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
Editor-in-Chief
Since January 1, 2016, Editor-in-Chief of Advances in Applied Clifford Algebras (AACA), a Springer journal dedicated to publishing high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras, and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication ``Online First" and is organized into six sections:
- Analysis
- Differential Geometry and Dirac Operators
- Mathematical Structures
- Theoreical and Mathematical Physics
- Applications
- Book Reviews
For more information see
http://www.springer.com/birkhauser/physics/journal/6
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:
January 9, 2016