List of Publications:
2023

G. Sobczyk, Global and Local Duality in Grassmann Algebras

G. Sobczyk, Global and Local Nilpotent Basis of Matrices

G. Sobczyk, Itinerent Quantum Integers: The Language of Quantum Computers

G. Sobczyk, Calculus of Compatible Nilpotents

G. Sobczyk, Geometric Algebras of Light Cone Projective Graph Geometries
2022

R. Santilli, G. Sobczyk, Representation of nuclear magnetic moments via a Clifford algebra formulation of Bohm’s hidden variables
2021

G. Sobczyk, Spheroidal Domains and Geometric Analysis in Euclidean Space, Contemporary Mathematics, Vol. 2 Issue 3, (2021).
2020

G. Sobczyk, Periodic Table of Geometric Numbers, DOI: 10.13140/RG.2.2.16033.35681

G. Sobczyk, Notes on Plucker's Relations in Geometric Algebra, Advances in Mathematics, 106959, 363, 25 March 2020.

G. Sobczyk, Geometric Matrices of Dual Null Vectors
2019

Mathematica Package: Geometric Matrices

Clemson University Talk: "Matrix Gateway to Geometric Algebra, Spacetime and Spinors"

Talk: Geometric Matrices, 52nd Congreso Nacional de La SMM, Oct. 2125, 2019, Monterrey, NL.
2018
2017
2016
2015
 Geometric Spinors, Relativity and the Hopf Fibration
 Spacetime Algebra of Dirac Spinors
 Vector Analysis of Spinors
 Geometric Number Systems and Spinors
 Geometry of Spin ½ Particles, Revista Mexicana de Fisica 61 (2015) pp. 211223.

Geometric Numbers: The Language of Quantum Mechanics, Invited Lecturer at the National Youth Science Foundation, West Virgina, June 26, 2015.
2014

Vector Analysis of Spinors, Talk: Universidad de Las Americas – Puebla, October 2014.

Geometry of Bivectors, November 4, 2014.
2013

The Spectral Basis of a Linear Operator, Talk: AMS/MAA Joint Mathematical Meeting, San Diego, Calif., January 10, 2013.

New Foundations in Mathematics: The Geometric Concept of Number, Springer 2013.

Conformal Mappings in Geometric Algebra, February 2012 Issue of AMS Notices.

Unitary Geometric Algebra, To appear in Special Issue of Advances in Applied Clifford Algebras in Memory of Professor Jaime Keller (2012).
2010
2009
· Garret Sobczyk, The Symmetric Group and Twisted Symmetric Product in Geometric Algebra, October 13, 2009.

Do Black Holes Really Exist?, Talk presented at El Tercer Congreso Nacional Universitario de Fisica, Universidad de Las Americas – Cholula, Puebla, February 20, 2009.
2008
· Garret Sobczyk and Tolga Yarman, Unification of SpaceTimeMatterEnergy, Appl. Comput. Math. 7 (2008), no.2, pp.255268.
· G. Sobczyk and Omar Leon Sanchez, Fundamental Theorem of Calculus, to appear, Advances in Applied Clifford Algebras.
· G. Sobczyk, Geometric Matrix Algebra, Linear Algebra and its Applications, 429 (2008) 11631173.
2007

arXiv:0710.0143 [ps, pdf, other]
Title: Generalized Taylor's Theorem
Authors: Garret Sobczyk
Comments: 3 pages
Subjects: Numerical Analysis (math.NA) 
arXiv:0710.0092[ps, pdf, other]
Title: Geometry of moving planes
Authors: Garret Sobczyk
Comments: 16 pages, 4 figures
Subjects: Mathematical Physics (mathph) 
arXiv:0710.0084[ps, pdf, other]
Title: Special relativity in complex vector algebra
Authors: Garret Sobczyk
Comments: 11 pages, 3 figures, PIRT Moscow, July 2007
Subjects: Mathematical Physics (mathph) 
The Spectral Basis and Rational Interpolation, submitted to Proceedings of “Curves and Surfaces”, Avignon 2006.
2006

4. arXiv:math/0602405 [ps, pdf, other]

Title: The Spectral Basis and Rational Interpolation

Authors: Garret Sobczyk

Comments: 8 pages, 2 figures

Subjects: Numerical Analysis (math.NA); Rings and Algebras (math.RA)


The Spectral Basis and Rational Interpolation, (accepted) Proceedings of “Curves and Surfaces”, Avignon 2006.

