ID: math/9809110

What is moonshine?

September 19, 1998

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Summary on Theoretical Aspects

October 17, 2009

82% Match
Jacques Soffer
High Energy Physics - Phenom...

During the five days of this conference a very dense scientific program has enlighted our research fields, with the presentation of large number of interesting lectures. I will try to summarize the theoretical aspects of some of these new results.

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Moonshine elements in elliptic cohomology

December 6, 2007

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Jack Morava
Algebraic Topology
Representation Theory

This is a historical talk about the recent confluence of two lines of research in equivariant elliptic cohomology, one concerned with connected Lie groups, the other with the finite case. These themes come together in (what seems to me remarkable) work of N. Ganter, relating replicability of McKay-Thompson series to the theory of exponential cohomology operations.

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Moonshine

November 24, 2014

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John F. R. Duncan, Michael J. Griffin, Ken Ono
Representation Theory
Number Theory

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...

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Monstrous and Generalized Moonshine and Permutation Orbifolds

November 27, 2008

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Michael P. Tuite
Quantum Algebra

We consider the application of permutation orbifold constructions towards a new possible understanding of the genus zero property in Monstrous and Generalized Moonshine. We describe a theory of twisted Hecke operators in this setting and conjecture on the form of Generalized Moonshine replication formulas.

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The Monster, the Baby Monster and Traces of Singular Moduli

May 15, 2017

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Victor Godet
Representation Theory
Number 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.

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The algebraic meaning of genus-zero

December 12, 2005

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T. Gannon
Number Theory
Quantum Algebra

The Conway--Norton conjectures unexpectedly related the Monster with certain special modular functions (Hauptmoduls). Their proof by Borcherds et al was remarkable for demonstrating the rich mathematics implicit there. Unfortunately Moonshine remained almost as mysterious after the proof as before. In particular, a computer check - as opposed to a general conceptual argument - was used to verify the Monster functions equal the appropriate modular functions. This, the so-calle...

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Hecke operators in equivariant elliptic cohomology and generalized moonshine

June 20, 2007

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Nora Ganter
Algebraic Topology
Group Theory

This paper studies connections between generalized moonshine and elliptic cohomology with a focus on the action of the Hecke correspondence and its implications for the notion of replicability.

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Generalised Umbral Moonshine

August 28, 2016

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Miranda C. N. Cheng, Lange Paul de, Daniel P. Z. Whalen
Representation Theory
Number Theory

Umbral moonshine describes an unexpected relation between 23 finite groups arising from lattice symmetries and special mock modular forms. It includes the Mathieu moonshine as a special case and can itself be viewed as an example of the more general moonshine phenomenon which connects finite groups and distinguished modular objects. In this paper we introduce the notion of generalised umbral moonshine, which includes the generalised Mathieu moonshine [Gaberdiel M.R., Persson ...

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The Limits of Mathematics---The Book

July 7, 1994

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G. J. IBM Research Division Chaitin
Chaotic Dynamics

This is a revised version of the course notes handed to each participant at the limits of mathematics short course, Orono, Maine, June 1994.

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An Overview of Penumbral Moonshine

September 20, 2021

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John F. R. Duncan, Jeffrey A. Harvey, Brandon C. Rayhaun
Representation Theory

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 groups and vector-valued modular forms of a certain kind. We call this penumbral moonshine. We introduce and explain some features of this phenomenon in this work.

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