*W. David Joyner*

*Research Interests*: graph theory, error-correcting codes, representation theory and applications, harmonic analysis on groups, applications of number theory/group theory to communication theory and cryptography, analytic number theory.

Ph.D.: University of Maryland-College Park, 1983-05-23

*Other interests*: Writing, chess, photography, video, history of mathematics and history of cryptography.

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 – 12/2018), now retired
- 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:

- Technical editor for Cryptologia 1999-2000, and now am on its editorial board.
- Edited or co-edited three books (see below).
- Some refereeing for various professional journals.

Software:

- Contributed code and documentation to Sagemath and SymPy. I also help maintain the Sagemath email lists (for teaching, support, and development, resp.).
- From 2000-2009, I was the maintainer of the GUAVA package, a package for GAP containing many routines for exploring error-correcting codes. Curently the maintainer is Joe Fields.
- Creator and current maintainer of the TORIC package for computing with toric varieties.

### Research Publications:

- “Zeta functions and their associated operators,” unpublished paper from 1981
- “A note on gaps between zeroes of L-functions,” unpublished paper dating from 1984.
- “Summation operators and ‘explicit formulas'”,
*Port. Math.*44(1987)119-130. (paper – basically my PhD thesis) - “On the metaplectic analog of Kazhdan’s ‘endoscopic’ lifting”,
*Isr. J. Math.*61 (1988)113-154. (paper) - “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
- “On twisted orbital integral identities for PGL(3) over a p-adic field”,
*Can. J. Math.*31(1991)1098-1130. paper - “On the Montgomery-Dyson hypothesis”, in
**Proceedings of the Amalfi Analytic Number Theory Conference**, Univ. de Salerno, 1992. paper - “Remarks on the Bruggeman-Kutznetsov formula”,
**Proceedings of the Amalfi Analytic Number Theory Conference**, Univ. de Salerno, 1992. - “Simple local trace formulas for unramified p-adic groups”,
*Pac. J. Math.***154**(1992)103-129.

paper (pdf) - with Roland Martin, “Decomposing Lie Algebra Representations Using Crystal Graphs”,
*SAC Newsletter*, no. 2, June 1997, pp. 27-34. paper - with R. Martin, “Using crystal graphs to decompose Lie algebra representations”,
*SIGSAM Bull.***31**Dec. 1997. - with R. Martin, “Branching rules for Lie algebra representations using crystal graphs”,
*Maple Tech.***25**(1998)23-27. paper - “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 - 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

paper - “On the unitary dual of the metaplectic cover of SL(2,F), for F p-adic,” unpublished paper, 1999.
- “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 - “On finite dimensional representations of non-connected reductive groups,”
*J. of Lie Theory***10**(2000)269-284. On the JLT web page - “Invariant distributions on the n-fold metaplectic covers of GL(r,F), F p-adic,”
*J. Fourier Anal. and Appl.***7**(2001)343-358.

paper - 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 - 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. paper - with Michael Fourte, “Odd King Tours on Even Chessboards,”
*Journal of Recreational Mathematics***31**(2003)173-177.

paper - “Arithmetic of characters of generalized symmetric groups,”
*Archiv der Mathematik*, vol 81 (2003)113–120.

