Curriculum Vitae

Garret Sobczyk
Departamento de Fisico-Matematicas
UNIVERSIDAD DE LAS AMERICAS-PUEBLA
Apartado Postal #321, Sta. Catarina Martir
72820 Puebla, Pue., Mexico
email: garret_sobczyk@yahoo.com
FAX: (52-22)-29-2066

Degrees and Qualifications:

1971 Ph.D. in Mathematics, Arizona State University
Dissertation: Thesis1, Thesis 2, page 108
1967 M.S. in Mathematics, Arizona State University.
1964 B.A. in Mathematics, Western State College, Gunnison, Colorado.
1961 High School Diploma, P.K. Younge, Gainesville, Florida.

Professional and Academic Experience:

2008-present Professor Emeritus, Universidad de las Americas, Puebla, Mexico
1993-2008 Professor, Department of Physics and Mathematics, Universidad de las Americas, Puebla, Mexico.
1991-1993 Professor, Department of Mathematics, National Autonomous University of Mexico, Mexico City.
1987-1990 Associate Professor of Mathematics, Department of Science Mathematics, Lander College, Greenwood, South Carolina 29646.
1983-1987 Associate Professor of Mathematics, Department of Mathematics, Spring Hill College, Mobile, Alabama.
1979-1983 Research Associate, Institute for Theoretical Physics, University of Wroclaw, Wroclaw, Poland.
1977-1979 NSF Exchange Fellow, University of Stoney Brook \& University of Wroclaw, Wroclaw, Poland.
1976-1977 Systems Analyst/Computer Programmer, Medical University of South Carolina, Charleston, South Carolina.
Part-time Mathematics Instructor, College of Charleston, Charleston, SC.
1975-1976 Research Grant, Arizona State University.
1973-1974 Research Fellow, Polish Academy of Science, Warsaw, Poland.
1971-1973 Visiting Assistant Professor, Department of Mathematics, Arizona State University, Tempe, Arizona.
1966-1971 Graduate Student/Teaching Assistant: 1966-71, Arizona State University, Tempe, Arizona.
1964-1966 Seismic Analyst/Computer Programmer, United Electro-Dynamics, Teledyn Inc., Alexandria, Virginia.

Tesis Presentadas: (Licenciado)

Miriam Salomé Castillo Gil, Base Espectral de los Operadores Lineales y sus Aplicaciones, Agosto 2001.
Alejandro Hernández Pérez, algebra de vectores complejos en relatividad especial, Abril 20, 2002.
Alberto Carabarin Aguirre, polinomios de interpolación generalizados, May 2003.

Tesis Presentadas: (Doctorado)

Jose Maria Pozo Soler, Clifford algebra in General Relativity and Higher Dimensions, Barcelona, novembre 2002.

1998

No Nonsense Linear Algebra (108 pages), http://gente.pue.udlap.mx/GenteUDLA/personal/SOBCZYK.HTM

1997

Spectral Integral Domains in the Classroom, Aportaciones Matematicas Serie Comunicaciones 20 (1997) 1-19
The Generalized Spectral Decomposition of a Linear Operator, The College Mathematics Journal, January 1997.

1996

A Unipodal Algebra Package for Mathematica, Clifford Algebras With Numeric and Symbolic Computations, Edited by R. Ablamowicz and P. Lounesto, Birkhauser Pub., pp. 189-199, May 1996.
Structure of Factor Algebras and Clifford Algebra, Linear Algebra and Its Applications, 241-243:803-810, Elsevier Science Inc., 1996.
A Universal Geometric Algebra, Advanced Mathematics: Computations and Applications, Editors: A.S. Alekseev, N.S. Bakhvalov, NCC Publisher, Novosibirsk, pp. 447-456, 1996.
- Chapters in book:
  - Chapter 3, Introduction to Geometric Algebras (pp. 37-44)
  - Chapter 4, Linear Transformations (pp. 45-52)
  - Chapter 5, Directed Integration (pp. 53-64)
Clifford (Geometric) Algebras with Applications in Physics, Mathematics, and Engineering, Editor: W.E. Baylis, Birkhauser, 1996.

