Postcards from the edge, or Snapshots of the theory of generalised Moonshine
T. Gannon
TL;DR
This paper explores the theory of Generalised Moonshine, extending the classical Monstrous Moonshine phenomenon, and provides insights into its underlying mathematical structures and connections.
Contribution
It offers a comprehensive overview of the theory of Generalised Moonshine, highlighting new perspectives and connections beyond the classical Monstrous Moonshine.
Findings
Snapshots of the mathematical structure of Generalised Moonshine
Connections between Moonshine phenomena and other areas of mathematics
Insights into the extension of Monstrous Moonshine beyond the Monster group
Abstract
In 1978, John McKay made an intriguing observation: 196884=196883+1. Monstrous Moonshine is the collection of questions (and a few answers) inspired by this observation. Like moonlight itself, Moonshine is an indirect phenomenon. Just as in the theory of moonlight one must introduce the sun, so in the theory of Moonshine one should go well beyond the Monster. Much as a talk discussing moonlight may include a few words on sunsets or comet tails, so will we see snapshots of the Theory of Generalised Moonshine.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Algebraic Geometry and Number Theory