Brief Vita for Johan G. F. Belinfante

Personal Data

Born in Leiden, the Netherlands

Citizenship: U. S. (Naturalized, 1955)

My father, Frederik Jozef Belinfante (1913-1991), was a theoretical physicist, a student of H. A. Kramers.
He is best known for his pioneering work with Wolfgang Pauli on the connection between spin and statistics, and for his work on quantizing gravity.

My wife, Irene Ann Belinfante, is a retired civil engineer. She was a group leader in the Bridge Department of the Georgia Department of Transportation.

Education

• B.S. Physics 1958 Purdue University
• Ph.D. Physics 1961 Princeton University
• NSF Postdoc. Fellow Physics 1962 Calif. Inst. of Technology
  Scientific advisor: Murray Gell-Mann

Ph.D. Thesis (Major Professor: Marvin L. Goldberger):

"The Effects of the Nucleon-Antinucleon Intermediate State on P-Wave Pion-Pion Scattering Resonances", Princeton University Ph. D. Dissertation in Physics. (1961)

Employment History

• Research Investigator, Physics, Univ. of Pa., 1962-64
• Asst. & Assoc. Prof., Physics & Math.,Carnegie-Mellon 1964-73
• Associate Professor, Mathematics, Georgia Tech 1973-79
• Professor, Mathematics, Georgia Tech 1979-2008
• Professor Emeritus, Mathematics, Georgia Tech, 2008-present

Fields of Interest:

• Computer-Assisted Theorem Proving, especially in NBG set theory.
• Set Theory, Combinators, Lambda Calculus and Logic for Computer Science
• Algorithms in Abstract Algebra, especially Finite Group Theory and Classical Lie Algebras
• Mathematical Physics, Elementary Particles, Foundations of Quantum Mechanics

Major Publication - Book

• A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods, Second Edition, by Johan G. F. Belinfante and Bernard Kolman, 1989.
  Society for Industrial and Applied Mathematics. Series: Classics in Applied Mathematics 2. Softcover, xi + 164 pages. ISBN 0-89871-243-2 Order info.
• Chapters:
  1. Lie Groups and Lie Algebras
  2. Representation Theory
  3. Constructive Methods

Research Grant

• National Science Foundation Grant 0313744
  ITR: Automated Discovery and Proof in Arithmetic Based on Gödel's Class Theory
  2003-2007

Thesis Students

• Vishnu Kumar Agrawala, Doctor of Philosophy in Physics, Carnegie-Mellon University, 1967
  A Study of Broken SU(6) Symmetry for Baryons in a Bootstrap Static Model Bethe-Salpeter Formalism.
• Tiffany D. Goble, Master of Science in Mathematics, Georgia Institute of Technology, 2004 August 17
  Automated Reasoning: Computer Assisted Proofs in Set Theory Using Gödel's Algorithm for Class Formation. PDF file