1995

The Hyperbolic Number Plane, The College Mathematics Journal, September 1995.
BOOK REVIEW: Clifford Algebras and Spinor Structures: A Special Volume Dedicated to the Memory of Albert Crumeyrolle, Edited by Rafael Ablamowicz, Pertti Lounnesto, Kluwer. Advances in Applied Clifford Algebras, Vol. 1, 1995.

1994

Generalized Finite Fourier Transforms, Proceedings, 14th IMACS World Congress on Computational and Applied Mathematics, Geogia Institute of Technology, July 1994.
Clifford Algebra Techniques in Linear Algebra, Collection of Papers Dedicated to the memory of Albert Crumeyrolle, Kluwer (1994).
Derivations of Endomorphisms, Proceedings, Differential Geometry Methods in Theoretical Physics, Ixtapa, 1993, Advances In Applied Clifford Algebras, S1 pp455-459 (1994).

1991-1993

Jordan Form in Clifford Algebra, Clifford Algebras and their Applications in Mathematical Physics, Editors: F. Brackx et al. (Kluwer, Dordrecht, 1993) p.33-41.
Jordan Form in Associative Algebras, Spinors, Twistors, Clifford Algebras and Quantum Deformations, Editors: Z. Oziewicz et al. (Kluwer, Dordrecht, 1993) p. 357-364.
(with Marius Mitrea), Conference Report, Advances in Applied Clifford Algebras, 3, No. 1, 99-104, Mexico 1993.
Linear Transformations in Unitary Geometric Algebra, Foundations in Physics, Vol. 23, No. 10, 1375-1385, 1993.
The Early Years, Foundations in Physics, 23, No. 10, 1291-1293, 1993.
(with J. Cruz-Guzman), Remarks on Circulant Matrices and Polynomial Number Systems, Advances in Applied Clifford Algebras 2, No. 2, 205-214 (1992).
Noncommutative Extensions of Number: An Introduction to Clifford's Geometric Algebra, Aportaciones Matem\'aticas Comunicaciones 11, 207-218 (1992).
Program: Spinor Analysis of Space and Time, Universidad Nacional Autonoma de Mexico, Facultad de Estudios Superiores, Cuautitlan, VI Foro Interno de Investigacion, January 1992.
Report: Unipodal Algebra and Roots of Polynomials, with D. Hestenes and P. Reany, Advances in Applied Clifford Algebras, Vol. 1, No. 1, p.51-64, Dec. 1991.
Unipotents, Idempotents, and a Spinor Basis for Matrices, Advances in Applied Clifford Algebras, Vol. 2, No. 1, p.53-64, July 1992.
Geometry of Complex Vectors and Algebraic Roots, Differential Geometric Methods in Theoretical Physics, p.397-407, Edited by S. Catto, and A. Rocha, World Scientific Press, 1992.
Simplicial Calculus with Geometric Algebra, in Clifford Algebras and Their Applications in Mathematical Physics, Edited by A. Micali, R. Boudet, and J. Helmstetter, (Kluwer Academic Publishers, Dordrecht 1992).
Clifford's Geometric Algebra and Hermitian Operators, p. 112 in 13th International Conference on General Relativity and Gravitation, Abstracts of Contributed Papers, Edited by Pedro W. Lamberti and Omar E. Ortiz, Cordoba, Argentina, 1992.

1980-1990

Graphing Rational Functions Without Plotting, Lander College Science Newsletter, No. 51, April 1990.
Killing Vectors and Embedding of Exact Solutions in General Relativity, in Clifford Algebras and their Applications in Mathematical Physics, Edited by S.R. J.Chisholm, Kluwer, 227-244 (1986).
Vector Calculus with Complex Variables, Lecture Notes, Spring Hill College, 1986 (First taught at Spring Hill College in Fall Semester 1984. Revised and taught as a two semester course in the Fall and Spring Semesters 1986-87.)
CLIFFORD ALGEBRA TO GEOMETRIC CALCULUS: A Unified Language for Mathematics and Physics, coauthored with D. Hestenes, Reidel Publishing Co, 1984, (314 pages).
Clifford Analytical Techniques in Lie-Admissible Mechanics, (with K. Morawiecki), Proceedings of Conference on Non Potential Interactions, Orleans, France, 1982.
Plebanski Classification of the Tensor of Matter, Acta Physica Polonica, Vol. B11, No.6, 1981.
A Complex Gibbs-Heaviside Vector Algebra for Space-time, Acta Physica Polonica, Vol. B12, No.5, 407-418, 1981.
Spacetime Vector Analysis, Physics Letters, 84A, 45-49, 1981.
Algebraic Classification of Important Tensors in Physics, Physics Letters, 84A, 49- 54, 1981.
Spacetime Algebra Approach to Curvature, J. Mathematical Physics, Vol. 24, 1981.
Conjugations and Hermitian Operators in Spacetime, Acta Physica Polonica, Vol.B12, No.6, 509-521, 1981.

