Unravelling Mathieu moonshine

Rational Generalised Moonshine from Abelian Orbifoldings of the Moonshine Module

We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p = 2, 3, 5, 7 and the other of order pk for k = 1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients ...

Problems in moonshine

The talk at the I.C.C.M. was an introduction to moonshine. As there are already several survey articles on what is known about moonshine ([B94], [B99], [D-M94], [DM96], [F-H98], [J]), this paper differs from the talk and will concentrate mainly on what we do not know about it. Moonshine is not a well defined term, but everyone in the area recognizes it when they see it. Roughly speaking, it mea...

P. Mathieu

Generalized Moonshine Ii: Borcherds Products

The goal of this paper is to construct infinite dimensional Lie algebras using infinite product identities, and to use these Lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex algebras and Lie algebras. The Lie algebras that we construct conjecturally appear in an orbifold conformal field theory with symmetries given by the monster ...

Moonshine: Distilling with Cheap Convolutions

Model distillation compresses a trained machine learning model, such as a neural network, into a smaller alternative such that it could be easily deployed in a resource limited setting. Unfortunately, this requires engineering two architectures: a student architecture smaller than the first teacher architecture but trained to emulate it. In this paper, we present a distillation strategy that pr...