Professor W. David Joyner Arrived USNA: August, 1987 Research Interests: error-correcting codes, representation theory and applications, harmonic analysis on groups, applications of number theory/group theory to communication theory and cryptography, computer algebra, analytic number theory. Ph.D.: University of Maryland-College Park, 05/23/83 Current research interests: Currently I am working on various projects related to the understanding of how to compute relate function-theoretic properties of a map f: GF(p)^n --> GF(p) to graph-theoretic properties of its edge-weighted Cayley graph. Other interests: Writing, chess, photography, history of mathematics and cryptography. Brief Research Biography Education Employment USNA Faculty Researcher of the Year Award, 2007. Editorial: Software: Research Publications:
  1. "Zeta functions and their associated operators" (unpublished, from 1981)
  2. "A note on gaps between zeroes of L-functions," unpublished dating from 1984.
  3. "Summation operators and 'explicit formulas'", Port. Math. 44(1987)119-130. (basically my PhD thesis)
  4. "On the metaplectic analog of Kazhdan's 'endoscopic' lifting", Isr. J. Math. 61 (1988)113-154.preprint version
  5. "On the Kuznetsov-Bruggeman Formula for a Hilbert Modular Surface Having One Cusp", Math. Zeit. 203(1990)59-104, Errata, Math. Zeit.205(1990)163.Corrected version
  6. "On twisted orbital integral identities for PGL(3) over a p-adic field", Can. J. Math. 31(1991)1098-1130.preprint version
  7. "On the Montgomery-Dyson hypothesis", in Proceedings of the Amalfi Analytic Number Theory Conference, Univ. de Salerno, 1992.pdf
  8. "Remarks on the Bruggeman-Kutznetsov formula", Proceedings of the Amalfi Analytic Number Theory Conference, Univ. de Salerno, 1992.
  9. "Simple local trace formulas for unramified p-adic groups", Pac. J. Math.154(1992)103-129. corrected preprint version(pdf only - sorry, the source file seems to have been lost)
  10. with Roland Martin, "Decomposing Lie Algebra Representations Using Crystal Graphs",SAC Newsletter, no. 2, June 1997, pp. 27-34.
  11. with R. Martin, "Using crystal graphs to decompose Lie algebra representations",SIGSAM Bull.31Dec. 1997.
  12. with R. Martin, "Branching rules for Lie algebra representations using crystal graphs",Maple Tech.25(1998)23-27.
  13. "A correspondence for the generalized Hecke algebra of the metaplectic cover of SL(2,F), F p-adic,"New York J. of Math.4(1998) 223-235. On the NYJM web page
  14. with David Jabon, "On stable characters of tamely ramified supercuspidal representations of small unitary groups",Far East J. of Math. Sci. 1 (1999)443-454 preprint version.
  15. "On the unitary dual of $\overline{SL(2,F)}, F p-adic," unpublished preprint, 1999.
  16. "A correspondence for the supercuspidal representations of the metaplectic cover of SL(2,F), F p-adic," Archiv der Math. vol 73(1999)332-340
  17. "On finite dimensional representations of non-connected reductive groups,"J. of Lie Theory 10(2000)269-284. On the JLT web page
  18. "Invariant distributions on the n-fold metaplectic covers of GL(r,F), F p-adic,"J. Fourier Anal. and Appl.7(2001)343-358.
  19. with Salahoddin Shokranian, "Remarks on codes from Goppa curves: MAPLE applications," in Coding Theory and Cryptography: From Enigma and Geheimschreiber to Coding Theory, Springer-Verlag, 2000.citeseer
  20. with Dennis Spellman, Georgia M. Benkart, Anthony M. Gaglione, Mark E. Kidwell, Mark D. Meyerson and William P. Wardlaw, "Principal ideals and associate rings,"JP Journal of Algebra, number theory, and applications 2(2002)181-193./li>
  21. with Michael Fourte, "Odd King Tours on Even Chessboards," Journal of Recreational Mathematics31(2003)173-177.
  22. "Arithmetic of characters of generalized symmetric groups," Archiv der Mathematik, vol 81 (2003)113--120.
  23. with Helena Verrill, "Notes on toric varieties," preprint at math arxivs . "Computing with toric varieties," J. Symb. Comp. Volume 42 (2007)511-532 .
  24. "Toric codes over finite fields", AAECC, vol. 15, Number 1 (2004)63 - 79. A version may be found at math arXivs
  25. with Will Traves, "Representations of finite groups on Riemann-Roch spaces," available at math arXivs.
  26. with Pablo Legarraga, "Smoothness Properties of Varieties of Borels and Schubert Varieties," (appeared in Revista UMA, vol. 45, 2004, pp 69-74). A similar version (using different methods) under the title "On the variety of Borels in relative position w" is available at math arXivs.