Before 1980

Computerized Pedigrees in Family Practice, Am J Human Genetics, Vol. 9-10, July 1976.
Geometric Structures, Polish Academy of Science, Warsaw 1974.
Mappings of Surfaces in Euclidean Space Using Geometric Algebra, Dissertation, Arizona State University, Tempe Arizona, June 1971.
Fixing Seismograms with Polynomials, Technical Reports No. 45, United Electro- Dynamics, Teledyne Inc., 1965.

Other Professional Accomplishments (Selected)

2003

Sabbatical: Computer Science and Information Technology, Florida State University, August Ð December 2003.
University of Bandung, Indonesia, Nov. 6 - 22. Invited Lectures on Geometric Algebra:
1. Introduction to Geometric Algebra and its relationship to matrix algebra.
2. Simplicial Geometric Calculus.
3. Differential Geometry of Vector Manifolds.
4. Topics from Projective Geometry.
Invited Speaker, Institute for Theoretical Physics, University of Wroclaw, Wroclaw, Poland. June 30.
Plenary speaker: Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries, NATO Advanced Studies Institute: Computational Non-Commutative Algebras and Applications, July 6 Ð 19, Ciocco, Italy.

2002

Member of Doctoral Thesis Committee: Jose Marie Pozo, Clifford Algebra in General Relativity and Higher Dimensions, Barcelona, Spain, December 20, 2002.
Director of Honors Thesis: ÒAlgebra of Complex Vectors in Special RelativityÓ, Alejandro Hernandez Perez, April 2002.
Invited Speaker, Generalized Hemite Interpolation, 7th International Conference on Parametric Optimization and Related Topics, Puebla, México, March 2002.
Invited Speaker, The Relative Matrix Representation of a Clifford Geometric Algebra, Second International Workshop Graphs Operads Logic, Parallel Computation, and Mathematical Physics, Cuautitlan, FES-C, Cuautitlan Izcalli, May 2002.
Invited Speaker: Matrices, Clifford Algebras and Groups AlgebrasÓ, The School of Computational Science and Information Technology, Florida State University, June 2002.
Invited Speaker: Clifford Algebras and Group Rings, (with Jose Pozo) 6th International Conference on Clifford Algebras and their Applications in Mathematical Physics, May 2002.
Invited Speaker: Complex Vector Algebra in Special Relativity, (with Alejandro Hernandez) 6th International Conference on Clifford Algebras and their Applications in Mathematical Physics, May 2002.
Invited Speaker: Algebra Geometrica de Clifford y Aplicaciones, Escuela de Ciencias, CIFMA & UDLA, April 2002.
Organizer: Special Lecture Series on Clifford Geometric Algebras and Applications, 6th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Oct. 2002.
Conference Organizer, Advisory Board, and Scientific Program Organizer: 6th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Oct. 2002.

2001

Director of Honors Thesis: ÒThe Spectral Basis of Linear Operators and their ApplicattionsÓ, Miriam Salome Castillo Gil, Aug. 2001.
Invited Speaker, La Estructura Modular de Numeros en La Teoria de Numeros, Benemerita Universidad Automoma de Puebla, Facultad de Ciencias Fisico Matematica, February 2, 2001.

2000

Invited Speaker, La Base Espectral y La Interpolacion Hermite Generalizada, 2000 A–o Mundial de Las Matematicas en Puebla Primer Encuentro: ÒMatematicas y SociedadÓ, Puebla.
Invited Speaker, The Horosphere and the Schwartzian Derivative, XXXIII Congreso Nacional de La Sociedad Matematica Mexicana, October 2000.
Invited Speaker, The Horosphere and the Conformal Group, IV SEMANA DE MATEMATICAS, Benemerita Universidad Autonoma de Puebla, 10 Ð14 April 2000.

