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In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the j function. The initial numerical observation was made by John McKay in 1978, and the phrase was coined by John Conway and Simon P. Norton in 1979.[1][2][3]
The monstrous moonshine is now known to be underlain by a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James Lepowsky, and Arne Meurman in 1988, which has the monster group as its group of symmetries. This vertex operator algebra is commonly interpreted as a structure underlying a two-dimensional conformal field theory, allowing physics to form a bridge between two mathematical areas. The conjectures made by Conway and Norton were proven by Richard Borcherds for the moonshine module in 1992 using the no-ghost theorem from string theory and the theory of vertex operator algebras and generalized Kac–Moody algebras.
^A short introduction to Monstrous Moonshine
Valdo Tatitscheff
January 24, 2019
^J. Conway and S. Norton. Monstrous Moonshine. Bull. Lond. Math. Soc., 11:308–
339, 1979
^Mathematicians Chase Moonshine’s Shadow Erica Klarreich
March 12, 2015 https://www.quantamagazine.org/mathematicians-chase-moonshine-string-theory-connections-20150312/
and 22 Related for: Monstrous moonshine information
In mathematics, monstrousmoonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular...
further developed by John Horton Conway and Simon Norton who called it monstrousmoonshine because it seemed so far fetched. In 1992, Richard Borcherds constructed...
baby monster. Conway and Norton suggested in their 1979 paper that monstrousmoonshine is not limited to the monster, but that similar phenomena may be...
Conway and Norton formulated the complex of conjectures known as monstrousmoonshine. This subject, named by Conway, relates the monster group with elliptic...
similar to the situation with monstrousmoonshine during the 1980s: Atkin, Fong, and Smith showed by computation that a moonshine module exists in 1980, but...
both trivial. Conway and Norton suggested in their 1979 paper that monstrousmoonshine is not limited to the monster, but that similar phenomena may be...
James Lepowsky, and Arne Meurman. R. Borcherds used it to prove the monstrousmoonshine conjectures, by applying the Goddard–Thorn theorem of string theory...
awarded the Fields Medal in 1998. He is well known for his proof of monstrousmoonshine using ideas from string theory. Borcherds was born in Cape Town,...
Leech Lattice. Conway and Norton suggested in their 1979 paper that monstrousmoonshine is not limited to the monster. Larissa Queen and others subsequently...
H. Conway and Simon P. Norton suggested in their 1979 paper that monstrousmoonshine is not limited to the monster, but that similar phenomena may be...
transpositions. Conway and Norton suggested in their 1979 paper that monstrousmoonshine is not limited to the monster, but that similar phenomena may be...
group. The monster group is one of two principal constituents in the monstrousmoonshine conjecture by Conway and Norton, which relates discrete and non-discrete...
function and the modular discriminant, which connection is deepened by Monstrousmoonshine, a development that related modular functions to the Monster group...
are shown. Conway and Norton suggested in their 1979 paper that monstrousmoonshine is not limited to the monster. Larissa Queen and others subsequently...
3 elements. Conway and Norton suggested in their 1979 paper that monstrousmoonshine is not limited to the monster, but that similar phenomena may be...
monster group. Conway and Norton suggested in their 1979 paper that monstrousmoonshine is not limited to the monster, but that similar phenomena may be...
umbral moonshine conjecture. This conjecture was formulated by Miranda Cheng, John Duncan, and Jeff Harvey, and is a generalization of the monstrous moonshine...
3 elements. Conway and Norton suggested in their 1979 paper that monstrousmoonshine is not limited to the monster, but that similar phenomena may be...
2-2-3 triangles that share the fixed type 3 side. In analogy to monstrousmoonshine for the monster M, for Co3, the relevant McKay-Thompson series is...
algebras have proven useful in purely mathematical contexts such as monstrousmoonshine and the geometric Langlands correspondence. The related notion of...
reflected there, as well as some new ones, such as came out of the monstrousmoonshine theory. Analogues of several special functions have been defined...
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