John McKay (mathematician)

John McKay (born 1939) is a dual British/Canadian citizen, a mathematician at Concordia University, known for his discovery of monstrous moonshine, his joint construction of some sporadic simple groups, for the McKay (McKay-Alperin) conjecture in representation theory, and for the McKay correspondence relating certain finite groups to Lie groups.

McKay earned his Bachelor and Diploma in 1961 and 1962 at the University of Manchester, and his Ph.D. in 1971 from the University of Edinburgh.[1] Since 1974 he works at the Concordia University, since 1979 as a professor in Computer Science.

He was elected a fellow of the Royal Society of Canada in 2000, and won the 2003 CRM-Fields-PIMS prize.

In April 2007 a Joint Conference was organized by the University of Montreal and Concordia University honouring four decades of the work of John McKay.

Publications

  • McKay, J. (1965). "Algorithm 262: Number of restricted partitions of N". Comm. ACM 8 (8): 493. doi:10.1145/365474.366060.
  • McKay, J. (1965). "Algorithm 263: Partition generator". Comm. ACM 8 (8): 493. doi:10.1145/365474.366063.
  • McKay, J. (1965). "Algorithm 264: Map of partitions into integers". Comm. ACM 8 (8): 493. doi:10.1145/365474.365501.
  • McKay, J. (1967). "On the representation of symmetric polynomials". Comm. ACM 10 (7): 428–429. doi:10.1145/363427.363452.
  • McKay, J. (1967). "Symmetric group characters". Comm. ACM 10 (7): 451–452. doi:10.1145/363427.363475.
  • McKay, J.; Bratley, P. (1967). "Algorithm 305: Symmetric polynomials". Comm. ACM 10 (7). doi:10.1145/363427.363465.
  • McKay, J.; Bratley, P. (1967). "Algorithm 313: Multi-dimensional partition generator". Comm. ACM 10 (10): 666. doi:10.1145/363717.363783.
  • McKay, J.; Atkin, A. O. L.; Bratley, P.; Macdonald, I. G. (1967). "Some computations for m-dimensional partitions". Proc. Camb. Phil. Soc. 63 (4): 1097–1100. doi:10.1017/S0305004100042171.
  • McKay, J.; Bratley, P. (1968). "More amicable numbers". Math Comp. 22 (103): 677–678. doi:10.1090/s0025-5718-1968-0225706-9. JSTOR 2004549.
  • McKay, J. (1968). "Remark on algorithm 307: Symmetric group characters". Comm. ACM 11 (1): 14. doi:10.1145/362851.362867.
  • McKay, J. (1968). "Remark on algorithm 305: Symmetric Polynomials". Comm. ACM 11 (4): 272. doi:10.1145/362991.363049.
  • McKay, J. (1968). "On the evaluation of multiplicative combinatorial expressions". Comm. ACM 11 (6): 492. doi:10.1145/363347.363357.
  • McKay, J. (1968), "A method of computing the character table of a finite group", in Churchhouse, R. F.; Herz, Computers in mathematical research, North-Holland Publishing
  • McKay, J.; Higman, G. (1969). "The construction of Janko's simple group of order 50232960". Bulletin of the London Mathematical Society 1 (2): 89–94. doi:10.1112/blms/1.2.219-t.
  • McKay, J.; Bratley, P.; Lunnon, W. F. (1970). "Amicable numbers and their distribution". Math. Comp. 24 (110): 431–432. doi:10.1090/s0025-5718-1970-0271005-8. JSTOR 2004490.
  • McKay, J. (1970). "Algorithm 371: Partitions in natural order". Comm. ACM 13 (1): 52. doi:10.1145/361953.361980.
  • McKay, J. (1970). "Algorithm 391: Unitary symmetric polynomials". Comm. ACM 13: 512. doi:10.1145/362705.362719.
  • McKay, J. (1970), "The construction of the character table of a finite group from generators and relations", in Leech, Computational problems in abstract algebra, Pergamon Press, pp. 89–100