Un Enfoque Modular a la Interpolación Racional, (with Omar León Sánchez), submitted to “Miscelánea Matemática” (May 2006).

Geometric matrix algebra, (accepted) Proceedings of “International Linear Algebra Society”, Amsterdam, October

Generalized Rolle’s Theorem and Extended Modular Polynomials, submitted to “NOTES” of “The American Mathematical Monthly”, November 2006.

Geometric Algebra, Spectral Basis and Interpolation, Talk, Universidad de Las Americas – Puebla, Feb. 24, 2006.
2005

“Hybrid Matrix Geometric Algebra”, with G. Erlebacher, Proceedings of International Workshop on Geometric Invariance and Applications in Engineering (IWMM&GIAE), Beijing, China, (to appear).
2004

First Order Linear Ordinary Differential Equations in Associative Algebras, (with Gordon Erlebacher), Electronic Journal of Differential Equations, Vol. 2004(2004), No. 01, pp. 118. ISSN: 10726691. URL: http://ejde.math.txstate.edu or ftp ejde.math.txstate.edu (login: ftp)

Chapter 7: Software for Clifford (geometric) algebras, (with R. Ablamowicz), in Lecture on Clifford Geometric Algebras and Applications, Editor with Rafal Ablamowicz, International Conference on Clifford Algebras and their Applications in Mathematical Physics, Birkhauser 2004. http://www.amazon.com

Relativity in Clifford’s Geometric Algebras of Space and Spacetime, W. E. Baylis, G. E. Sobczyk, International Journal of Theoretical Physics, Vol. 43, No. 10, Oct. 2004, pp13861399.

Clifford´s Geometric Algebras in Multilinear Algebra and NonEuclidean Geometries, in Computacional NonCommutative Algebras and Applications, Edited by Jim Byrnes, NATO Science Series, Kluwer Academic Publishers 2004.

“Quantum Hermite Interpolation Polynomials”, in PARAMATRIC OPTIMIZATION AND RELATED TOPICS VII, Edited by J. Guddat, H. Jongen, J. Ruckmann, M. Todorov, Aportaciones Matemáticas 18 Investigación, Sociedad Matemática Mexicana, 2004, pp. 105 – 112.

Lecture on Clifford Geometric Algebras and Applications, Editor with Rafal Ablamowicz, International Conference on Clifford Algebras and their Applications in Mathematical Physics, Birkhauser 2004. http://www.frontlist.com/detail/0817632573
2003

Quantum Hermite Interpolation Polynomials, Proceedings of 7th International Conference on Parametric Optimization and Related Topics, Sept. 2002.

Clifford Geometric Algebras in Multilinear Algebra and NonEuclidean Geometries, NATO Advanced Studies Institute: Computational NonCommutative Algebras and Applications (To Appear).
2002

Generalized Vandermonde Determinants and Applications, Aportaciones Matematicas Vol. 30: 4153, 2002. (Divulgación)

Geometric Algebra in Linear Algebra and Geometry,(With Jose M‡ria Pozo) Acta Applicandae Mathematicae, Vol. 71: 207244, 2002. (Investigación)
2001

The Missing Spectral Basis in Algebra and Number Theory, The American Mathematical Monthly, Vol. 108, No. 4, April 2001, 289387. (Investigación)

Edited Book (with Eduardo BayroCorrochano) Geometric Algebra with Applications in Science and Engineering, Birkhauser 2001.

