**CRM Proceedings & Lecture Notes**

Volume: 30;
2001;
268 pp;
Softcover

MSC: Primary 20; 11;

Print ISBN: 978-0-8218-2879-3

Product Code: CRMP/30

List Price: $88.00

Individual Member Price: $70.40

**Electronic ISBN: 978-1-4704-3944-6
Product Code: CRMP/30.E**

List Price: $88.00

Individual Member Price: $70.40

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# Proceedings on Moonshine and Related Topics

Share this page *Edited by *
*John McKay; Abdellah Sebbar*

A co-publication of the AMS and Centre de Recherches Mathématiques

This volume contains the proceedings of the Moonshine workshop held at the
Centre de Recherches Mathématiques (CRM) in Montréal. A glance at
the contents will reveal that the connection of some papers to Moonshine is not
immediate; however, Moonshine has proved to be a very fertile area, and it does not
stretch the imagination to believe that many more threads will be drawn
together before we understand what is really going on.

In this volume, all the classical Moonshine themes are presented, namely the
Monster simple group and other finite groups, automorphic functions and forms
and related congruence groups, and vertex algebras and their representations.
These topics appear in either a pure form or in a blend of algebraic geometry
dealing with algebraic surfaces, Picard-Fuchs equations, and hypergeometric
functions.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Readership

Graduate students and research mathematicians interested in algebra, number theory, algebraic geometry, and mathematical physics.

# Table of Contents

## Proceedings on Moonshine and Related Topics

- Cover Cover11
- Title page iii4
- Dedication v6
- Contents vii8
- Preface ix10
- Invariants for finite dimensional groups in vertex operator algebras associated to basic representations of affine algebras 112
- Transformation laws for theta functions 1526
- Algebro-geometric isomonodromic deformations linking Hauptmoduls: Variation of the mirror map 2738
- On McKayβs connection between the affine πΈβ diagram and the monster 3748
- Sylow 2-subgroups of simple groups 4354
- Yoshida surfaces with Picard number πβ₯17 7182
- Hypergeometric modular forms and supersingular elliptic curves 7990
- Fusion rules for ternary and β€βΓβ€β code vertex operator algebras 8596
- The regular representations and the π΄_{π}(π)-algebras 99110
- Linear dependencies among completely replicable functions 117128
- Arithmetic semistable elliptic surfaces 119130
- Modular invariance of trace functions on VOAs in many variables 131142
- The mirror map for a family of πΎ3 surfaces induced from the simplest 3-dimensional reflexive polytope 139150
- From moonshine to the monster 163174
- Hypergeometric functions and non-associative algebras 173184
- Extended affine root systems. V. Elliptic eta-products and their Dirichlet series 185196
- Deflating infinite Coxeter groups to finite groups 223234
- Genus two meromorphic conformal field theory 231242
- Picard-Fuchs equations of some families of elliptic curves 253264
- Back Cover Back Cover1280