3 papers
math.GR2026
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…
math.RT2025
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…
math.RT2025
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…