Selected Publications

• Belinfante, Johan G. F., Reasoning about iteration in Gödel's class theory, in Automated Deduction - CADE-19, Proceedings of the 19th International Conference on Automated Deduction, Miami Beach, FL, USA July/August 2003, edited by F. Baader, Springer Verlag, Berlin, Lecture Notes in Artificial Intelligence, vol. 2741, pp. 228-242 (2003). PDF file
• Belinfante, Johan G. F., Computer Proofs about Finite and Regular Sets: The Unifying Concept of Subvariance, in special issue on First Order Theorem Proving, edited by P. Baumgartner and H. Zhang, Journal of Symbolic Computation, vol. 36, pp. 271-285 (2003).
• Belinfante, Johan G. F., The Unifying Concept of Subvariance, in FTP 2000, Third International Workshop on First-Order Theorem Proving, St. Andrews, Scotland, July 2000, edited by P. Baumgartner and H. Zhang, pages 56-67, Fachberichte Informatik, Universität Koblenz-Landau. PDF files for text of talk and for slides.
• Belinfante, Johan G. F., Gödel's Algorithm for Class Formation, in Automated Deduction - CADE-17, edited by D. McAllester, June 2000, Lecture Notes in Artificial Intelligence, volume 1831, pages 132-147, Springer-Verlag, Berlin. ISBN 3-540-67664-3. PDF file (corrected version).
• Belinfante, Johan G. F., Clifford Algebras and the Construction of the Basic Spinor and Semi-Spinor Modules over Complex Orthogonal Lie Algebras, Proceedings of the Fifth International Conference on Clifford Algebras and their Applications in Mathematical Physics, vol. I. Algebras and Physics, edited by R. Ablamowicz and B. Fauser, pages 323-339. Birkhäuser, ISBN 0-8176-4182-3 (July, 2000). PDF file
• Belinfante, Johan G. F., Computer Proofs in Gödel's Class Theory with Equational Definitions for Composite and Cross, Journal of Automated Reasoning, vol. 22 (1999), pp. 311-339
• Belinfante, Johan G. F., On Computer-Assisted Proofs in Ordinal Number Theory, Journal of Automated Reasoning, vol. 22 (1999), pp. 341-378.
• Belinfante, Johan G. F., On Quaife's Development of Class Theory, Association for Automated Reasoning News Letter, No. 37, 4 pp., August, 1997. Postscript by Art Quaife. PDF file
• Belinfante, Johan G. F., On a Modification of Gödel's Algorithm for Class Formation, Association for Automated Reasoning News Letter, No. 34, pp. 10-15, October, 1996. PDF file.
• Belinfante, Johan G. F. and Kolman, Bernard, A survey of Lie groups and Lie algebras with applications and computational methods. Reprint of the 1972 original. Classics in Applied Mathematics, 2. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989. x+164 pp. ISBN: 0-89871-243-2 Math Reviews 90k:22033 (Reviewer: Joris Van der Jeugt) 22E70 (22-01 81C40)
• Belinfante, Johan G. F., S/K/ID: Combinators in Forth, The Journal of Forth Application and Research, vol. 4, pp. 555-580 (1987). PDF file
• Zunde, Pranas and Belinfante, Johan G. F., Lattice characterization of feedback effect on system structure. Proceedings of the Fifth European Meeting of Cybernetics and Systems Research, 1980 April 8-11, University of Vienna. Progress in cybernetics and systems research, Vol. VIII, 205-212, Hemisphere, Washington, D.C.-London, 1982. 93B05 (93B25) Math Reviews 84j:93022. PDF file
• Belinfante, Johan G. F., Computers in Lie algebras. Lie theories and their applications (Proc. Ann. Sem. Canadian Math. Congress, Queen's University, Kingston, Ontario, June 20 - July 8, 1977), pp. 248-267, Queen's Papers in Pure and Applied Math., No. 48, Queen's Univ., Kingston, Ontario, 1978. (Math Reviews 80h:17003. Reviewer: Bernard Kolman) 17-04. PDF file
• Belinfante, Johan G. F., Integer Clebsch-Gordan coefficients for Lie algebra representations. Computers in nonassociative rings and algebras (Special Session, 82nd Annual Meeting American Math. Society, San Antonio, Texas, 1976), pp. 209-234. Academic Press, New York, 1977. (Math Reviews 56 12078. Reviewer: I. Stewart) 17B10 (81.17). PDF file
• Belinfante, Johan G. F. and Kolman, Bernard, A survey of Lie groups and Lie algebras with applications and computational methods. Society for Industrial and Applied Mathematics, Philadelphia, 1972. ix+164 pp. (Math Reviews 53 10993. Reviewer: Holman, Wayne J.) 22E70
• Belinfante, Johan G. F., Transition probability spaces. Journal of Mathematical Physics 17 (1976), no. 3, 285-291. (Math Reviews 52 16316. Reviewer: E. G. Beltrametti) 81.06
• Belinfante, Johan G. F., Lie algebras and inhomogeneous simple materials. Lie algebras: applications and computational methods (Conf., Drexel Univ., Philadelphia, Pennsylvania, 1972). SIAM Journal Applied Math. 25 (1973), 260-268. (Math Reviews 51 7425. Reviewer: C.-C. Wang) 73.17