  27. with Amy Ksir, "Representations of finite groups on Riemann-Roch spaces, II" is available at math arxivs. (published version was renamed "Decomposing representations of finite groups on Riemann-Roch spaces" Proc. Amer. Math. Soc. 135 (2007), 3465-3476. )
  28. (with Amy Ksir) "Automorphism groups of some AG codes" IEEE Trans. Info. Theory, vol 52, July 2006, pp 3325-3329. IEEE version, math arXiv version.
  29. "Open Source Computer Algebra Systems - Maxima", ACM Communications in Computer Algebra, Volume 40, Number 3/4 - September/December 2006 - Issue 157/158. pdf.
  30. with Robert Guralnick and Daniel Goldstein, "A Question about Pic(X) as a G-module," is available at math arXivs. (Computational Aspects of Algebraic Curves, (Editor: T. Shaska) Lecture Notes in Computing, WorldScientific, 2005.)
  31. with Alexander Konovalov, "Applications of the computer algebra system GAP in coding theory," 2nd International conference Modern coding methods in electronic systems October 26-27, 2004, Sumy, Ukraine. Abstracts. Sumy University Publishers, Sumy, 2004. Pages 18-19.
  32. "Conjectural permutation decoding of some AG codes" Communications in Computer Algebra (formerly "SIGSAM Bull"), vol 39, March 2005, pages 166-172.
  33. (with Amy Ksir) "Modular representations on some Riemann-Roch spaces of modular curves X(N)" (Computational Aspects of Algebraic Curves, (Editor: T. Shaska) Lecture Notes in Computing, WorldScientific, 2005.)
  34. (with S. McMath, F. Crabbe) "Continued fractions and Parallel SQUFOF", International Journal of Pure and Applied Mathematics volume 34, Number 1 (2007)19-38. See math arXivs.
  35. (with William Stein) "SAGE: System for Algebra and Geometry Experimentation", Communications in Computer Algebravol 39, June 2005, pages 61-64.
  36. "GUAVA: An error-correcting codes package" Communications in Computer Algebra, vol 39, June 2005, pages 65-68.
  37. "Mathematics of Ghaly's machine", Integers.
  38. "Quadratic residue codes and hyperelliptic curves", Discrete Mathematics and Theoretical Computer Science, vol 10(2008) 129-146.
  39. "Open Source Computer Algebra Systems - Axiom", ACM Communications in Computer Algebra, Volume Volume 42, Number 2 - June 2008 - Issue 164. pdf.
  40. (with Amy Ksir, Will Traves) "Automorphism groups of GRS codes" in Advances in coding theory and cryptology, (T. Shaska, W. C. Huffman, D. Joyner, V. Ustimenko, editors), World Scientific, 2007.
  41. (with Amy Ksir, Roger Vogeler) "Group representations on Riemann-Roch spaces of some Hurwitz curves" Albanian Journal of Mathematics,Volume 1, Number 2 (2007)67-85 (electronic version). math arXivs.
  42. "A primer on computational group homology and cohomology." . Proceedings of the Gaglione conference, entitled Aspects of Infinite Groups (ed. Ben Fine, G. Rosenberger, D. Spellman), World Scientific Press, 2008.
  43. (with David Kohel). "Groups and SAGE", in Computational Group Theory and the Theory of Groups, AMS "Contemporary Mathematics" series vol. 470 (ed. Luise-Charlotte Kappe, Arturo Magidin, Robert Morse), 2008, pp. 115-140. (Here is the pdf.)
  44. with Amy Ksir and Darren Glass, "Codes from Riemann-Roch spaces for y2= xp-x over GF(p)", Algebraic and Combinatorial Coding Theory in Honour of the Retirement of Vera Pless, a special issue ofInternational. J. of Information and Coding Theory, (editors: Philippe Gaborit, Jon-Lark Kim, Patrick Sole, and Isaac Woungang), 2010.
  45. with Amy Ksir and Caroline Melles, "Automorphism Groups on Tropical Curves: Some Cohomology Calculations."Beitrage zur Algebra und Geometrie, Volume 53, Issue 1 (2012)41-56.
  46. with Chris Christensen and Jenna Torres, "Lester Hill's error-detecting codes", to appear in Cryptologia, 2011.
  47. with Ondrej Certik, Aaron Meurer, Brian Granger, "Open Source Computer Algebra Systems: SymPy" to appear in ACM Communications in Computer Algebra, (2012, December). Available: latex source
  48. with Charles Celerier, David Joyner, Caroline Melles, David Phillips, "On the Walsh-Hadamard transform of monotone Boolean functions" in Tbilisi Mathematical Journal Special Issue on Sage and Research, vol 5(2012)19-35
  49. "Zeros of Some Self-Reciprocal Polynomials", in Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center (Applied and Numerical Harmonic Analysis series), ed. Travis D Andrews, Radu Balan, John J. Benedetto, Wojciech Czaja, Kasso A. Okoudjou, Birkhauser, Boston, 2013.
