Abstract
This text is a short and elementary introduction to the ‘monstrous moonshine’ aiming to be as accessible as possible. We first review the classification of finite simple groups out of which the monster naturally arises and the latter’s features that are needed to state the moonshine conjecture of Conway and Norton. Then, we motivate modular functions and forms from the classification of complex tori, with the definitions of the J-invariant and its q-expansion as a goal. We eventually provide evidence for the monstrous moonshine correspondence, state the conjecture, and then introduce the ideas that led to its proof. Lastly, we give a brief account of some recent developments and current research directions in the field.
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Acknowledgement
I am thankful to A. Thomas and S. Tornier for their feedback, to R. Duque for his diligent proofreading, and to the anonymous referee whose comments improved the quality of this article.
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Valdo Tatitscheff is a postdoctoral researcher at Heidelberg University, in Germany. His research interest lies at the interface between string theory, cluster algebras and higher Teichmüller theory.
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Tatitscheff, V. Monstrous Moonshine. Reson 27, 2107–2126 (2022). https://doi.org/10.1007/s12045-022-1508-x
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DOI: https://doi.org/10.1007/s12045-022-1508-x