Applications of Lie Algebras and the Algebra of Incidence, (with Eduardo Bayro  Corrochano), in Geometric Algebra with Applications in Science and Engineering, Chapter 13, pp. 252277, Birkhauser 2001. (Investigación)

Realizations of the Conformal Group (with Jose Maria Pozo) in Geometric Algebra with Applications in Science and Engineering, Chapter 3, pp. 4260, Birkhauser 2001. (Investigación)

Universal Geometric Algebra, in Geometric Algebra with Applications in Science and Engineering, Chapter 2, pp. 1840, Birkhauser 2001. (Investigación)
1997

Spectral Integral Domain in the Classroom, Aportaciones matematicas, Serie Comunicaciones 20 (1997), 169188. DVI

The Generalized Spectral Decomposition of a Linear Operator, The College Mathematics Journal, January (1997), 2738.
1996

A Unipodal Algebra Package for MATHEMATICA, Clifford Algebras with Numeric and Symbolic Computations, Edited by R. Ablamowicz and P. Lounesto, Birkhauser Pub., pp. 189199, May 1996.

Structure of Factor Algebras and Clifford Algebra, Linear Algebra and Its applications, 241243:803810, Elsevier Science Inc., 1996.

A Universal Geometric Algebra, Advanced Mathematics: Computations and Applications, Edito/rs: A.S. Alekseev, N.S. Bakhvalov, NCC Publisher, Novosibirsk, pp. 447456, 1996.

Chapter 3, Introduction to Geometric Algebras (pp. 3744)

Chapter 4, Linear Transformations (pp. 4552)

Chapter 5, Directed Integration (pp. 5364)


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, Vol. 26, No. 4, September (1995), 268280. Pictures

Book Review: Clifford Algebras and Spinor Structures: A Special Volume Dedicated to the Memory of Albert Crumeyrolle, Edited by Rafael Ablamowicz,Pertti Lounesto, Kluwer 194. Advances in Applied Clifford Algebras, Vol. 1, 1995.
1994

Generalized Finite Fourier Transforms, Proceedings, 14th IMACS World Congress on Computational and Applied Mathematics, Georgia 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 (1994).
19911993

Jordan Form in Clifford Algebra, Clifford Algebras and their Applications in Mathematical Physics, Editors: F. Brackx et al. (Kluwer, Dordrecht, 1993) p.3341.

Jordan Form in Associative Algebras, Spinors, Twistors, Clifford Algebras and Quantum Deformations, Editors: Z. Oziewicz et al. Kluwer, Dordrecht, 1993) p. 357364.

With Marius Mitrea, Conference Report, Advances in Applied Clifford Algebras, 3, No. 1, 99104, Mexico 1993.

Linear Transformations in Unitary Geometric Algebra, Foundations in Physics, Vol. 23, No. 10, 13751385, 1993.The Early Years, Foundations in Physics, 23, No. 10, 12911293, 1993.

With J. CruzGuzman, Remarks on Circulant Matrices and Polynomial Number Systems, Advances in Applied Clifford Algebras 2, No. 2, 205214 (1992).

Noncommutative Extensions of Number: An Introduction to Clifford's Geometric Algebra, Aportaciones Matemáticas Comunicaciones 11, 207218 (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.5164, Dec. 1991.

Unipotents, Idempotents, and a Spinor Basis for Matrices, Advances in Applied Clifford Algebras, Vol. 2, No. 1, p.5364, July 1992.

Geometry of Complex Vectors and Algebraic Roots, Differential Geometric Methods in Theoretical Physics, p.397407, 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.
19801990

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, 227244 (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 198687.

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 LieAdmissible 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 GibbsHeaviside Vector Algebra for Spacetime, Acta Physica Polonica, Vol. B12, No.5, 407418, 1981.

Spacetime Vector Analysis, Physics Letters, 84A, 4549, 1981.

Algebraic Classification of Important Tensors in Physics, Physics Letters, 84A, 4954, 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, 509521, 1981.
Before 1980

Computerized Pedigrees in Family Practice, Am J Human Genetics, Vol. 910, July 1976.

Geometric Structures, Polish Academy of Science, Warsaw 1974.

Dissertation: Mappings of Surfaces in Euclidean Space Using Geometric Algebra Thesis1, Thesis 2, page 108

Fixing Seismograms with Polynomials, Technical Reports No. 45, United ElectroDynamics, Teledyne Inc., 1965.