Professor W. David Joyner

Current research interests: Currently I am working on various projects related to the understanding of how to compute modular representations of a Galois group of a curve acting on a Riemann-Roch space. Also, I contribute to SAGE, a great new free and open source computer algebra system developed mainly by William Stein.

Other interests: Linux, chess, computers, science fiction.

Brief Research Biography

Education
• University of Maryland, College Park (Ph.D. in Mathematics, May 1983; advisor: John Benedetto)
• Georgia Institute of Technology, Atlanta (B.S. in Applied Mathematics, June 1981)

Employment
• U. S. Naval Academy, Annapolis, MD (8/1987 - present)
• Institute for Advanced Study, Princeton N.J. (Member, 4/1985 - 7/1987, NSF Fellow)
• Princeton University (Instructor, 9/1985-6/1986, NSF Fellow)
• University of California at San Diego, La Jolla, Ca. (Assist. Prof., 7/1984-3/1985, NSF Fellow)
• University of Maryland, College Park (Research Instructor and Graduate Teaching Assistant, 9/1983-5/1984)
• Georgia Institute of Technology, Atlanta (Undergraduate Teaching Assistant and Graduate Teaching Assistant, 9/1979-8/1981)

USNA Faculty Researcher of the Year Award, 2007.

Editorial:

• I was a technical editor for Cryptologia 1999-2000.
• I'm currently on the editorial boards of
  • Cryptologia,
  • Albanian Journal of Mathematics.
• I've edited or co-edited three books (see below).
• Some (minor) work on Wikipedia (correction to a few items involving coding theory, for example).
• Some refereeing for various professional journals and and am a reviewer for Zentralblatt fuer Mathematik.

Software:

• Contributed code and documentation, and have helped with refereeing and testing, to SAGE. I also help monitor the email lists (for teaching, support, and development, resp.).
• I was the maintainer of the GUAVA package, a package for GAP containing many routines for exploring error-correcting codes, from 2000 to 2009. Curently the maintainer is Joe Fields, though I stay as a developer.
• Creator and current maintainer of the TORIC package for computing with toric varieties.
• I also help with maintaining the GAP website, as well as server on its support team and development team.
• I maintain opensourcemath.org, which provides links and mirrors for various (free and) open source mathematics software and text-book projects.

Research Publications:

1. "A note on gaps between zeroes of L-functions," unpublished preprint dating from 1984.
2. "Summation operators and 'explicit formulas'", Port. Math. 44(1987)119-130. pdf
3. "On the metaplectic analog of Kazhdan's 'endoscopic' lifting", Isr. J. Math. 61 (1988)113-154.
   preprint version
4. "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
5. "On twisted orbital integral identities for PGL(3) over a p-adic field", Can. J. Math. 31(1991)1098-1130.
   preprint version
6. "On the Montgomery-Dyson hypothesis", in Proceedings of the Amalfi Analytic Number Theory Conference, Univ. de Salerno, 1992.
7. "Remarks on the Bruggeman-Kutznetsov formula", Proceedings of the Amalfi Analytic Number Theory Conference, Univ. de Salerno, 1992.
8. "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)
9. with Roland Martin, "Decomposing Lie Algebra Representations Using Crystal Graphs", SAC Newsletter, no. 2, June 1997, pp. 27-34.
preprint version
10. with R. Martin, "Using crystal graphs to decompose Lie algebra representations", SIGSAM Bull 31 Dec. 1997.
11. with R. Martin, "Branching rules for Lie algebra representations using crystal graphs", Maple Tech 25(1998)23-27. preprint version
12. "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
13. 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.
14. "On the unitary dual of $\overline{SL(2,F)}, F p-adic," unpublished preprint, 1999.
15. "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
16. "On finite dimensional representations of non-connected reductive groups," J. of Lie Theory. 10(2000)269-284. On the JLT web page
17. "Invariant distributions on the n-fold metaplectic covers of GL(r,F), F p-adic," J. Fourier Anal. and Appl. 7(2001)343-358.
    preprint version
18. 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 (there is a Magma version at the math arXivs
19. 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.
    preprint version
20. "Representations of finite groups on Riemann-Roch space of a toric variety," preprint, 2002.
21. with Michael Fourte, "Odd King Tours on Even Chessboards," Journal of Recreational Mathematics 31(2003)173-177.
    preprint version
22. "Arithmetic of characters of generalized symmetric groups," Archiv der Mathematik, vol 81 (2003)113--120.
    preprint version 1, preprint version 2
23. with Helena Verrill, "Notes on toric varieties," preprint at math arxivs and preprint (the latter version contains an index). "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. It is available, but only in Ukrainian, and as a pdf file.
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 Algebra, vol 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. (with Amy Ksir, Tony Shaska) "Bases for Riemann-Roch spaces of hyperelliptic curves," preprint, 2006. Partially implemented in SAGE.
38. "Mathematics of Ghaly's machine", Integers.
39. "Quadratic residue codes and hyperelliptic curves", preprint math arxivs. Discrete Mathematics and Theoretical Computer Science, vol 10(2008) 129-146.
40. "Open Source Computer Algebra Systems - Axiom", ACM Communications in Computer Algebra, Volume Volume 42, Number 2 - June 2008 - Issue 164.
    pdf.
41. (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. See math arXivs.
42. (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.
43. "A primer on computational group homology and cohomology." See arXivs. Proceedings of the Gaglione conference, entitled Aspects of Infinite Groups (ed. Ben Fine, G. Rosenberger, D. Spellman), World Scientific Press, 2008.
44. (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 source tarball.)
45. with Amy Ksir and Darren Glass, "Codes from Riemann-Roch spaces for y² = x^p-x over GF(p)", Accepted for publication in Algebraic and Combinatorial Coding Theory in Honour of the Retirement of Vera Pless, a special issue of International. J. of Information and Coding Theory, (editors: Philippe Gaborit, Jon-Lark Kim, Patrick Sole, and Isaac Woungang), 2010.

Books:

1. Distribution theorems of L-functions, Pitman Research Notes, vol 142, Longman Scientific and Technical, 1986. See also errata.
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 book web page
4. Adventures with group theory: Rubik's cube, Merlin's machine, and other mathematical toys, 2nd ed., The Johns Hopkins Univer. Press, 2008. book web page
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 amazon.com or free as a pdf, with latex source. Released under an open source cc-by-sa license.
8. with Jon-Lark Kim, Unsolved problems in coding theory, to be published by Birkhäuser/Springer-Verlag in 2010.

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. See also maple packages.
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. 2001-2, 2003-4, 2005-2006
6. Developed course teaching Python and coding theory (Spring 2009-2010, to appear)
7. 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), 1 Trident (McMath, 2005); 1 Bowman (Catalano, 2008).
8. Faculty Representative: Chess Club (1998-2004).
9. Integrity Development Seminar facilitator (1998- 1999).
10. Civilian Faculty Affairs committee during it's last year and served on committee to create by-laws of the new Faculty Senate (1992-3).
11. Colloquium committee chairman 1999-2008.
12. Math Dept internet webmaster (2004-)
13. Honors committee (2003-), co-chair (Sep. 2005-2008).