paper - with Helena Verrill, “Notes on toric varieties,” preprint at math arxivs. “Computing with toric varieties,”
*J. Symb. Comp.*Volume 42 (2007)511-532 . - “Toric codes over finite fields”, AAECC, vol. 15, Number 1 (2004)63 – 79. A version may be found at math arXivs
- with Will Traves, “Representations of finite groups on Riemann-Roch spaces,” available at math arXivs.
- 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. - 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. ) - (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. - “Open Source Computer Algebra Systems – Maxima”,
*ACM Communications in Computer Algebra*, Volume 40, Number 3/4 – September/December 2006 – Issue 157/158. - 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.) - 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. - “Conjectural permutation decoding of some AG codes”
*Communications in Computer Algebra (formerly “SIGSAM Bull”),*vol 39, March 2005, pages 166-172. - (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.) - (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. - (with William Stein) “SAGE: System for Algebra and Geometry Experimentation”,
*Communications in Computer Algebra,*vol 39, June 2005, pages 61-64. *“*GUAVA: An error-correcting codes package*” Communications in Computer Algebra, vol 39, June 2005, pages 65-68.*- “Mathematics of Ghaly’s machine”,
*Integers* - “Quadratic residue codes and hyperelliptic curves”, Discrete Mathematics and Theoretical Computer Science, vol 10(2008) 129-146.
- “Open Source Computer Algebra Systems – Axiom”, ACM Communications in Computer Algebra, Volume Volume 42, Number 2 – June 2008 – Issue 164.
- (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. - (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. - “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. - (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.) - with Amy Ksir and Darren Glass, “Codes from Riemann-Roch spaces for
*y*over GF(p)”,^{2}= x^{p}-x**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. pdf - 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. - with Chris Christensen and Jenna Torres, “Lester Hill’s error-detecting codes”, Cryptologia, 36(2011)88-103.
- with Ondrej Certik, Aaron Meurer, Brian Granger, “Open Source Computer Algebra Systems: SymPy,”
*ACM Communications in Computer Algebra*, (2012, December). Available: pdf - 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 - “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, Birkhäuser, Boston, 2013. Available: paper. - book review: “Review of Algebraic Shift Register Sequences by Mark Goresky and Andrew Klapper” in Cryptologia, Vol. 37(2013)175-183.
- book review: “Review of Cryptographic Boolean Functions and Applications by Thomas Cusick and Pantelimon Stănică” in
*Cryptologia*, Vol. 37(2013)189-192. - “A note on cryptologic aspects of the Waberski trial”, 7 pages, 2013. pdf
- “Elizebeth Smith Friedman, up to 1934”, 20 pages, 2013. pdf
- with Charles Celerier, Caroline Melles, David Phillips, Steven Walsh, “Explorations of edge-weighted Cayley graphs and p-ary bent functions”, arxiv link.

A shorter version was published in INTEGERS, vol. 16 (2016) - The Man Who Discovered God’s Number, College Math Journal, Sep. 2014 (http://dx.doi.org/10.4169/college.math.j.45.4.258)
- with T. Shaska, “Self-inversive polynomials, curves, and codes”, pdf, in
**Algebraic curves and their fibrations in mathematical physics and arithmetic geometry**, Eds A. Malmendier, T. Shaska,*Contemporary Math.*, American Math. Soc. (to appear, 2018). - “Hill vs Hamming” (pdf, expository), 2016. See also this blog post and this article.
- (with Alfred J. Menezes, Paul C. van Oorschot, Tony Shaska),
*Coding theory*, coding theory chapter for the new edition of**CRC Handbook of Discrete and Combinatorial Mathematics**, to appear. - “An Application of Matrix Theory to Baseball Rankings”, Mathematica Militaris, 22(2017)29-39.
- “Review of A Life in Code by Stuart G. Smith and The Woman Who Smashed Codes by Jason Fagone”, Cryptologia, 2018
- (with C. Melles), “On p-ary Bent Functions and Strongly Regular Graphs”, 2018, submitted.

*Books:*

**Distribution theorems of L-functions**, Pitman Research Notes, vol 142, Longman Scientific and Technical, 1986. See also errata- with G. Nakos,
**Linear algebra and its applications**, Brooks-Cole (ITP), 1998. - (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 **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, errata page- with Rick Kreminski and JoAnn Turisco,
**Applied Abstract Algebra**, The Johns Hopkins Univ Press, 2004. book web page - (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. - 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. - with Jon-Lark Kim,
**Selected unsolved problems in coding theory**, Birkhäuser/Springer-Verlag, 2011. Available at amazon.com - with Marshall Hampton,
**Differential equations with Sage**, Johns Hopkins University Press, 2012. - with Caroline Melles,
**Adventures in Graph Theory**, Birkhauser, 2018.

Screencasts/videos:

- Screencast on Love, War and Zombies – Systems of Differential Equations using Sage, with slides.
- Lanchester’s equations video
- The Bifid and Vigenere ciphers and Sage screencast
- Fourier series – using Sage video

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