  50. book review: "Review of Algebraic Shift Register Sequences by Mark Goresky and Andrew Klapper" in Cryptologia, Vol. 37(2013)175-183.
  51. book review: "Review of Cryptographic Boolean Functions and Applications by Thomas Cusick and Pantelimon Stanica" in Cryptologia, Vol. 37(2013)189-192.
  52. "A note on cryptologic aspects of the Waberski trial", 7 pages, 2013.
  53. "Elizebeth Smith Friedman, up to 1934", 20 pages, 2013.
  54. with Charles Celerier, Caroline Melles, David Phillips, Steven Walsh, "Explorations of edge-weighted Cayley graphs and p-ary bent functions", arxiv link
  55. The Man Who Discovered God's Number, College Math Journal, Sep. 2014 (
  1. Distribution theorems of L-functions, Pitman Research Notes, vol 142, Longman Scientific and Technical, 1986.
  2. with G. Nakos, Linear algebra and its applications, Brooks-Cole (ITP), 1998.
  3. (editor) Coding Theory and Cryptography: From Enigma and Geheimschreiber to Coding Theory, (Proceedings of a conference held at the USNA, Oct 1998), Springer-Verlag, 2000
  4. Adventures with group theory: Rubik's cube, Merlin's machine, and other mathematical toys, 2nd ed., The Johns Hopkins Univer. Press, 2008.
  5. with Rick Kreminski and JoAnn Turisco, Applied Abstract Algebra, The Johns Hopkins Univ Press, 2004. book web page
  6. (co-editor) Advances in coding theory and cryptology, (T. Shaska, W. C. Huffman, D. Joyner, V. Ustimenko, editors) Series on Coding Theory and Cryptology, 2. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007. x+267 pp.
  7. with William Granville, Differential calculus and Sage, Createspace, 2009. Available at or free as a pdf, with latex source. Released under an open source cc-by-sa license.
  8. with Jon-Lark Kim, Selected unsolved problems in coding theory, Birkhäuser/Springer-Verlag, 2011. Available at
  9. with Marshall Hampton, Differential equations with Sage, Johns Hopkins University Press, 2012.
  10. with Caroline Melles, Adventures in Graph Theory, in preparation, Birkhauser, 2015 or 2016.
  11. with David Phillips, Graph theory and Algorithms and Optimization book, in preparation, 2016 or 2017
  1. Screencast on Love, War and Zombies - Systems of Differential Equations using Sage.
Selected Teaching and Administration:
  1. Extensive development of MAPLE software packages both for teaching (Vector Calculus, Differential Equations, Finite Group Theory, and Coding Theory), research (Representation theory of Lie algebras using crystal bases), and mathematical recreation (Rubik's cube simulation, knight tours on a chess board, ...). Some of these packages are now available in the share library of MAPLE V5.
  2. Course Coordinator: Calc III with Maple (Fall 1995-6,1996-7), Linear Algebra II (Spring 1993-4), Matrix theory (Fall 2002-3), Discrete Math (Spring 2002-2003), DEs (2003-2005, 2007-2008)
  3. Course Development: Developed Mathematics of the Rubik's cube, a course to teach elementary group theory (Fall and Spring 1996-7). Notes are available on the www. Developed reading course on Representation Theory of the Rubik's Cube to teach elementary representation theory of symmetric groups and generalized symmetric groups (Fall 1997-8).
  4. Developed Applied Abstract Algebra course teaching coding theory, cryptography, and other applications of Abstract Algebra (1999-2001). The notes have been published as a text book by Johns Hopkins Univ. Press. Developed MAPLE, GAP and MAGMA computer labs for Applied Abstract Algebra course. AAA course web page
  5. Developed Error-correcting codes course teaching coding theory (2001-2002, 2003-2004, 2005-2006). Developed MAPLE, GAP and MAGMA computer labs for Error-correcting codes courses. 2005-2006
  6. Developed course teaching Python and coding theory (Spring 2009-2010, class webpage)
  7. Developed "capstone" course teaching computational Fourier transforms (class webpage)
  8. Developed "capstone" course teaching coding theory and cryptography (class webpage)
  9. Honors students: 1 VGEP student (Paul Miller, 1992), several honors students (Ann Luers, 1997; Justin Montague, 1999; Aron Foster, 2004; Irons, 2005; Lennon, 2005; McGowan, 2005; Brock, 2006; Coy, 2006;McDonald, 2006, Hogan, 2010, Tucker-Davis, 2011; Celerier, 2012, Walsh, 2014.), 1 Trident (McMath, 2005); 1 Bowman (Catalano, 2008).
  10. Colloquium committee chairman 1999-2008.
  11. Math Dept internet webmaster (2004-)
  12. Math Dept Validation and Placement committee (2013-).

David Joyner 572C Holloway Rd Mathematics Dept US Naval Academy Annapolis, MD 21402