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Softcover ISBN:  9780821828793 
Product Code:  CRMP/30 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470439446 
Product Code:  CRMP/30.E 
List Price:  $93.00 
MAA Member Price:  $83.70 
AMS Member Price:  $74.40 
Softcover ISBN:  9780821828793 
eBook ISBN:  9781470439446 
Product Code:  CRMP/30.B 
List Price:  $192.00 $145.50 
MAA Member Price:  $172.80 $130.95 
AMS Member Price:  $153.60 $116.40 

Book DetailsCRM Proceedings & Lecture NotesVolume: 30; 2001; 268 ppMSC: Primary 20; 11
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, PicardFuchs equations, and hypergeometric functions.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
ReadershipGraduate students and research mathematicians interested in algebra, number theory, algebraic geometry, and mathematical physics.

Table of Contents

Chapters

Invariants for finite dimensional groups in vertex operator algebras associated to basic representations of affine algebras

Transformation laws for theta functions

Algebrogeometric isomonodromic deformations linking Hauptmoduls: Variation of the mirror map

On McKay’s connection between the affine $E_8$ diagram and the monster

Sylow 2subgroups of simple groups

Yoshida surfaces with Picard number $\rho \geq 17$

Hypergeometric modular forms and supersingular elliptic curves

Fusion rules for ternary and $\mathbb {Z}_2 \times \mathbb {Z}_2$ code vertex operator algebras

The regular representations and the $A_{n}(V)$algebras

Linear dependencies among completely replicable functions

Arithmetic semistable elliptic surfaces

Modular invariance of trace functions on VOAs in many variables

The mirror map for a family of $K$3 surfaces induced from the simplest 3dimensional reflexive polytope

From moonshine to the monster

Hypergeometric functions and nonassociative algebras

Extended affine root systems. V. Elliptic etaproducts and their Dirichlet series

Deflating infinite Coxeter groups to finite groups

Genus two meromorphic conformal field theory

PicardFuchs equations of some families of elliptic curves


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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, PicardFuchs equations, and hypergeometric functions.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
Graduate students and research mathematicians interested in algebra, number theory, algebraic geometry, and mathematical physics.

Chapters

Invariants for finite dimensional groups in vertex operator algebras associated to basic representations of affine algebras

Transformation laws for theta functions

Algebrogeometric isomonodromic deformations linking Hauptmoduls: Variation of the mirror map

On McKay’s connection between the affine $E_8$ diagram and the monster

Sylow 2subgroups of simple groups

Yoshida surfaces with Picard number $\rho \geq 17$

Hypergeometric modular forms and supersingular elliptic curves

Fusion rules for ternary and $\mathbb {Z}_2 \times \mathbb {Z}_2$ code vertex operator algebras

The regular representations and the $A_{n}(V)$algebras

Linear dependencies among completely replicable functions

Arithmetic semistable elliptic surfaces

Modular invariance of trace functions on VOAs in many variables

The mirror map for a family of $K$3 surfaces induced from the simplest 3dimensional reflexive polytope

From moonshine to the monster

Hypergeometric functions and nonassociative algebras

Extended affine root systems. V. Elliptic etaproducts and their Dirichlet series

Deflating infinite Coxeter groups to finite groups

Genus two meromorphic conformal field theory

PicardFuchs equations of some families of elliptic curves