1999

Invited Speaker, Lie Algebras of Bivectors and Applications, Workshop on Geometric Methods for Neuralcomputing, Image Processing and Robotics, CIMAT, Guanajuato, July 1999.
Invited Speaker, Lie Algebra of Bivectors, 5th International Clifford Algebra Conference, Ixtapa, July 1999.
Ivited Speaker, Realizations of the Conformal Group, (with Jose Mária Pozo), 5th International Clifford Algebra Conference, Ixtapa, July 1999.
Co-organizer (with Eduardo Bayro-Corrochano) of Applied Clifford Algebra in Cybernetics, Robotics, Image Processing and Engineering. An International Workshop as a Special Parallel Session of the 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics.
The 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics (International Advisory Board and Scientific Committee). Ixtapa, June 29th - July 6th.
Invited Speaker, Polynomial Number Magic, MAA Session on Innovations in Teaching Abstract Algebra, AMS - MAA Joint Meeting, San Antonio, Tex., Jan. 13.

1998

International Board Member, ADVANCES IN APPLIED CLIFFORD ALGEBRAS, D.F. Mexico
Invited Speaker, Mathematical Results in Quantum Mechanics, Mathematics of Quantum Computing, Prague, June 1998.
Invited Lecturer: 1. Lie Algebras and Lie Groups in Clifford Algebra, 2. Lie Algebras of Bivectors, 3. Spectral Integral Domains of Idempotents and Nilpotents, 4. Singular Value Decomposition using Spectral Integral Domains, Christian-Albrechts, Universitat, Institut fur Kognitive Systeme, Kiel, Germany, June 10 - 20, 1998.
Invited Talk, Spectral Integral Domains in Number Theory, Institut fur Matematik, TU-Bergakademie, Freiburg, Germany, June 20 - 22, 1998.
Invited Speaker, Analysis Conference, CINVESTAV, The use of Nilpotents in Analysis, Mexico, D.F., April 1998.

1997

Invited Speaker, XXIX Congreso Nacional de La Sociedad Matematica Mexicana, s, October 1997.
Invited Speaker, XXIX Congreso Nacional de La Sociedad Matematica Mexicana, Principal Correlation of a Linear Operator, October 1997.
Invited Speaker, Harvard University, Quantum Computing by NMR Seminar Series, Geometric Extension of Number and Applications, June 11, 1997
Invited Speaker, NMR, Clifford Algebras and Quantum Computers, Institute For Advanced Studies Park City Mathematics Institute, July 7, 1997.

1996

Invited Speaker, CONFERENCE ON MODERN ALGEBRA AND APPLICATIONS, "Idempotents, Nilpotents, and the Euclidean Algorithm", Nashville, TN, USA, May 14-18,1996.
Invited Speaker XXIX Congreso Nacional de la Sociedad Matemática Mexicana, two talks: The Primary Decomposition of a Linear Operator, and Bivectors of Linear Operators, San Luis Potosi, October 6-8, 1996.
The Petrov and Plebanski Classifications of the Tensor of Matter, Invited Speaker, Instituto de Ciencias Nucleares, UNAM, October 1996.
Research Seminar on CLIFFORD ANALYSIS, Conducted at the Universidad de las Americas - Puebla, Fall Semester 1996. (Lecturer and Participant)
Teaching Seminar: Teaching Calculus and Calculus Reform, Conducted at the UDLAP-P, Fall Semester 1996. (Lecturer and Participant)
Mathematics Olympics: Tutored High School Students in preparation for the National Mathematics Olympics Exam.
Design of a Mathematics Laboratory at UDLAP-P. Special Topic: The Use of MATEMATICA in Teaching Linear Algebra and Calculus
Referee for the Interational Journals:
1. Foundations of Physics, Editor - Alwyn van der Merwe.
2. Acta Applicandae Mathematicae, Editor - M. Hazewinkel.

