Curriculum Vitae Jay A. Wood November 21, 2013 Jay A. Wood Professor of Mathematics 269-387-4812 (office) Department of Mathematics 269-343-0020 (home) Western Michigan University 269-387-4530 (fax) 1903 W. Michigan Ave. Email: jay.wood@wmich.edu Kalamazoo, MI 49008 5248 http://homepages.wmich.edu/ jwood/ Education Ph.D. Mathematics, University of California, Berkeley, 1982. Dissertation: An algebraization theorem for local hypersurfaces in projective space. Advisor: Shoshichi Kobayashi. M.A. Mathematics, University of California, Berkeley, 1978. A.B. Mathematics, University of Notre Dame, 1976, with highest honors, Phi Beta Kappa. Academic and administrative appointments July 2000 present: Professor of mathematics, Western Michigan University. September 2010 May 2011: Acting chair, Department of Mathemtics, WMU. July 2007 August 2008: Interim chair, Department of Statistics, WMU. January 2004 June 2007: Associate vice president and director of academic collective bargaining, WMU. July 2001 December 2003: Chair, Department of Mathematics, WMU. July 2000 June 2001: Chair, Department of Mathematics and Statistics, WMU. Spring 2000: Visiting professor of mathematics, University of Notre Dame and Université de Toulon et du Var. 1990 2000: Assistant, to Associate, to Professor of mathematics, Purdue University Calumet. 1989 1990: Visiting assistant professor of mathematics, Lehigh University. 1986 1990: Assistant professor of mathematics, Bowdoin College. 1984 1986: Visiting assistant professor of mathematics, University of Notre Dame. 1983, 1985: National Aeronautics and Space Administration summer faculty fellowship, Jet Propulsion Laboratory, California Institute of Technology. 1
1982 1984: L. E. Dickson instructor of mathematics, University of Chicago. 1976 1982: Teaching assistant in mathematics, University of California, Berkeley. Memberships in professional societies American Mathematical Society (AMS), 1978 1982, 1987 present Mathematical Association of America (MAA), 1988 present Institute of Electrical and Electronics Engineers (IEEE), 1998 present Publications Refereed journal articles Osculation by algebraic hypersurfaces, Journal of Differential Geometry, 18 (1983), 563 573. A simple criterion for local hypersurfaces to be algebraic, Duke Mathematical Journal, 51 (1984), 235 237. Spinor groups and algebraic coding theory, Journal of Combinatorial Theory, series A, 50 (1989), 277 313. Witt s extension theorem for mod four valued quadratic forms, Transactions of the American Mathematical Society, 336 (1993), 445 461. With Benson, David J., Integral invariants and the cohomology of BSpin(n), Topology, 34 (1995), 13 28. With Ward, Harold N., Characters and the equivalence of codes, Journal of Combinatorial Theory, series A, 73 (1996), 348 352. The Chern character for classical matrix groups, Proceedings of the American Mathematical Society 126 (1998), 1237 1244. Duality for modules over finite rings and applications to coding theory, American Journal of Mathematics, 121 (1999), 555 575. The structure of linear codes of constant weight, Transactions of the American Mathematical Society, 354 (2002), 1007 1026. The chain rule for matrix exponential functions, College Mathematics Journal, 35 (2004), 220 222. Code equivalence characterizes finite Frobenius rings, Proceedings of the American Mathematical Society, 136 (2008), 699 706. Anti-isomorphisms, character modules and self-dual codes over non-commutative rings, International Journal of Information and Coding Theory, special issue in Honour of the Retirement of Vera Pless, 1 (2010), 429 444. Relative one-weight linear codes, to appear in Designs, Codes and Cryptography: DOI 10.1007/s10623-012-9769-0. (Accepted Oct 15, 2012; available online.) 2
Refereed conference proceedings Maximal abelian subgroups of spinor groups and error-correcting codes, in Algebraic Topology, Mark Mahowald, Stewart Priddy, eds., Contemporary Mathematics, vol. 96, American Mathematical Society, Providence, 1989, pp. 333 350. Self-orthogonal codes and the topology of the spinor groups, in Coding Theory and Design Theory, Part I, Coding Theory, D. Ray-Chaudhuri, ed., IMA volumes in Mathematics and its Applications, volume 20, Springer-Verlag, New York, 1990, pp. 219 239. Nilpotent elements in the Bockstein spectral sequence for BSpin(n), in Algebraic Topology: Oaxtepec 1991, Martin C. Tangora, ed., Contemporary Mathematics, volume 146, American Mathematical Society, Providence, 1993, pp. 453 469. Extension theorems for