  • McKay, J. (1970), "Multi-dimensional partitions", in Welsh, Combinatorial theory and its applications, Academic Press
  • McKay, J. (1971), "Subgroups and permutation characters", in Birkhoff; Hall, Proc. Symp. Pure Math. AMS-SIAM, pp. 171–181
  • McKay, J.; Wales, D. (1971). "The multiplier of the Higman-Sims simple group". Bulletin of the London Mathematical Society 3 (3): 283–285. doi:10.1112/blms/3.3.283.
  • McKay, J.; Wales, D. (1971). "The multiplier of the simple groups of order 604800 and 50232960". Journal of Algebra 17 (2): 262–272. doi:10.1016/0021-8693(71)90033-0.
  • McKay, J. (1971). "Groups and subgroups, presentations and representations". Proc. 2nd ACM symposium on symbolic and algebraic manipulation. p. 104. doi:10.1145/800204.806274.
  • McKay, J. (1972). "Irreducible representations of odd degree". Journal of Algebra 20 (2): 416–418. doi:10.1016/0021-8693(72)90066-X.
  • Lam, C. W. H.; McKay, J. (1973). "Arithmetic over a finite field, Algorithm 469". Comm. ACM 16 (11): 699. doi:10.1145/355611.362544.
  • McKay, J.; Regener, E. (1974). "Algorithm 482:Transitivity sets". Comm. ACM 17 (8): 470. doi:10.1145/361082.361098.
  • McKay, J. (1974), "Computing with finite simple groups", Proceedings 2nd International conference in group theory 372, Springer-Verlag, pp. 448–452
  • Jonsson, W.; McKay, J. (1976). "More about the Mathieu group". Canadian Journal of Mathematics 28: 929–937. doi:10.4153/cjm-1976-090-x. MR 0427103.
  • McKay, J. (1976). "The largest degrees of irreducible characters of the symmetric group". Mathematics of Computation 30 (135): 624–631. JSTOR 2005331.
  • Fischer, J.; McKay, J. (1978). "The non-abelian simple groups G, |G| < 106 - maximal subgroups". Mathematics of Computation 32 (144): 1293–1302. JSTOR 2006354. MR 0498831.
  • Erbach, D. W.; Fischer, J.; McKay, J. (1979). "Polynomials with PSL(2,7) as Galois group". Journal of Number Theory 11 (1): 69–75. doi:10.1016/0022-314X(79)90020-9. MR 0527761.
  • McKay, J. (1979). "Some remarks on computing Galois groups". SIAM Journal on Computing 8: 344–347. doi:10.1137/0208026. MR 0539252.
  • Cannon, J.; McKay, J.; Young, K. C. (1979). "The non-abelian simple groups G, |G| < 105 - minimal presentations". Communications in Algebra 7 (13): 1397–1406. doi:10.1080/00927877908822409.
  • McKay, J. (1979). "The non-abelian simple groups G, |G\| < 106 - character tables". Comm. in Algebra 7 (13): 1407–1445. doi:10.1080/00927877908822410.
  • McKay, J.; Young, K. C. (1979). "The non-abelian simple groups G, |G| < 106 - minimal generating pairs". Mathematics of Computation 33 (146): 812–814. JSTOR 2006317.
  • McKay, J. (1980). "Graphs singularities and finite groups". Proc. of 1979 Santa Cruz group theory conference. AMS Symposia in Pure Mathematics 37. pp. 183–186. ISBN 0-8218-1440-0.
  • McKay, J. (1981). "Cartan matrices, finite groups of quaternions, and Kleinian singularities". Proc. AMS 81: 153–154. doi:10.1090/S0002-9939-1981-0589160-8.
  • McKay, J.; Patera, J.; Sharp, R.T. (1981). "Second and fourth indices of plethysms". J. Math. Phys. 22 (12): 2770–2774. doi:10.1063/1.525183. MR 0638081.
  • Ford, D. J.; McKay, J. (1982), "Representations and Coxeter graphs", The Geometric Vein, Springer-Verlag
  • Lam, C. W. H.; Thiel, L.; Swiercz, S.; McKay, J. (1983). "The nonexistence of ovals in a projective plane of order 10". Discrete Math 45 (2–3): 319–321. doi:10.1016/0012-365X(83)90049-3. MR 0704249.
