Brief Review: Terry Gannon 'Moonshine Beyond the Monster'

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SUMMARY

The discussion centers on Terry Gannon's book 'Moonshine Beyond the Monster' and its foundational paper 'Monstrous Moonshine: the first 25 years' available on ArXiv. The paper serves as a comprehensive survey, detailing the connections between modular forms, the E8 lattice, and the Monster group, while also discussing Borcherds-Kac-Moody algebras. Key concepts such as imaginary time in D26 and the relationships between Mathieu groups and Golay codes are mentioned, although the latter is not fully explored. The book and paper are praised for their depth, with extensive references enhancing their academic value.

PREREQUISITES
  • Understanding of modular forms
  • Familiarity with E8 lattice theory
  • Knowledge of Borcherds-Kac-Moody algebras
  • Basic concepts of group theory, particularly the Monster group
NEXT STEPS
  • Read Terry Gannon's 'Moonshine Beyond the Monster' for an in-depth exploration of the subject
  • Study the ArXiv paper 'Monstrous Moonshine: the first 25 years' for foundational insights
  • Investigate the implications of imaginary time in D26 within theoretical physics
  • Research the connections between Mathieu groups and Golay codes for further understanding
USEFUL FOR

Mathematicians, theoretical physicists, and researchers interested in modular forms, group theory, and the interplay between algebra and geometry will benefit from this discussion.

Dcase
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While perusing the 'Never Ending Book' Site, I came across this link to the Terry Gannon ArXiv paper 'Monstrous Moonshine: the first 25 years'.
http://www.arxiv.org/PS_cache/math/pdf/0402/0402345.pdf

Lieven le Bruyn refers to this as a survey paper [33 pages with 124 references].
It appears to form the framework of the Gannon book, ‘Moonshine Beyond the Monster’ [477 pages, 575 references].

Gannon comprises a masterful effort relating modular forms, E8 and the Leech Lattice to the Monster and VOA for the complex-24D.

He explains the Cartan-like structure of Borcherds-Kac-Moody algebras.

He touches upon the concept of imaginary time for D26.

He does not appear to discuss the string-25D.

He relates Mathieu groups and the bi-monster as "mini-monster" and "maxi-monster", respectively, but does not address their apparent relation to Golay codes.
 
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Dcase said:
While perusing the 'Never Ending Book' Site, I came across this link to the Terry Gannon ArXiv paper 'Monstrous Moonshine: the first 25 years'.
http://www.arxiv.org/PS_cache/math/pdf/0402/0402345.pdf

A very nice find! Thanks. The paper and the references therein are very helpful.
 
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Dcase said:
Terry Gannon ArXiv paper 'Monstrous Moonshine: the first 25 years'.
http://www.arxiv.org/PS_cache/math/pdf/0402/0402345.pdf

Yeah, thanks, Dcase! Fantastic review. Somehow he manages to put

196 884 = 196 883 + 1

on the second line. And over 6 pages of references!

:smile:
 
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