John McKay (mathematician)

John K. S. McKay (18 November 1939 – 19 April 2022) was a British-Canadian mathematician and academic who worked at Concordia University, known for his discovery of monstrous moonshine, his joint construction of some sporadic simple groups, for the McKay conjecture in representation theory, and for the McKay correspondence relating certain finite groups to Lie groups.

Biography

McKay was educated at Dulwich College, earned his Bachelor and Diploma in 1961 and 1962 at the University of Manchester, and his PhD in 1971 from the University of Edinburgh. Since 1974 he worked at 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 organised by the Université de Montréal and Concordia University honouring four decades of the work of John McKay.

See also

• ADE classification
• Centre de Recherches Mathématiques

Publications

• McKay, J. (1965). "Algorithm 262: Number of restricted partitions of N". Comm. ACM. 8 (8): 493. doi:10.1145/365474.366060. S2CID 38345023.
• McKay, J. (1965). "Algorithm 263: Partition generator". Comm. ACM. 8 (8): 493. doi:10.1145/365474.366063. S2CID 42406548.
• McKay, J. (1965). "Algorithm 264: Map of partitions into integers". Comm. ACM. 8 (8): 493. doi:10.1145/365474.366060. S2CID 38345023.
• McKay, J. (1967). "On the representation of symmetric polynomials". Comm. ACM. 10 (7): 428–429. doi:10.1145/363427.363452. S2CID 6567684.
• McKay, J. (1967). "Symmetric group characters". Comm. ACM. 10 (7): 451–452. doi:10.1145/363427.363475. S2CID 35621790.
• McKay, J.; Bratley, P. (1967). "Algorithm 305: Symmetric polynomials". Comm. ACM. 10 (7): 450. doi:10.1145/363427.363465. S2CID 2516435.
• McKay, J.; Bratley, P. (1967). "Algorithm 313: Multi-dimensional partition generator". Comm. ACM. 10 (10): 666. doi:10.1145/363717.363783. S2CID 52857652.
• 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. Bibcode:1967PCPS...63.1097A. doi:10.1017/S0305004100042171. S2CID 122796911.
• 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. S2CID 1464597.
• McKay, J. (1968). "Remark on algorithm 305: Symmetric Polynomials". Comm. ACM. 11 (4): 272. doi:10.1145/362991.363049. S2CID 26735889.
• McKay, J. (1968). "On the evaluation of multiplicative combinatorial expressions". Comm. ACM. 11 (6): 492. doi:10.1145/363347.363357. S2CID 31908553.
• McKay, J. (1968), "A method of computing the character table of a finite group", in Churchhouse, R. F.; Herz (eds.), 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. S2CID 207632838.
• McKay, J. (1970). "Algorithm 391: Unitary symmetric polynomials". Comm. ACM. 13 (8): 512. doi:10.1145/362705.362719. S2CID 18952245.
• McKay, J. (1970), "The construction of the character table of a finite group from generators and relations", in Leech (ed.), Computational problems in abstract algebra, Pergamon Press, pp. 89–100
• McKay, J. (1970), "Multi-dimensional partitions", in Welsh (ed.), Combinatorial theory and its applications, Academic Press
• McKay, J. (1971), "Subgroups and permutation characters", in Birkhoff; Hall (eds.), 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). "Proceedings of the second ACM symposium on Symbolic and algebraic manipulation - SYMSAC '71". 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. S2CID 62794130.
• McKay, J.; Regener, E. (1974). "Algorithm 482:Transitivity sets". Comm. ACM. 17 (8): 470. doi:10.1145/361082.361098. S2CID 26781915.
• McKay, J. (1974), "Computing with finite simple groups", Proceedings 2nd International conference in group theory, vol. 372, Springer-Verlag, pp. 448–452
• Jonsson, W.; McKay, J. (1976). "More about the Mathieu group". Canadian Journal of Mathematics. 28 (5): 929–937. doi:10.4153/cjm-1976-090-x. MR 0427103. S2CID 120770926.
• McKay, J. (1976). "The largest degrees of irreducible characters of the symmetric group". Mathematics of Computation. 30 (135): 624–631. doi:10.2307/2005331. JSTOR 2005331.
• Fischer, J.; McKay, J. (1978). "The non-abelian simple groups G, |G| < 10⁶ - maximal subgroups". Mathematics of Computation. 32 (144): 1293–1302. doi:10.2307/2006354. 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 (3): 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. doi:10.2307/2006317. JSTOR 2006317.
• McKay, J. (1980). "Graphs singularities and finite groups". Proc. of 1979 Santa Cruz group theory conference. AMS Symposia in Pure Mathematics. Vol. 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. Bibcode:1981JMP....22.2770M. 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. (ed.), Computing in Groups, Academic Press, pp. 297–299, MR 0760664