• Lie algebras: applications and computational methods. Papers presented at the Conference on Lie Algebras: Applications and Computational Methods at Drexel University, Philadelphia, Pennsylvania, 1972 June 15-16. Edited by Bernard Kolman. Reprinted from SIAM Journal Applied Math. 25 (1973), no. 2, 163-323. Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1973. vii+155 pp.17BXX (Math Reviews 50 7269) (33A75 81.22)
• Agrawala, Vishnu K. and Belinfante, Johan G., An algorithm for computing SU(n) invariants. Nordisk Tidskrift for Informationsbehandling (Sweden) BIT 11 (1971) 1-15. (Math Reviews 44#2423. Reviewer: N. Burgoyne) 81.22
• Belinfante, J. G. F. and Winternitz, P., One-parameter subgroups of unitary groups with indefinite metric and in particular of the conformal group. Journal of Mathematical Physics 12 (1971) 1041-1054. (Math Reviews 44#1329. Reviewer: R. Delbourgo) 81.22 (22.00)
• Belinfante, J. G. F., One-Parameter Subgroups of the Conformal Group of Spacetime and in General of Unitary Groups with an Indefinite Metric, Lectures in Theoretical Physics, vol. XIII, De Sitter and Conformal Groups and their Applications, pp. 31-50, (Proceedings of the Conference on De Sitter and Conformal Groups and their Applications, held at the University of Colorado, Boulder, Colorado, 1970 June 29-July 3), published by the Colorado Associated University Press, Boulder, Colorado (1971).
• Agrawala, Vishnu K. and Belinfante, Johan G., Weight Diagrams for Lie Group Representations: A Computer Implementation of Freudenthal's Algorithm in ALGOL and FORTRAN}, Nordisk Tidskrift for Informationsbehandling (Sweden) BIT 9, 301-314 (1969).
• Belinfante, J. G. and Kolman, B., An introduction to Lie groups and Lie algebras, with applications. III: Computational methods and applications of representation theory. SIAM Review 11 (1969) 510-543. (Math Reviews 40#7389.) 22.60
• Belinfante, J. G. and Agrawala, V. K., Graphical Formulation of Recoupling Theory for any Compact Group, Annals of Physics (USA) 49, pp. 130-170 (1968).
• Belinfante, J. G., Kolman, B., and Smith, H. A., An introduction to Lie groups and Lie algebras, with applications. II. The basic methods and results of representation theory. SIAM Review 10 (1968) 160-195. (Math Reviews 38#4609. Reviewer: R. Steinberg) 22.60
• Belinfante, J. G., Kolman, B. and Smith, H. A., An introduction to Lie groups and Lie algebras, with applications. SIAM Review 8 (1966) 11-46. (Math Reviews 34#275. Reviewer: Robert Hermann) 22.00
• Belinfante, J. G., On the Cutkosky-Leon Normalization Conditions, Il Nuovo Cimento, Tenth Series, 44A, pp. 740-744 (1966).
• Belinfante, J. G. and Renninger, G. H., Ambiguity of the Meson-Baryon Couplings in a Bootstrap Static Model of SU(6) Symmetry, The Physical Review, Second Series, 148, pp. 1573-1578 (1966)
• Cutkosky, R. E., Belinfante, J. G. and Renninger, G. H., Symmetry Properties of Bootstrap Models, High Energy Physics and Elementary Particles, pp. 865-875 (Proceedings of International Summer School, sponsored by the International Center for Theoretical Physics, Trieste, 1965 May 3 - June 30), published by the International Atomic Energy Agency, Vienna, Austria (1965)
• Belinfante, Johan G., Intermultiplet Mass Formula for Mesons, The Physical Review, Second Series 140B, p. 154 (1965).
• Belinfante, J. G. and Cutkosky, R. E., Baryon supermultiplet. Physical Review Letters 14 (1965) 33-35. (Math Reviews 31#1974. Reviewer: R. L. Warnock) 81.22
• Belinfante, J. G., Harmonic-oscillator model of the spin of the ω-meson. Il Nuovo Cimento (10) 32 (1964) 1384-1391. (Math Reviews 29#1939. Reviewer: F. R. Halpern) 81.99
• Belinfante, Johan G., Existence of scattering solutions for the Schrödinger equation. Journal of Mathematical Physics 5 (1964) 1070-1074. (Math Reviews 29#1899. Reviewer: A. O. Barut) 81.46
• Belinfante, Johan G., Semiclassical Theory of Infrared Divergence, American Journal of Physics 32, pp. 655-656 (1964).
• Belinfante, Johan G. and Unal, Burhan C., Potential scattering. Journal of Mathematical Physics 4 (1963) 372-387. (Math Reviews 27#1140. Reviewer: V. De Alfaro) 81.30
• Belinfante, Johan G., Impulse approximation. The Physical Review (2) 128 (1962) 2403-2406. (Math Reviews 26#3440. Reviewer: K. K. Gupta) 81.41
• Belinfante, Johan G., Coulomb Wave Functions, Los Alamos Scientific Laboratory Report LAMS-2616, Los Alamos, NM (1961).
• Belinfante, Johan G., Nucleon-Antinucleon Mechanism for Pion-Pion Scattering Resonances, The Physical Review, Second Series 123, pp. 306-307 (1961)

