John McKay

John KS McKay (born June 16, 1939 in Kent ) is an English mathematician who deals with group theory.

McKay attended the University of Manchester from 1958 , where he worked on the early computers developed there, and received his doctorate in 1970 from the University of Edinburgh under Walter Munn. In the 1960s he was at Caltech and then for a few years at McGill University in Canada and then went to Concordia University in Canada, where he is now a professor.

McKay is known for the discovery (1978) of the "Monstrous Moonshine", the strange connection between the representations of the largest sporadic simple group, the monster, and the Fourier expansion coefficients of the elliptic module function , which are all linear combinations of the degrees of irreducible representations of the monster group :

{\ displaystyle j (\ tau) = {\ frac {1} {q}} + 744 + 196884q + 21493760q ^ {2} + 864299970q ^ {3} + \ cdots}

with . McKay noticed that 196884 is the dimension of Griess algebra, which is one larger than the dimension of the smallest representation of the monster group. ${\ displaystyle \, q = e ^ {2 \ pi i \ tau}}$

The Moonshine properties were studied by John Conway , Simon Norton and Richard Borcherds (who later received the Fields Medal in 1998 for proving the conjecture).

He was also involved in the construction of some sporadic simple finite groups, such as the hero group with Graham Higman .

Another assumption by McKay is the McKay correspondence between the Coxeter-Dynkin diagrams of Lie algebras of the type and the irreducible representations of the finite subgroups of (i.e. the three-dimensional rotation group) or their double superposition ${\ displaystyle A, D, E}$ ${\ displaystyle SO (3)}$ ${\ displaystyle SU (2)}$

His work was recognized at a conference in April 2007 in honor of Concordia University with the University of Montreal. In 2000 he became a Fellow of the Royal Society of Canada . In 2003 he received the CRM Fields Prize from the Canadian mathematical research institute Center de Recherches Mathématiques .

Fonts

with Abdellah Sebbar: Replicable functions, an introduction. In: Pierre Cartier , Bernard Julia , Pierre Moussa, Pierre Vanhove (Eds.): Frontiers in Number Theory, Physics and Geometry II. On Conformal Field Theories, Discrete Groups and Renormalization. Springer, Berlin et al. 2007, ISBN 978-3-540-30307-7 , pp. 373-386.

Web links

Remarks

^ Conway, Norton: Monstrous Moonshine. In: Bulletin of the London Mathematical Society . Vol. 11, No. 3, 1979, pp. 308-339, doi : 10.1112 / blms / 11.3.308 . McKay first shared his observations with John Griggs Thompson , who found further confirmation and mentioned them to Conway.
↑ named after Dieter Held (* 1936).
^ McKay: Graphs, Singularities and Finite Groups. In: Bruce Cooperstein, Geoffrey Mason (Ed.): The Santa Cruz Conference on Finite Groups (= Proceedings of Symposia in Pure Mathematics. 37). American Mathematical Society, Providence RI 1980, ISBN 0-8218-1440-0 , pp. 183-186, 265; David Ford, McKay: Representations and Coxeter Graphs. In: Chandler Davis, Branko Grünbaum , Frank A. Sherk (Eds.): The Geometric Vein. The Coxeter commemorative publication. Springer, New York NY et al. 1981, ISBN 0-387-90587-1 , pp. 549-554, doi : 10.1007 / 978-1-4612-5648-9_36 .

personal data
SURNAME	McKay, John
ALTERNATIVE NAMES	McKay, John KS
BRIEF DESCRIPTION	English mathematician
DATE OF BIRTH	June 16, 1939
PLACE OF BIRTH	Kent

[1] Conway, Norton: Monstrous Moonshine. In: Bulletin of the London Mathematical Society . Vol. 11, No. 3, 1979, pp. 308-339, doi : 10.1112 / blms / 11.3.308 . McKay first shared his observations with John Griggs Thompson , who found further confirmation and mentioned them to Conway.

[2] ter Dieter Held (* 1936).

[3] McKay: Graphs, Singularities and Finite Groups. In: Bruce Cooperstein, Geoffrey Mason (Ed.): The Santa Cruz Conference on Finite Groups (= Proceedings of Symposia in Pure Mathematics. 37). American Mathematical Society, Providence RI 1980, ISBN 0-8218-1440-0 , pp. 183-186, 265; David Ford, McKay: Representations and Coxeter Graphs. In: Chandler Davis, Branko Grünbaum , Frank A. Sherk (Eds.): The Geometric Vein. The Coxeter commemorative publication. Springer, New York NY et al. 1981, ISBN 0-387-90587-1 , pp. 549-554, doi : 10.1007 / 978-1-4612-5648-9_36 .