see a joint package with Dr. Jane Liu called RJGrobner
• Hecke algebras (q-Young tableaux, representations, q-spinors)
• Multilinear algebras (Quantum Clifford algebras, Rota-Stein Cliffordization)
• Category theory and its applications, e.g., automata theory
• Quaternions and dual quaternions in robotics
• Development of Maple modules for effective teaching of mathematics
• Continuous development of Maple modules such as CLIFFORD/Bigebra, SymGroupAlgebra, SP, etc.

Software

• CLIFFORD - A Maple Package for Clifford Algebra Computations with Bigebra, SchurFkt, GfG - Groebner for Grassmann, Cliplus, Define, GTP, Octonion, SP, SymGroupAlgebra, and code_support (Copyrights by Rafal Ablamowicz and Bertfried Fauser)
• Version 16 for Maple 16 [with experimental paralellizing of the Clifford product to be added soon]
• Version 15 for Maple 15 [coming soon - it is safe to use version 13 in Maple 15] [with experimental paralellizing of the Clifford product]
• Version 14 for Maple 14 [coming soon - it is safe to use version 13 in Maple 14]
• Version 13 for Maple 13
• Old versions for: Maple 12, Maple 11, Maple 10, Maple 9, Maple 8, Maple 7, Maple 6, Maple V

• Additional modules that use CLIFFORD/Bigebra:
  
• SchurFkt - A Maple Package for the Hopf Algebra of Symmetric Functions for Maple 12
• GfG - A Maple package for Computing Groebner Bases for Ideals in Grassmann Algebras for Maple 12
• TNB - A Maple package written by Troy Brachey for computing Groebner GLB and GLIB bases in Grassmann algebras [18Kb zip file]
  
  
• Additional modules not using CLIFFORD/Bigebra:
  • SP - A Maple 12 Package for Symmetric Polynomials
  • RJgrobner - A Maple 12 Package for Commutative Groebner Bases
  • code_support - A Maple 12 Package for Maintaining and Manipulating Help Pages
  • SINGULARPLURALlink - A Maple 12 package for interfacing Maple with Singular:Plural ver. 3-0-4 to compute Groebner bases in polynomial rings and Grassmann and Clifford Cl(Q) algebras [252Kb zip file]
  • SymGroupAlgebra - A Maple 12 package for computations in the group algebra of a symmetric group
• How to cite this software and publications citing it:
• Citing
• Publications

Publications

• Recent Publications

Theses Directed

• Sheela Brachey, Schur Polynomials and the Irreducible Representations of S_n, May 2009
• Jason Knight, Various Methods for Calculating Reducible and Irreducible Representations of the Symmetric Group, May 2009
• Troy Brachey, Groebner Basis Algorithms for Grassmann Algebras in a Maple Package, May 2008
• Bennie Hodges: Applications of Category Theory to Basic Principles of Automata Theory, May 2007
• Sean Tunney: On the Continuous Families of Idempotents in the Clifford Algebra of the Euclidian Plane, May 2003
• Michael Baswell: Clifford Algebra Space Singularities of a Redundant Variable Geometry Truss Manipulator, May 2000 (co-directed with Joe Anderson)

Conferences

• AGACSE 2012 Applied Geometric Algebras in Science and Engineering 2012, July 2-4 La Rochelle, France
• ICCA 9: The 9th Conference on Clifford Algebras and their Applications in Mathematical Physics (ICAA 9), Weimar, July 15-20, 2011
• 45th Annual Technical Meeting of the Society of Engineering Science, University of Illinois at Urbana-Champaign, October 12-15, 2008
• International Conference of Numerical Analysis and Applied Mathematics 2008, ICNAAM 2008, Kos, Greece, 16-20 September 2008
• The Third International Conference on Applications of Geometric Algebra in Computer Science and Engineering, AGACSE'2008 Leipzig, August 17-19, 2008
• ISSAC 2008 - International Symposium on Symbolic and Algebraic Computation, Hagenberg, Austria, July 20-23, 2008
• ICCA 8: The 8th Conference on Clifford Algebras and their Applications, 26-30 May 2008, Brazil
• 44th Annual Technical Meeting Society of Engineering Science October 21- 24, 2007
• Advanced Mathematical Tools: A Frontier Between Mathematics and Engineering
• ISSAC 2007 - The International Symposium on Symbolic and Algebraic Computation, Waterloo, Ontario, Canada, July 29-August 1, 2007
• RISC Summer 2007 at Hegenberg, Linz, Austria
• 6th Annual Hawaii International Conference on Statistics, Mathematics and Related Fields, January 17 - 19, 2007, Honolulu Hawaii
• 43rd Annual Technical Meeting, Society of Engineering Science, August 13-16th, 2006, PennState, University Park
• Advanced Mathematical Tools: A Frontier Between Mathematics and Engineering
• ISSAC 2006 - International Symposium on Symbolic and Algebraic Computation, July 9-12, 2006, Genova, Italy
• Special Semester on Groebner Bases and Related Methods, February - July 2006, Linz, Austria
• ICCA 7: The 7th Conference on Clifford Algebras and their Applications in Mathematical Physics (ICAA 7), Toulouse, May 19-29, 2005
• ICCA 6: The 6th Conference on Clifford Algebras and their Applications in Mathematical Physics, Tennessee Technological University, Cookeville, May 20-25, 2002

Resources

• Institutes:
  
• Max Planck Institute, Leipzig, Germany
• RISC - Linz, Austria, Research Institute for Symbolic Computations
• SISSA - Trieste, Italy, International School for Advanced Studies
• Encyclopedias, libraries and databases:
  
• Wikipedia - Free Online Encyclopedia of Mathematics
• MathWorld at Wolfram.com
• Groebner basis bibliography
• Los Alamos National Laboratory
• MathSciNet of AMS
• arXiv.org - e-Print Archive
• TTU Library Online Catalog
• Societies and agencies:
  
• American Mathematical Society
• Mathematical Association of America
• Society for Industrial and Applied Mathematics
• National Security Agency
• Mathematics software:
  
• AXIOM, Maple, Mathematica
• CLUCalc, CoCoA, Macaulay 2, Maxima
• FELIX, Bergman, FGb, SALSA, SINGULAR
• Schur Group Theory Software, MAGMA Computational Algebra System
• The Geometer's Sketchpad, Cinderella
• Clifford (geometric) algebra resources:
• Pertti Lounesto's counterexamples
• Pertti Lounesto's CLICAL
• Geometric Calculus at Fukui University
• Other Scientific Resources:
  
• Birkhauser, Kluwer, Springer, Geometry Center
• LaTeX resources:
• TTU master thesis LaTeX2e style and input files
• "A Graduate Student's Guide to LaTeX and AMS-LaTeX" (387KB .pdf)
• MikTeX, TeXnicCenter
• TeX resources

Advanced Courses Taught

• MATH 6910 Special Topics: Research in Group Theory (fall 2010)
• MATH 6910 Special Topics: Representations of the Symmetric Group (fall 2008)
• MATH 6991 Noncommutative Groebner Bases for Grassmann and Clifford Algebras (fall 2007)
• MATH 6910 Special Topics: Computational Algebraic Geometry II (fall 2006)
• MATH 6910 Special Topics: Computational Algebraic Geometry I (summer 2006)
• MATH 4750/5750 Category Theory of Sets (spring 2006)
• MATH 6910 Special Topics: Geometric Algebra and Robotics (fall 2005)
• MATH 6910 Special Topics: Clifford Algebras (fall 2004)
• MATH 6910 Special Topics: Theory of Quadratic Forms and Clifford Algebras (summer 2004)

Last updated: April 7, 2013