May 27, 2021
These notes stem from lectures given by the first author (JM) at the 2008 "Moonshine Conference in Kashiwa" and contain a number of new perspectives and observations on Monstrous Moonshine. Because many new points have not appeared anywhere in print, it is thought expedient to update, annotate and clarify them (as footnotes), an editorial task which the second author (YHH) is more than delighted to undertake. We hope the various puzzles and correspondences, delivered in a personal and casual manner, will serve as diversions intriguing to the community.
Similar papers 1
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...
September 19, 1998
This is an informal write up of my talk in Berlin. It gives some background to Goddard's talk (math.QA/9808136) about the moonshine conjectures.
April 19, 2019
Monsters lurk within mathematical as well as literary haunts. I propose to trace some pathways between these two monstrous habitats. I start from Jeffrey Jerome Cohen's influential account of monster culture and explore how well mathematical monsters fit each of his seven theses. The mathematical monsters I discuss are drawn primarily from three distinct but overlapping domains. Firstly, late nineteenth-century mathematicians made numerous unsettling discoveries that threaten...
May 2, 2016
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 Congress on Mathematical Physics, and for a lecture series at the Centre International de Recontres Mathematiques school on "Mathematics of String Theory."
In this note, we provide evidence for new (super) moonshines relating the Monster and the Baby monster to some weakly holomorphic weight 1/2 modular forms defined by Zagier in his work on traces of singular moduli. They are similar in spirit to the recently discovered Thompson moonshine.
September 24, 2002
A content-free expository article about the monster simple group.
November 24, 2014
Monstrous moonshine relates distinguished modular functions to the representation theory of the monster. The celebrated observations that 196884=1+196883 and 21493760=1+196883+21296876, etc., illustrate the case of the modular function j-744, whose coefficients turn out to be sums of the dimensions of the 194 irreducible representations of the monster. Such formulas are dictated by the structure of the graded monstrous moonshine modules. Recent works in moonshine suggest deep...
June 25, 1999
In these notes, based on lectures given in Istanbul, we give an introduction both to Monstrous Moonshine and to the classification of rational conformal field theories, using this as an excuse to explore several related structures and go on a little tour of modern math. We will discuss Lie algebras, modular functions, the finite simple group classification, vertex operator algebras, Fermat's Last Theorem, category theory, (generalised) Kac-Moody algebras, denominator identiti...
February 26, 2016
Kasha-eating dragons introduce advanced mathematics. The goal of this paper is twofold: to entertain people who know advanced mathematics and inspire people who don't.
April 11, 2018
Monstrous Moonshine was extended in two complementary directions during the 1980s and 1990s, giving rise to Norton's Generalized Moonshine conjecture and Ryba's Modular Moonshine conjecture. Both conjectures have been unconditionally resolved in the last few years, so we describe some speculative conjectures that may extend and unify them.