35 citations · 250 across the 28 of their papers we have counts for
24 papers · 1 filter
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…
From the Monster to Thompson to O'Nan
John F. R. Duncan
The commencement of monstrous moonshine is a connection between the largest sporadic simple group---the monster---and complex elliptic curves. Here we explain how a closer look at…
Pariah moonshine
John F. R. Duncan, Michael H. Mertens, Ken Ono
Finite simple groups are the building blocks of finite symmetry. The effort to classify them precipitated the discovery of new examples, including the monster, and six pariah group…
Meromorphic Jacobi Forms of Half-Integral Index and Umbral Moonshine Modules
Miranda C. N. Cheng, John F. R. Duncan
In this work we consider an association of meromorphic Jacobi forms of half-integral index to the pure D-type cases of umbral moonshine, and solve the module problem for four of th…
Super Vertex Algebras, Meromorphic Jacobi Forms and Umbral Moonshine
John F. R. Duncan, Andrew O'Desky
The vector-valued mock modular forms of umbral moonshine may be repackaged into meromorphic Jacobi forms of weight one. In this work we constructively solve two cases of the meromo…
Derived Equivalences of K3 Surfaces and Twined Elliptic Genera
John F. R. Duncan, Sander Mack-Crane
We use the unique canonically-twisted module over a certain distinguished super vertex operator algebra---the moonshine module for Conway's group---to attach a weak Jacobi form of…
Proof of the Umbral Moonshine Conjecture
John F. R. Duncan, Michael J. Griffin, Ken Ono
The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock…
The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System
John F. R. Duncan, Jeffrey A. Harvey
We use canonically-twisted modules for a certain super vertex operator algebra to construct the umbral moonshine module for the unique Niemeier lattice that coincides with its root…
Moonshine
John F. R. Duncan, Michael J. Griffin, Ken Ono
Monstrous moonshine relates distinguished modular functions to the representation theory of the monster. The celebrated observations that 196884=1+196883 and 21493760=1+196883+2129…
The Moonshine Module for Conway's Group
John F. R. Duncan, Sander Mack-Crane
We exhibit an action of Conway's group---the automorphism group of the Leech lattice---on a distinguished super vertex operator algebra, and we prove that the associated graded tra…
Umbral Moonshine and the Niemeier Lattices
Miranda C. N. Cheng, John F. R. Duncan, Jeffrey A. Harvey
In this paper we relate umbral moonshine to the Niemeier lattices: the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier latt…
Umbral Moonshine
Miranda C. N. Cheng, John F. R. Duncan, Jeffrey A. Harvey
We describe surprising relationships between automorphic forms of various kinds, imaginary quadratic number fields and a certain system of six finite groups that are parameterised…
The Largest Mathieu Group and (Mock) Automorphic Forms
Miranda C. N. Cheng, John F. R. Duncan
We review the relationship between the largest Mathieu group and various modular objects, including recent progress on the relation to mock modular forms. We also review the connec…
On Rademacher Sums, the Largest Mathieu Group, and the Holographic Modularity of Moonshine
Miranda C. N. Cheng, John F. R. Duncan
Recently a conjecture has been proposed which attaches (mock) modular forms to the largest Mathieu group. This may be compared to monstrous moonshine, in which modular functions ar…
Rademacher sums, moonshine and gravity
John F. R. Duncan, Igor B. Frenkel
In 1939 Rademacher derived a conditionally convergent series expression for the elliptic modular invariant, and used this expression- the first Rademacher sum - to verify its modul…
Vertex operators and sporadic groups
John F. Duncan
In the 1980's, the work of Frenkel, Lepowsky and Meurman, along with that of Borcherds, culminated in the notion of vertex operator algebra, and an example whose full symmetry grou…
Arithmetic groups and the affine E8 Dynkin diagram
John F. Duncan
Several decades ago, John McKay suggested a correspondence between nodes of the affine E8 Dynkin diagram and certain conjugacy classes in the Monster group. Thanks to Monstrous Moo…
Moonshine for Rudvalis's sporadic group II
John F. Duncan
In Part I we introduced the notion of enhanced vertex operator superalgebra, and constructed an example which is self-dual, has rank 28, and whose full symmetry group is a seven-fo…
Moonshine for Rudvalis's sporadic group I
John F. Duncan
We introduce the notion of vertex operator superalgebra with enhanced conformal structure, which is a refinement of the notion of vertex operator superalgebra. We exhibit several e…
Super-moonshine for Conway's largest sporadic group
John F. Duncan
We study a self-dual N=1 super vertex operator algebra and prove that the full symmetry group is Conway's largest sporadic simple group. We verify a uniqueness result which is anal…