1995

International Board Member, ADVANCES IN APPLIED CLIFFORD ALGEBRAS, D.F. Mexico.
Referee for the International Journals:
1. Foundations of Physics, Editor - Alwyn van der Merwe.
2. Advances In Applied Cliffords Algebras, Editor - Jaime Keller.
Representation theory in Clifford Analysis, Invited speaker, Complex Analysis, Computations and Applications Conference, Institute of Control Sciences, Moscow, May 1995.
Invited Speaker, University of Crakow, Poland, STRUCTURE EQUATION OF A LINEAR OPERATOR, June1995.
Invited Speaker, Helsinki University of Technology, JORDAN CANONICAL FORM IN CLIFFORD ALGEBRA, JULIO 1995.
Universal Geometric Algebra, Invited speaker, Advanced Mathematics, Computations and Applications, Novosibirsk, Russia, June 1995.
Banff Clifford Algebra Lecture Series, Principal speaker, Geometric (Clifford) Algebras in Physics, July 30-August 12, 1995, Banff, Canada.
Graded Algebras of Endomorphisms, Invited speaker, Joint Meeting of American Mathematical and Mexican Mathematical Societies, Guanajuato, Mexico, December 1995.

1990-1994

The Clifford Algebra and Matrix Algebra Connection, Presented at the Mexican Mathematical Society, Queretaro, October 1994.
Graded Linear Algebra, Presented at the Fourth Conference of the International Linear Algebra Society, Roterdam, August 1994.
Generalized Finite Fourier Transforms, Presented at the 14th IMACS World Congress on Computational and Applied Mathematics, Georgia Institute of Technology, July 1994.
Associate Editor and Referee (11 articles) for International Journal, ADVANCES IN APPLIED CLIFFORD ALGEBRAS, Published by Facultad de Estudios Superiores, Cuautitlan, Universidad Nacional Autonoma de Mexico.
Invited Contributing Editor and Referee of Special Edition of Foundations in Physics, Vol. 23, No. 10, October 1993.
Organizing Committee, International Summer School in Clifford Algebra, Banff, CANADA, 1995.
Local Organizing Committee, XXIII Differential Geometry Methods in Theoretical Physics, (to be held in Ixtapa, Mexico, Sept. 1993).
Invited Speaker with J.M. Torres Merino, Active Lorentz Transformations, XXXVI CONGRESO NACIONAL DE FISICA, Acapulco, October 1993.
Invited Speaker, Jordan Form in Associative Algebras, IIIrd International Clifford Algebra Workshop, Deintz, Belgium, May 3-7, 1993.
Invited Speaker with Jesus Cruz Guzman, Método para el calculo de propieda des espectrales de funciones matriciales para modelos de degradacion de imagenes, OCTAVA CONFERENCIA INTERNACIONAL: Las Computadoras en Las Instituciones de Educacion y de Investigacion, Mexico, D.F., November 1992.
Special Seminar Series (5 lectures) on Geometric Algebra: A Unified Language for Mathematics and Physics, Department of Applied Mathematics and Theoretical Physics and Cavendish Laboratory, Cambrige University, Cambridge, U.K., October 7-21, 1992.
Extended Functions in Geometric Algebra, delivered at the Second Max Born Symposium on Spinors, Twistors and Clifford Algebras, Wojnowice Castle Wroclaw, Poland, September 1992.
The Pauli Algebra and Special Relativity, delivered at the Institute of Theoretical Physics, University of Wroclaw, Poland, October 1992.
Polynomial Number Systems, delivered at the Mathematics Institute of the Polish Academy of Science, Warsaw, October 1992.
Classification of Important Tensors in Physics, delivered at the Department of Applied Mathematics and Physics of the University of Warsaw, November 1992.
Clifford's Geometric Algebra, delivered at the Department of Mathematics of the University of Vilnius, Lithuania, October 1992.
Invited Speaker with J.M. Torres Merino, Ecuacines Basicas de la Fisica en el Algebra de Clifford, XXXV CONGRESO NACIONAL DE FISICA, Puebla, October 1992.
The Eigenprojector Problem: Oversight of the Century?, delivered at the Institute of Mathematics in Guanajuato (July 1992), and at Centro de Investigacion y de studios Avanzados del I. P. N. in Mexico City, August 1992.
Invited Speaker, 13th International Conference on General Relativity and Gravitation, Cordoba, Argentina, June 1992.
Invited Speaker: Noncommutative Extensions of Number, Mexican Mathematical Society, Oaxtepec, Morelos, November 1991.
Invited Speaker, Applications of Geometry to Quantum Fields, Mexican Mathematical Society, Guanajuato, December 1991.
Referee for the BOLETIN de la SOCIEDAD MATEMATICA MEXICANA, Published by the Sociedad Matematica Mexicana.
Clifford Analysis, Invited Series of Seminars given at Polytechnico University, Mexico City D.F., March and April 1992.
Geometry of Complex Vectors and Algebraic Roots, presented at the XXth International Conference on Differential Geometric Methods in Theoretical Physics, New York City, June 1991.
Co-organizer of the Sobczyk Memorial Fund and Lecture Series in honor of my Father, Professor Andrew Sobczyk, Clemson University, April 1983-present.
Algebraic Roots of the Classical Cubic and Quartic Equations, seminar given at the University of Scranton, May 1991.
Invited guest lecturer at the Institute of Theoretical Physics, University of Wroclaw, July 1991.
Complex Vectors and Clifford Algebra Calculations on a Microcomputer, seminar given at the University of South Carolina, April 1991.
Geometric Concept of Number, Seminar given at the University of Scranton, November 1990.
Director, Lander College 13th Annual Science Olympiad (1990). The purpose of this annual event is to promote interest in Science in Upstate South Carolina High Schools.