• Dummit, D.; Kisilevsky, H.; McKay, J. (1985). "Multiplicative products of η-functions". Finite groups—coming of age (Montreal, Que., 1982). Contemporary Mathematics. Vol. 45. Providence, RI: American Mathematical Society. pp. 89–98. doi:10.1090/conm/045/822235. MR 0822235.
• McKay, J., ed. (1985). Finite groups—coming of age (Montreal, Que., 1982). Contemporary Mathematics. Vol. 45. Providence, RI: American Mathematical Society. doi:10.1090/conm/045. ISBN 9780821850473.
• 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. Vol. 204. Springer-Verlag. pp. 535–536. doi:10.1007/3-540-15984-3_324. ISBN 978-3-540-15984-1.
• McKay, J.; Stauduhar, R. (1987). "Coda to a theorem of Schur". Crelle's Journal. 377: 219–220.
• McKay, J. (1987). "On computing discriminants". Amer. Math. Monthly. 94 (6): 523–527. doi:10.2307/2322843. JSTOR 2322843.
• McKay, J. (1988), "Advances in computational Galois theory", in Tangora (ed.), Computers in Algebra, vol. 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 (eds.), Computer Algebra, vol. 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 (3): 221–229. doi:10.1007/bf02864394. S2CID 121956370.
• Darmon, H.; McKay, J. (1991). "A continued fraction and fixed-point-free permutations". Amer. Math. Monthly. 98 (1): 25–26. doi:10.2307/2324031. 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), "Completely replicable functions", in Liebeck; Saxl (eds.), Groups, Combinatorics and Geometry, LMS Lecture Note Series, vol. 165, Cam. Univ. Press, pp. 87–98, doi:10.1017/CBO9780511629259.010, MR 1200252
• 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. Bibcode:1994MaCom..63..749C. 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 (13): 5175–5193. doi:10.1080/00927879408825127.
• McKay, J. (1995). "A note on the elliptic curves of Harada-Lang". In Arasu, K. T. (ed.). 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. Comput. 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. Bibcode:1996MaCom..65.1295C. 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. Bibcode:1997MaCom..66..823M. doi:10.1090/S0025-5718-97-00831-4. JSTOR 2153898.
• McKay, J.; Stauduhar, R. P. (1997). "Proceedings of the 1997 international symposium on Symbolic and algebraic computation – ISSAC '97". Proceedings of ISSAC'97. Maui. pp. 75–77. doi:10.1145/258726.258752. ISBN 0897918754.
• Noro, M.; McKay, J. (1997). "Proceedings of the second international symposium on Parallel symbolic computation - PASCO '97". Proceedings of PASCO'97. Maui. pp. 130–138. doi:10.1145/266670.266713. ISBN 0897919513.
• McKay, J. (1997). The essentials of moonshine. ICU Suzuki Conf.
• McKay, J.; Sebbar, A. (1998). "Fuchsian groups, Schwarzians, and lattices". Comptes rendus de l'Académie des Sciences de Paris. 327 (4): 343–348. Bibcode:1998CRASM.327..343M. 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. arXiv:math/9907089. doi:10.4153/cjm-1999-054-9. S2CID 13113096.
• 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 (1994): 261–294. arXiv:solv-int/9804006. Bibcode:2000RSPSA.456..261H. doi:10.1098/rspa.2000.0517. MR 1811320. S2CID 15397541.
• 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. S2CID 55439399.
• Matzat, B.; McKay, J.; Yokoyama, Y. (2000). "Algorithmic Methods in Galois Theory". J. Symb. Comput. 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, vol. 30
• Ford, D.J.; McKay, J. (2002). "Monstrous Moonshine – Problems Arising I, Tate Characters". {{cite journal}}: Cite journal requires |journal= (help)
• Cox, D. A.; McKay, J.; Stevenhagen, P. (2004). "Principal Moduli and Class Fields". Bulletin of the London Mathematical Society. 36 (1): 3–12. arXiv:math/0311202. doi:10.1112/S0024609303002583. S2CID 119718080.
• Conway, J.; McKay, J.; Sebbar, A. (2004). "On the discrete groups of Moonshine". Proc. Amer. Math. Soc. 132 (8): 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 [math.NT].
• McKay, John; Sevilla, David (2008). "Decomposing replicable functions". LMS Journal of Computation and Mathematics. 11: 146–171. arXiv:0803.3419. doi:10.1112/s1461157000000553. MR 2410918. S2CID 21855178.
• McKay, J. (2009), "Introduction and Background", Groups and Symmetries. From Neolithic Scots to John McKay, CRM Proceedings and Lecture Notes, vol. 47, Am. Math. Soc, pp. 1–2
• Conway, John; McKay, J.; Trojan, Allan (2010). "Galois groups over function fields of positive characteristic". Proc. AMS. 138 (4): 1205–1212. arXiv:0811.0076. doi:10.1090/S0002-9939-09-10130-2. S2CID 16864449.

External links

• John McKay web page at CRM
• CRM-Fields prize