35 citations · 250 across the 28 of their papers we have counts for
39 papers
Modular Functions and the Monstrous Exponents
John F. R. Duncan, Holly Swisher
We present a modular function-based approach to explaining, for primes larger than 3, the exponents that appear in the prime decomposition of the order of the monster finite simple…
Rational K3 Homotopy and the Largest Mathieu Group
Federico Carta, John F. R. Duncan, Yang-Hui He
We interpret the ranks of the rational homotopy groups of a K3 surface as dimensions of representations for the largest sporadic simple Mathieu group. We then construct a vertex al…
Class Numbers, Congruent Numbers and Umbral Moonshine
Miranda C. N. Cheng, John F. R. Duncan, Michael H. Mertens
In earlier work we initiated a program to study relationships between finite groups and arithmetic geometric invariants of modular curves in a systematic way. In the present work w…
Modular Products and Modules for Finite Groups
John F. R. Duncan, Jeffrey A. Harvey, Brandon C. Rayhaun
Motivated by the appearance of penumbral moonshine, and by evidence that penumbral moonshine enjoys an extensive relationship to generalized monstrous moonshine via infinite produc…
Two New Avatars of Moonshine for the Thompson Group
John F. R. Duncan, Jeffrey A. Harvey, Brandon C. Rayhaun
The Thompson sporadic group admits special relationships to modular forms of two kinds. On the one hand, last century's generalized moonshine for the monster equipped the Thompson…
An Overview of Penumbral Moonshine
John F. R. Duncan, Jeffrey A. Harvey, Brandon C. Rayhaun
As Mathieu moonshine is a special case of umbral moonshine, Thompson moonshine (in half-integral weight) is a special case of a family of similar relationships between finite group…