linear codes over finite rings, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, T. Mora, H. Mattson, eds., Lecture Notes in Computer Science, vol. 1255, Springer-Verlag, Berlin, 1997, pp. 329 340. Weight functions and the extension theorem for linear codes over finite rings, in Finite Fields: Theory, Applications and Algorithms R. C. Mullin and G. L. Mullen, eds., Contemporary Mathematics, vol. 225, American Mathematical Society, Providence, 1999, pp. 231 243. Factoring the semigroup determinant of a finite commutative chain ring, in Coding Theory, Cryptography and Related Areas, J. Buchmann, T. Høholdt, H. Stichtenoth, and H. Tapia-Recillas, eds., Springer-Verlag, Berlin, 2000, pp. 249 259. Foundations of linear codes defined over finite modules: the extension theorem and the MacWilliams identities, in Codes over Rings: (Ankara 2008), P. Solé, ed., Series on Coding Theory and Cryptology, vol. 6, World Scientific, Singapore, 2009, pp. 124 190. Applications of finite Frobenius rings to the foundations of algebraic coding theory, in the Proceedings of the 44th Symposium on Ring Theory and Representation Theory (Okayama University, Japan, September 25 27, 2011), O. Iyama, ed., Nagoya, Japan, 2012, pp. 223 245. Conference proceedings, approved by a review process Semigroup rings and the extension theorem for linear codes, Proceedings of the Thirty- Fifth Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, 1997, pp. 163 172. Codes of constant Lee or Euclidean weight, Proceedings of the Workshop on Coding and Cryptography, D. Augot, C. Carlet, eds., INRIA, Paris, France, 1999, pp. 307 314. Linear codes over Z/(2 k ) of constant Euclidean weight, Proceedings of the Thirty-Seventh Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, 1999, pp. 895 896. Understanding linear codes of constant weight using virtual linear codes, Proceedings of the Thirty-Eighth Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, 2000, pp. 1038 1046. 3
The structure of linear codes of constant weight, Proceedings of the International Workshop on Coding and Cryptography, D. Augot, C. Carlet, eds., INRIA, Paris, 2001, pp. 547 556. Restrictions on two-weight projective linear codes, Proceedings of the International Workshop on Coding and Cryptography, D. Augot, P. Charpin, G. Kabatianski, eds., INRIA, Versailles, 2003, pp. 453 459. Other publications Contribution to chapter 2.6.5 of Theory of Multicodimensional n + 1-Webs, by Vladislav V. Goldberg, Kluwer Academic Publishers, Dordrecht, Boston, London, 1988. Works submitted or in progress Extension theorem for bi-invariant weight functions over finite Frobenius principal ideal rings, joint work with Marcus Greferath, Thomas Honold, Cathy Mc Fadden, and Jens Zumbrägel, submitted to Journal of Combinatorial Theory, Series A, September 12, 2013, under review. Some applications of the Fourier transform in algebraic coding theory, submitted to the proceedings of the CIMPA school in Morelia, Mexico, August 21, 2013, under review. Recent lectures Exotic automorphisms of additive codes, special session on Algebraic Coding Theory, AMS sectional meeting, Louisville, Kentucky, October 5, 2013. Lecture series, Linear codes over finite rings and modules, Coding Theory Seminar, Eastern Kentucky University, Richmond, Kentucky, March 2013. Lecture one: The MacWilliams identities, March 4, 2013. Lecture two: The MacWilliams extension theorem over Frobenius rings, March 5, 2013. Lecture three: The MacWilliams extension theorem for general weights, March 6, 2013. Lecture series for the research school Algebra for Secure and Reliable Communication Modeling, Morelia, Michoacan, Mexico, October 2012. Linear codes over finite rings and modules, October 5, 2012. Characters and the MacWilliams identities, October 8, 2012. Characters and finite Frobenius rings, October 9, 2012. Ring involutions and self-dual codes, October 9, 2012. Quasi-cyclic codes, October 12, 2012. Equivalence of codes: sufficient conditions, October 12, 2012. Equivalence of codes: necessary conditions, October 13, 2012. Equivalence of codes: general weights, October 13, 2012. Finite Frobenius rings and the MacWilliams identities, Algebra and Communications Seminar, University College Dublin, Dublin, Ireland, November 14, 2011. Characterizing finite Frobenius rings via coding theory, Algebra and Communications Seminar, University College Dublin, Dublin, Ireland, November 7, 2011. Relative one-weight codes, special session on Coding Theory, AMS sectional meeting, Lincoln, Nebraska, October 14, 2011. 4