  • Butler, G.; McKay, J. (1983). "The transitive groups of degree up to eleven". Comm. in Algebra 11 (7): 863–911. doi:10.1080/00927878308822884.
  • Kolesova, G.; McKay, J. (1984), "Practical strategies for computing Galois groups", in Atkinson, M. D., Computing in Groups, Academic Press, pp. 297–299, MR 0760664
  • Dummit, D.; Kisilevsky, H.; McKay, J. (1985). "Multiplicative products of η functions". Contemporary Mathematics (American Math. Soc.) 45: 89–98. doi:10.1090/conm/045/822235. MR 0822235.
  • McKay, J., ed. (1985). "Finite groups - Coming of age". Contemporary Mathematics (American Math. Soc.) 45.
  • McKay, J.; Regener, E. (1985). "Actions of permutation groups on r-sets". Comm. in Algebra 13 (3): 619–630. doi:10.1080/00927878508823180. MR 0773753.
  • Soicher, L. H.; McKay, J. (1985). "Computing Galois groups over the rationals". J. Number theory 20 (3): 273–281. doi:10.1016/0022-314X(85)90022-8.
  • Ford, D.; McKay, J. (1986). From polynomials to Galois groups. International EUROCAL conference in computer algebra. Lecture Notes in Computer Science 204 (Springer-Verlag): 535–536. doi:10.1007/3-540-15984-3_324.
  • McKay, J.; Stauduhar, R. (1987). "Coda to a theorem of Schur". Crelle J. 377: 219–220.
  • McKay, J. (1987). "On computing discriminants". Amer. Math. Monthly 94 (6): 523–527. JSTOR 2322843.
  • McKay, J. (1988), "Advances in computational Galois theory", in Tangora, Computers in Algebra 111, Marcel Dekker, pp. 99–101
  • Conder, M.; McKay, J. (1988). "A necessary condition for transitivity of a finite permutation group". Bulletin of the London Mathematical Society 20 (3): 235–238. doi:10.1112/blms/20.3.235.
  • Ford, D.; McKay, J. (1989), "Computation of Galois groups from polynomials over the rationals", in Chudnovsky; Jenks, Computer Algebra 113, Marcel Dekker, pp. 145–150
  • McKay, J.; Strauss, H. (1990). "The q-series of monstrous moonshine & the decomposition of the head characters". Comm. in Algebra 18 (1): 253–278. doi:10.1080/00927879008823911.
  • Ford, D.; McKay, J. (1989). "Ramifications of Ramanujan's work on eta-products". Proc. Indian Acad. Sci. 99: 221–229. doi:10.1007/bf02864394.
  • Darmon, H.; McKay, J. (1991). "A continued fraction and fixed-point-free permutations". Amer. Math. Monthly 98 (1): 25–26. JSTOR 2324031.
  • McKay, J. (1991). "A generalized Hecke operator and functions like j(z)". AMS Abstracts 12: 283.
  • Alexander, D.; Cummins, C.; McKay, J.; Simons, C. (1992), Liebeck; Saxl, eds., "Groups, Combinatorics and Geometry", LMS Lecture Note Series (Cam. Univ. Press) 165: 87–98, MR 1200252 |chapter= ignored (help)
  • Casperson, D.; McKay, J. (1992). "An ideal decomposition algorithm". AMS Abstracts 13: 405.
  • Conway, J.; McKay, J. (April 1992). "The Mathieu groups as Galois groups". AMS Abstracts.
  • Casperson, D.; McKay, J. (1994). "Symmetric functions, m-sets, and Galois groups". Math. Comp. 63 (208): 749–757. doi:10.1090/S0025-5718-1994-1234424-5. JSTOR 2153295.
  • Ford, D.; McKay, J.; Norton, S. (1994). "More on replicable functions". Comm. in Algebra 22: 5175–5193. doi:10.1080/00927879408825127.
  • McKay, J. (1995). "A note on the elliptic curves of Harada-Lang". In Arasu, K. T. Groups, Difference Sets and the Monster. de Gruyter. p. 409. ISBN 3-11-014791-2.
  • Casperson, D.; Ford, D.; McKay, J. (1996). "Ideal Decompositions and Subfields". J. Symb. Comp. 21 (2): 133–137. doi:10.1006/jsco.1996.0005.
  • Conder, M.; McKay, J. (1996). "The marking of the Golay code". New Zealand J. Math. 25: 133–139. CiteSeerX: 10.1.1.42.8094.