1987-1989

Simplicial Calculus with Geometric Algebra, presented at the Second International Clifford Algebra Workshop, Montpellier, France, September 1989.
Orbits of the Mandelbrot Set, presented at the joint A.M.S./M.A.A. meeting, Phoenix, Arizona, January 1988.
Geometric Algebra and the Teaching of Calculus, A three part Lecture Series delivered at Gannon University, Erie, PA, 16541, June 6-9, 1988.
Referee for the journal, FOUNDATIONS OF PHYSICS, Alwyn van der Merwe, Editor.
Classical Integration Theorems Revisited, presented at the Alabama Academy of Science, March 1987.

1984-1986

Invited Principal Speaker at the First International Clifford Algebra Workshop, Canterbury, England, September 1985.
Geometric Interpretation of Superluminal Transformations Using Biquaternions, Alabama Academy of Science, Vol.57, No.3, 1986.
Faculty Research Grant, Spring Hill College, 1985.
Correlated Linear and Antilinear Mappings in Complex 3-Space, Alabama Academy of Science, Vol.55, No.3, July 1984.
Algebraic Classification of Important Tensors in Physics, Alabama Academy of Science, March 1984.

Before 1983

Presented Lecture Series on Clifford Algebra at the Institute of Theoretical Physics, University of Geneve, Geneve, 1983.
- Presented Lecture Series on Clifford Algebra at the Institute of Mathematics, Helsinki University of Technology, February 1983. Annual Report MAT-B12, Helsinki University of Technology, 1983.
Winter School of Theoretical Physics, Karpacz, Poland, Winter 1981.
Mathematics Summer School of the University of Tasmania, Hobart, Tasmania, February 1980.
Relativity Workshop, Liepzig, East Germany, April 1978.
Winter School of Theoretical Physics, Karpacz, Poland, 1977.
Differential Geometry Workshop, Karpacz, Poland, Summer 1973.

Professional Organizations

Elected Honary Member of the Mexican Chapter of Phi Kappa Delta, An International Honorary Society, April 1995.
Member of Mexican Academy of Sciences (SNI), 1994 - present.
Member of The American Mathematical Society, 1994 - present.
Member of the Mexican Mathematical Society, 1994 - present.
Member of The Mexican Society of Physics, 1993-present.
Member of The Mathematical Association of America, 1970-1972, 1982-present.
Member of the Polish Academy of Arts and Sciences of America, 1985-present.
Member of the International Society on General Relativity and Gravitation, 1992-93.
Member of the Mexican Society of Philosophy, and History and Mathematics, 1992-93.
Member Kosciuszko Foundation for Polish American Culture, New York City, 1990- present.