Two lectures on the theme Applications of finite Frobenius rings to algebraic coding theory. Symposium on Ring and Representation Theory Japan, Okayama University. Lecture one, September 25, 2011: Two theorems of MacWilliams over finite Frobenius rings. Lecture two, September 26, 2011: Using coding theory to characterize finite Frobenius rings. Finite Frobenius rings as a setting for algebraic coding theory, Hefei University of Technology, Hefei, Anhui, China, June 30, 2011. The MacWilliams identities, Huangshi Institute of Technology, Huangshi, Hubei, China, June 24, 2011. Lecture series: Two fundamental theorems of MacWilliams, Huazhong Normal University, Wuhan, Hubei, China, June-July 2011. Lecture one, June 22, 2011: The classical case over finite fields. Lecture two, June 28, 2011: The MacWilliams identities over finite rings. Lecture three, July 2, 2011: The MacWilliams extension theorem over finite rings. Five one-hour lectures at the International Workshop on Coding Theory and Cryptography, Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, Mexico, July 14 16, 2010. Lecture titles: Characters and the Poisson summation theorem, The MacWilliams identities for linear codes over finite rings and modules, Invariant theory and Gleason s theorem for self-dual codes, Linear codes over finite Frobenius rings, and Self-dual codes over non-commutative rings. Ring involutions and self-dual codes, special session on Advances in Algebraic Coding Theory, AMS sectional meeting, Lexington, Kentucky, March 27, 2010. Four one-hour lectures on the theme Dual codes and the MacWilliams identities, Workshop on Coding Theory and Geometry of Rational Surfaces, Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, Mexico, September 23 26, 2009. Individual lectures entitled A model theorem, Characters and the case of additive codes, The case of linear codes, and Self-duality in the non-commutative context. Self-dual codes over non-commutative rings, algebra seminar, Ohio University, Athens, Ohio, May 14, 2009. Frobenius rings and the extension theorem for linear codes, International School and Conference on Coding Theory, Centro de Investigación en Matemáticas, Guanajuato, Mexico, December 2, 2008. Four one-hour lectures on Dual codes and the MacWilliams identities, International School and Conference on Coding Theory, Centro de Investigación en Matemáticas, Guanajuato, Mexico, November 30 December 1, 2008. Eight one-hour lectures on linear codes over rings and modules, emphasizing the extension theorem and the MacWilliams identities, CIMPA-UNESCO-TÜBİTAK sponsored summer school on Codes over Rings, Middle East Technical University, Ankara, Turkey, August 18 29, 2008. Dual codes over finite rings cautions and compromises, special session on Algebraic Aspects of Coding Theory, AMS sectional meeting, Bloomington, Indiana, April 5, 2008. 5
Character-theoretic proofs of equivalence theorems (in honor of Thann Ward), special session on Algebraic Coding Theory (in honor of Harold N. Ward s retirement), AMS sectional meeting, Chicago, Illinois, October 6, 2007. Equivalence of linear codes over finite rings (in honor of Vera Pless), special session on Algebraic Coding Theory Honoring the Retirement of Vera Pless, AMS sectional meeting, Cincinnati, Ohio, October 22, 2006. Code equivalence and finite Frobenius rings, theory of rings and modules session, 28th Ohio State-Denison mathematics conference, Ohio State University, Columbus, OH, May 19, 2006. Highly symmetric weight functions on matrix rings, special session on codes and applications, AMS sectional meeting, Evanston, IL, October 23, 2004. An essay on equivalence of linear codes, III, special session on coding theory and cryptography, joint AMS/SMM international meeting, Houston, TX, May 14, 2004. An essay on equivalence of linear codes, II, special session on algebraic coding theory, AMS meeting, Ohio University, Athens, OH, March 26, 2004. An essay on equivalence of linear codes, special session on applications of number theory and algebraic geometry to coding, AMS meeting, University of Colorado, Boulder, CO, October 4, 2003. Restrictions on two-weight projective linear codes, International Workshop on Coding and Cryptography, INRIA, Versailles, France, March 28, 2003. The development of coding theory over finite rings, special session on algebraic coding theory, Joint Mathematics Meetings, San Diego, CA, January 7, 2002. The MacWilliams identities, department colloquium, Department of