Rafal Ablamowicz, Professor
Department of Mathematics, Box 5054,Tennessee Technological University, Cookeville, TN 38505, U.S.A.
Office: Bruner Hall 114, Tel: (931) 372-3622(931) 372-3622, Fax: (931) 372-6353, E-mail: rablamowicz at tntech.edu, Personal page: Sailing
Education
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 and characters of finite groups, and applications, e.g., principal vibration modes of chemical molecules
- Representations of the symmetric group in the package SymGroupAlgebra including representing S_{n} in a Clifford algebra Cl_{n,n}
- Crystallographic groups and their applications, e.g., to finding material constants matrix
- 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)
- 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 Package for Symmetric Polynomials
- RJgrobner - A Maple Package for Commutative Groebner Bases
- code_support - A Maple Package for Maintaining and Manipulating Help Pages
- SINGULARPLURALlink - A Maple 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 package for computations in the group algebra of a symmetric group
- MaterialConstants - A Maple package for computation of a material constants tensor
- How to cite this software and publications citing it:
Publications
Theses Directed
- Zachary Brown, Group Extensions, Semidirect Products, and Central
Products Applied to Salingaros Vee
Groups Seen as 2-Groups, November 2015 (co-directed with Bertfried Fauser)
- Azizah Eid Alqthani, On Decomposing CG-Modules of Finite Groups Using Irreducible Characters, July 2015
- Kehelwala D. Gayan Maduranga, Representations and Characters of Salingaros' Vee Groups, May 2013
- 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
- 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
- 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:
- Encyclopedias, libraries and databases:
- Societies and agencies:
- 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:
- Other Scientific Resources:
- LaTeX resources:
- Graduate Seminar September 3, 2015 (.zip file with all .tex files, 2.9 MB)
Advanced Courses Taught
- MATH 6950 Special Topics: Representations and Characters of Groups II (spring 2015)
- MATH 6910 Special Topics: Representations and Characters of Groups I (fall 2014)
- MATH 6910 Special Topics: Representations of the Symmetric Group (summer 2014)
- MATH 6950 Special Topics: Representations and Characters of Groups II (spring 2014)
- MATH 6910 Special Topics: Representations and Characters of Groups I (fall 2013)
- MATH 4993 Mathematical Research: Mathematics of Material Properties (fall 2013)
- 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)
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Last updated:
November 16, 2015