Unpublished Manuscript

• Belinfante, Johan G. F., Explicit Version of the Campbell-Baker-Hausdorff Formula: Integral Representation for ln (exp x exp y), submitted to the American Mathematical Monthly on 1982 October 22. PDF file of manuscript

Conferences and Talks

• The GOEDEL Program
  Presented 2011 January 8 at the New Orleans Meeting #1067 of the American Mathematical Society
  Special Session SS12A on Formal Mathematics for Mathematicians
  Organized by Kuperberg, Trybulec, Kornilowicz and Naumowicz
  PDF file of slides, PPTX file of slides.
• Arithmetic and Abstract Algebra in Gödel's Class Theory (with Claudia D. Huang)
  Presented 2005 August 11 at the Workshop AWARD-05, Argonne National Laboratory, Chicago, IL.
  PDF file of paper
• Research Horizons: Computer Assisted Reasoning.
  Talk for Georgia Tech Mathematics Graduate Students, 3 November 2004. PDF file of slides.
• CORE and HULL Constructors in Gödel's Class Theory (with Tiffany D. Goble)
  Presented 2004 July 5 at the Workshop WS-7, Computer Supported Mathematical Theory Development, organized by Christoph Benzmüller and Wolfgang Windsteiger at IJCAR 2004, Second International Joint Conference on Automated Reasoning, held 04 July - 08 July 2004 in Cork, County Cork, Ireland. Proceedings. PDF file of paper. PDF file of slides.
• Reasoning about Iteration in Gödel's Class Theory
  Presented 2003 July 31 at CADE-19 in Miami, Florida
  PDF file of slides.
• Associative Relations, presented 2003 July at the Argonne workshop AWARD-2003.
• Automated Reasoning about the Zermelo-von Neumann Cumulative Hierarchy.
  Presented 2002 March 8 at the American Mathematical Society Meeting 975 in Atlanta, GA.
  PDF file of paper and slides.
• Discovering Theorems using GOEDEL: a Case Study,
  Presented at Calculemus'2001 in Siena, Italy.
  PDF files for text of paper and for slides.
• Computer Proofs about Transitive Closure,
  Presented at IJCAR'2001 in Siena, Italy.
  PDF files for text of paper and for slides.
• The Unifying Concept of Subvariance.
  Presented at the Third International Workshop on First-Order Theorem Proving (FTP 2000), held at the University of St. Andrews, St. Andrews, Scotland, July 2000.
• Gödel's Algorithm for Class Formation.
  Presented at the 17th International Conference on Automated Deduction (CADE-17), held at Carnegie-Mellon University, Pittsburgh, PA, June 2000.
• Clifford Algebras and the Construction of the Basic Spinor and Semi-Spinor Modules over Complex Orthogonal Lie Algebras.
  Invited talk presented the Fifth International Conference on Clifford Algebras and their Applications, held in Ixtapa, Mexico, June 1999.
• On the Automated Hiding of Quantifiers in Gödel's Class Theory.
  Abstract 939-04-537, presented 1999 January 14 at the meeting of the American Mathematical Society in San Antonio, Texas.
  AMS Abstracts, vol. 20, no. 1, p. 15. Abstract in PDF format.
  Full text of the talk in PDF format.
• Experience with computer-assisted reasoning in set theory.
  Georgia Tech Mathematics Colloquium, 1998 January 29. Abstract in HTML format.
• What are Combinators?
  Mathematics and Computing Seminar presented 1989 October 17 at the Georgia Institute of Technology
• Simple Procedural Definitions of Combinators.
  Talk presented 1987 March 7 at the Third Southeastern Logic Symposium at the College of Charleston in Charleston, SC
• Combinators on the Commodore 64,
  Combinatorics Seminar presented 1986 October 30 at the Georgia Institute of Technology
• A Formula for ln (exp x exp y).
  Colloquium presented 1982 November 11 at the School of Mathematics, Georgia Institute of Technology
• The BCH Formula: Application of Special Functions to Lie Algebras.
  Invited talk presented 1982 October 30 at the American Mathematical Society Meeting Number 797 at College Park, MD
• Computers in Lie Algebras.
  Two hour invited lectures presented July 1977 at the Canadian Math Congress Conference on Lie Theories at Kingston, Ontario (published in Queen's Papers in Pure and Applied Math., (1978)
• Integer Clebsch-Gordan Coefficients for Lie Algebra Representations.
  Invited talk presented January 1976 at the Special Session on Nonassociative Algebras at the Meeting of the American Mathematical Society in San Antonio, TX. AMS Notices, vol. 23, page A-78 (1976)
• Zorn's Lemma - A Simplified Treatment. (Notes last updated May 1995.)
  Special Topics Seminar presented 1972 August 2 at the Carnegie-Mellon University Mathematics Department
• One-Parameter Subgroups of the Conformal Group of Spacetime and in General of Unitary Groups with an Indefinite Metric.
  Invited talk presented 1970 July 2 at the Symposium on the De Sitter and Conformal Groups at University of Colorado, Boulder, CO (proceedings published by the Colorado Associated University Press, Boulder, Colorado, 1971)

Meetings Chaired

• organized a special session on Computer Proofs in Set Theory and Logic for the American Mathematical Society Southeastern Sectional Meeting held 1997 October 10-12 at the Georgia Institute of Technology in Atlanta, Georgia.
• chaired a session on Set Theory and Foundations at the San Antonio meeting of the American Mathematical Society held on 1999 January 14.
• organized a Special Session on Automated Reasoning in Mathematics and Logic held March 8-10, 2002 at the AMS Meeting in Atlanta, GA.

Link back to Home Web Page for JGFB.

This vita is not complete. The more complete vita in PDF format includes teaching and service at Georgia Tech.

Modified 2012 December 6