  • Conway, J.; Hulpke, A.; McKay, J. (1996). "On transitive permutation groups". J. of Mathematics & Computation 1.
  • Cohn, H.; McKay, J. (1996). "Spontaneous generation of modular invariants". Math. Comp. 65 (215): 1295–1309. doi:10.1090/S0025-5718-96-00726-0. JSTOR 2153808.
  • Mattman, T.; McKay, J. (1997). "Computation of Galois groups over function fields". Math. Comp. 66 (218): 823–831. doi:10.1090/S0025-5718-97-00831-4. JSTOR 2153898.
  • McKay, J.; Stauduhar, R. P. (1997). "Finding relations among the roots of an irreducible polynomial". Proceedings of ISSAC'97. Maui. pp. 75–77. doi:10.1145/258726.258752.
  • Noro, M.; McKay, J. (1997). "Computation of replicable functions on RISA/Asir". Proceedings of PASCO'97. Maui. pp. 130–138. doi:10.1145/266670.266713.
  • McKay, J. (1997). The essentials of moonshine. ICU Suzuki Conf.
  • McKay, J.; Sebbar, A. (1998). "Fuchsian groups, Schwarzians, and lattices". Comptes Rendus Acad. Sci. Paris 327 (4): 343–348. doi:10.1016/S0764-4442(99)80045-7.
  • McKay, J. (1999). "The semi-affine Coxeter-Dynkin diagram and G < SU2". Can. J. Math. 51: 1226–1229. doi:10.4153/cjm-1999-054-9.
  • McKay, J. (1999). "Semi-affine Coxeter-Dynkin graphs and G < SU2". arXiv:math/9907089.
  • Harnad, J.; McKay, J. (2000). "Modular Solutions to Equations of Halphen Type". Proceedings of the Royal Society A 456: 261–294. doi:10.1098/rspa.2000.0517. MR 1811320.
  • Harnad, J.; McKay, J. (2000). "Modular Invariants and Generalized Halphen Systems". C. R. M. Proc. 25: 181–195. MR 1771721.
  • McKay, J.; Sebbar, A. (2000). "Fuchsian groups, Automorphic functions, and Schwarzians". Math. Annalen 318 (2): 255–275. doi:10.1007/s002080000116.
  • Matzat, B.; McKay, J.; Yokoyama, Y. (2000). "Algorithmic Methods in Galois Theory". J. Symb. Comp. 30: 631–872. doi:10.1006/jsco.2000.0389.
  • McKay, J.; Sebbar, A. (2001), "Arithmetic Semistable Elliptic Surfaces", Proceedings of Moonshine Workshop
  • McKay, J.; Sebbar, A. (2001), "Proceedings on Moonshine and Related Topics", CRM Proceedings and Lecture Notes 30
  • Ford, D.J.; McKay, J. (2002). "Monstrous Moonshine - Problems Arising I, Tate Characters".
  • Cox, D. A.; McKay, J.; Stevenhagen, P. (2004). "Principal Moduli and Class Fields". Bulletin of the London Mathematical Society 36 (1): 3–12. doi:10.1112/S0024609303002583.
  • Conway, J.; McKay, J.; Sebbar, A. (2004). "On the discrete groups of Moonshine". Proc. Amer. Math. Soc. 132: 2233–2240. doi:10.1090/S0002-9939-04-07421-0.
  • McKay, J.; Sebbar, Abdellah (2007). "Replicable Functions: An introduction". Frontiers in Number Theory, Physics, and Geometry, II. Springer. pp. 373–386. doi:10.1007/978-3-540-30308-4_10.
  • McKay, John; Sevilla, David (2008). "Aplicacion de la descomposicion racional univariada a monstrous moonshine". arXiv:0805.2311.
  • McKay, John; Sevilla, David (2008). "Decomposing replicable functions". LMS J. Comput. Math. 11: 146–171. doi:10.1112/s1461157000000553. MR 2410918.
  • McKay, J. (2009), "Introduction and Background", Groups and Symmetries. From Neolithic Scots to John McKay, CRM Proceedings and Lecture Notes 47, Am. Math. Soc, pp. 1–2
  • Conway, John; McKay, J.; Trojan, Allan (2010). "Galois groups over function fields of positive characteristic". Proc. of the AMS 138: 1205–1212. doi:10.1090/S0002-9939-09-10130-2.

References

  1. ↑ John McKay at the Mathematics Genealogy Project

External links