Moonshine beyond the monster describes the general theory of moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection. Download limit exceeded you have exceeded your daily download allowance. The jfunction is a complexvalued function with the property that any. The essentials of monstrous moonshine project euclid. In a recent paper, ono, rolen, and trebatleder relate a monstrous moonshine function to one of the mathieu moonshine functions by constructing products of rational functions of the monstrous hauptmodul via generalized borcherds lifts on mock modular forms.
How did string theory help borcherds solve the monstrous. Borcherds proof, monstrous moonshine and monstrous lie superalgebras, invent. Pdf this paper is an introduction to the monstrous moonshine correspondence aiming at an undergraduate level. Norton in 1979 it is now known that lying behind monstrous moonshine is a vertex operator algebra called the moonshine module or monster vertex algebra constructed by igor. Moonshine master toys with string theory quanta magazine. Tutorial for monstrous moonshine group theory and computational methods, icts, bangalore 05 november 2016 to 14 november 2016 modular forms 1. Open problem umbral moonshine ramanujan described mock theta functions in his last letters to hardy. Sporadic simple groups meet number theory i the largest sporadic group, denoted by f 1 or m, was called the monster by conway. Rademacher sums, moonshine and gravity 853 proof of the moonshine conjecture was given by borcherds in 3. The project gutenberg ebook of the moonstone, by wilkie. The monstrous moonshine conjecture explained request pdf. The jfunction is a modular form that is an invariant of isomor.
Monstrous moonshine and the entropy of the smallest black. It therefore is natural to consider a decomposition of. His web site offers the home distillation handbook. Pdf monstrous moonshine is true richard borcherds proved itand discovered spooky connections. Monstrous moonshine i am currently working with john duncan at emory on areas surrounding monstrous moonshine. Moonshine desmond coles july 2, 2018 abstract moonshine is the surprising connection between two very di erent mathematical objects, the monster group and the jfunction. Monstrous, mathieu and m umbral sam fearn durham university may 2nd, 2016 the energy produced by the breaking down of the atom is a very poor kind of thing.
Mason, monstrous moonshine of higher weight, acta mathematica, 185 2000, 101121. Monstrous moonshine and the entropy of the smallest black hole last update. In fact, the field remains relatively obscure and unknown even to seasoned mathematicians and physicists. Monstrous moonshine refers to the surprising relationship, discovered in the 1970s, between a certain function called the jfunction and the largest finite simple group of order 1054, called the monster group. Monstrous moonshine additional moonshine phenomena generalized monstrous moonshine modular moonshine uni cation. But the hints of a deep connection between the purest of mathematics and the physical. From a physical point of view, the ubiquity of k3 surfaces and the importance of bps spectra in the study of string theory makes this mathieu moonshine potentially much more relevant than the previous monstrous moonshine. However, in spite of all the subsequent spectacular developments related to the monster, the consensus of the experts cf. Anyone who expects a source of power from the transformation of these atoms is talking moonshine. What links here related changes upload file special pages permanent link page information wikidata item cite this. It is available on line for small fee in pdf format.
Modular moonshine ryba 1994 for each gin conjugacy class pa, there is a z 0graded vertex algebra v g over f p with a c mg action, such that the graded brauer character of each pregular h2c mg on v g is equal to the monstrous moonshine function t gh. The craft of whiskey distilling free ebook clawhammer. Construct a vertex operator algebrav, a graded algebra affording the moonshine representations of m. Uvadare digital academic repository umbral moonshine. The lifting procedure is that introduced in a paper by bruinierono. Monstrous moonshine bulletin of the london mathematical society.
The moonstone was the only object that interested him in the smallest degree. Department of physics indian institute of technology madras. When i tell people i study moonshine, it usually invites puzzled looks. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Conferences honorable mention poster at jmm 2020 will give talk at eagle undergraduate mathematics conference papers jasmine camero, trevor hyde, chiehmi lu, bianca thompson, eric zhu. After looking at it silently for so long a time that miss rachel began to get confused, he said to her in his cool immovable way, if you ever go to. In number theory, john proved as a graduate student the conjecture by edward waring that every integer could be written as.
The order of the monster is 246 320 59 76 112 3 17 19 23 29 31 41 47 59 71 i monstrous moonshineis the connection of the monster with a. Pdf, dvi and plain tex files of papers and preprints by r. Monstrous moonshine states a relationship between the jfunction and the monster group. The history of monstrous moonshine can be summarized as follows. Monstrous moonshine in a certain way, since we somehow \illegally obtain and smuggle information from one side of the theory to the other. The book has been translated from swedish to english and written under the pseudonym of ola norrman. In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group m and modular functions, in particular, the j function.
Generalized moonshine is now interpreted as a statement about orbifold conformal. He also investigated lattices in higher dimensions, and with neil sloane authored sphere packings, lattices, and groups 1988. A quick summary of the recent amazing discoveries about the fischergriess. Mock modular mathieu moonshine modules miranda c n cheng1, xi dong2, john f r duncan3, sarah harrison2, shamit kachru2 and timm wrase 2 1 introduction the investigation of moonshine connecting modular objects, sporadic groups, and 2d conformal field theories has been revitalized in recent years by the discovery of several new classes of examples. Representations of the moonshine module vertex operator algebra, contemp. Borcherds, richard 1992, monstrous moonshine and monstrous lie superalgebras pdf, invent.
Pdf a short introduction to monstrous moonshine researchgate. This paper is an introduction to the monstrous moonshine correspondence aiming at an undergraduate level. Cumulative biobibliography university of california, santa cruz chongying dong. Building a home distillation apparatus one of the best, references to start with is from gert strands company in sweden. Monstrous moonshine was extended in two complementary directions during the 1980s and 1990s, giving rise to nortons generalized moonshine conjecture and rybas modular moonshine conjecture. Sam bangs and moonshine pdf sam, bangs and moonshine is a popular 1966 book by evaline ness. First, let me state a simplified version of the monstrous moonshine wikipedia conjecture. Monstrous moonshine relates distinguished modular functions to the representation theory of the monster. The craft of whiskey distilling free ebook whether youre looking to open up a distillery, want to make your own moonshine whiskey down in the hollar, or simply like reading up on the topic of alcoholic beverages, youre going to want to know about this awesome free ebook weve uncovered. Secondquantized mathieu moonshine international press. In the classi cation of nite simple groups, the monster group is the largest sporadic group. Leech7 constructs the leech lattice, which talks to both sides of monstrous moonshine. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory. The conjecture states that the numbers 196,883 and 196,884 that appear at two seemingly totally different places of mathematics are so close for a rational.
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