• Corpus ID: 119711685

A short introduction to Monstrous Moonshine

@article{Tatitscheff2019ASI,
  title={A short introduction to Monstrous Moonshine},
  author={Valdo Tatitscheff},
  journal={arXiv: Number Theory},
  year={2019}
}
This paper is an introduction to the Monstrous Moonshine correspondence aiming at an undergraduate level. We review first the classification of finite simple groups and some properties of the monster $\mathbb{M}$, and then the theory of classical modular functions and modular forms, in order to define Klein's $J$-invariant. Eventually we turn to the correspondence itself, the historical framework in which it appeared, the ideas that were developped in its proof, and its status nowadays. 
View PDF on arXiv
2 Citations
Highly Influential Citations
1
Background Citations
1
Methods Citations
1

Figures from this paper

2 Citations

Conway, Knots and Groups

John Conway was one of the most versatile mathematicians in modern times, who made important contributions to several areas of mathematics. In this article, we highlight his contributions to two…

Mathematicians on the Radio: Seven Metaphors for Doing and Communicating Mathematics

ABSTRACT Metaphors are recognized as bridging scientists’ challenges in communication with the public. In mathematics, however, which often involves abstract concepts and relations, less attention…

References

SHOWING 1-10 OF 41 REFERENCES

Elementary introduction to Moonshine

These notes provide an elementary (and incomplete) sketch of the objects and ideas involved in monstrous and umbral moonshine. They were the basis for a plenary lecture at the 18th International…

Monstrous moonshine and monstrous Lie superalgebras

We prove Conway and Norton's moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by Frenkel, Lepowsky and Meurman. To do this we use the no-ghost…

O'Nan moonshine and arithmetic

Answering a question posed by Conway and Norton in their seminal 1979 paper on moonshine, we prove the existence of a graded infinite-dimensional module for the sporadic simple group of O'Nan, for…

Monstrous Moonshine: The First Twenty‐Five Years

Twenty‐five years ago, Conway and Norton published in this journal their remarkable paper ‘Monstrous Moonshine’, proposing a completely unexpected relationship between finite simple groups and…

Umbral Moonshine

We describe surprising relationships between automorphic forms of various kinds, imaginary quadratic number fields and a certain system of six finite groups that are parameterised naturally by the…

Monstrous moonshine

  • Ozlem Umdu
  • Mathematics
    100 Years of Math Milestones
  • 2019
Monstrous Moonshine states a relationship between the j-function and the Monster group. The j-function is a complex-valued function with the property that any modular function can be written as a…

TASI Lectures on Moonshine

  • V. AnagiannisMiranda C N Cheng
  • Physics
    Proceedings of Theoretical Advanced Study Institute Summer School 2017 "Physics at the Fundamental Frontier" — PoS(TASI2017)
  • 2018
The word moonshine refers to unexpected relations between the two distinct mathematical structures: finite group representations and modular objects. It is believed that the key to understanding…

Proof of the umbral moonshine conjecture

The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay–Thompson series are certain distinguished mock modular forms.…

Sporadic and Exceptional

We study the web of correspondences linking the exceptional Lie algebras $E_{8,7,6}$ and the sporadic simple groups Monster, Baby and the largest Fischer group. This is done via the investigation of…

The classification of finite simple groups I. Simple groups and local analysis

It is indeed unfortunate that Richard Brauer did not live to see the complete classification of the finite simple groups. He had devoted the past thirty years largely to their study and it is…