Mathematics, Central Michigan University, Mount Pleasant, MI, November 15, 2001. The structure of linear codes of constant weight, International Workshop on Coding and Cryptography, INRIA, Paris, France, January 9, 2001. Understanding linear codes of constant weight using virtual linear codes, Thirty-Eighth Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, Monticello, IL, October 6, 2000. Virtual linear codes of constant weight, coding theory seminar, Université de Toulon et du Var, La Garde, France, June 6, 2000. Linear codes over Z/(2 k ) of constant Euclidean weight, Thirty-Seventh Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, Monticello, IL, September 23, 1999. Classifying linear codes of constant weight, coding theory seminar, University of Illinois, Chicago, IL, May 3, 1999. Witt theorems for linear codes over finite Frobenius rings, International Conference on Algebra and its Applications, Ohio University, Athens, OH, March 27, 1999. 6
Codes of constant Euclidean weight, coding theory seminar, University of Notre Dame, Notre Dame, IN, February 9, 1999. Codes of constant Lee or Euclidean weight, Workshop on Coding and Cryptography, INRIA, Paris, France, January 13, 1999. An application of semigroup rings to coding theory, special session on algebraic coding, AMS meeting, DePaul University, Chicago, IL, September 13, 1998. Music and math: the composition Faster, Composition Forum, Interlochen Center for the Arts, Interlochen, MI, August 5, 1998. Some examples from the representation theory of compact, connected Lie Groups, Geometry and Topology Conference, Lehigh University, Bethlehem, PA, June 13, 1998. Some foundational issues in algebraic coding theory over finite rings, International Conference on Coding Theory, Cryptography and Related Areas, Guanajuato, Mexico, April 21, 1998. An application of the group determinant to coding theory, coding seminar, University of Illinois, Chicago, IL, March 17, 1998. A mathematical overview of cyclic codes, coding theory seminar, University of Notre Dame, Notre Dame, IN, March 3, 1998. Semigroup rings and the extension theorem for linear codes, Thirty-Fifth Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, Monticello, IL, September 29, 1997. Linear codes over finite rings, contributed paper, Fourth International Conference on Finite Fields and their Applications, University of Waterloo, Ontario, August 12, 1997. Revisiting the work of Adams on Chern characters, Geometry/Topology Conference, Lehigh University, Bethlehem, PA, June 20, 1997. Connective K-theory and the Chern character, special session on algebraic topology, AMS meeting, Wayne State University, Detroit, MI, May 4, 1997. Two theorems of MacWilliams: finite rings and Morita duality, coding theory seminar, University of Notre Dame, Notre Dame, IN, February 25, 1997. Two theorems of MacWilliams: the classical case of finite fields, coding theory seminar, University of Notre Dame, Notre Dame, IN, February 18, 1997. The Chern character and the Adams spectral sequence, algebraic topology seminar, Lehigh University, Bethlehem, PA, September 16, 1996. The image of the Chern character for compact, connected Lie groups, Workshop in Algebraic Topology, Instituto de Matemáticas, Morelia, Mexico, August 15, 1996. 7
Research grants received All the grants which follow were funded by the National Security Agency, Mathematical Sciences Program, Grants for Research in Mathematics and Cryptology. Applications of Equivariant Cohomology Theory to Self-Orthogonal Codes, June 1988 May 1989. Self-Orthogonal Codes and Equivariant Morse Theory, June 1989 May 1991. Self-Orthogonal Codes and Equivariant Cohomology, June 1991 May 1993. Spinor Groups and Cohomology, March 1994 March 1996. Characters, Coding Theory, and Spinor Groups, April 1996 April 1997. Professional Service AMS Committee on Academic Freedom, Tenure, and Employment Security, 2000-2006. Co-organizer of Midwest Topology Seminar, October 1999, November 2002, AMS Special Session on Algebraic Coding Theory, April 2000, and AMS Special Session on Linear Codes over Rings and Modules, October 2008. Organizer AMS Special Session on Algebraic Coding Theory (in honor of Harold N. Ward s retirement), October 2007. Referee for articles submitted to mathematics journals. Reviewer for Mathematical Reviews. The MacWilliams identities, department colloquium, Western Michigan University, Kalamazoo, MI, March 1, 2012. Finite fields, Math Club talk, Western Michigan University, Kalamazoo, MI, November 8, 2013. 8