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Full Description
This volume contains the proceedings of the Moonshine workshop held at the Centre de Recherches Mathematiques (CRM) in Montreal. 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.
Contents
Invariants for finite dimensional groups in vertex operator algebras associated to basic representations of affine algebras by A. Baker and H. Tamanoi Transformation laws for theta functions by C. Dong and G. Mason Algebro-geometric isomonodromic deformations linking Hauptmoduls: Variation of the mirror map by C. F. Doran On McKay's connection between the affine $E_8$ diagram and the monster by G. Glauberman and S. P. Norton Sylow 2-subgroups of simple groups by K. Harada and M. L. Lang Yoshida surfaces with Picard number $\rho \geq 17$ by W. L. Hoyt and C. F. Schwartz Hypergeometric modular forms and supersingular elliptic curves by M. Kaneko and N. Todaka Fusion rules for ternary and $\mathbb{Z}_2 \times \mathbb{Z}_2$ code vertex operator algebras by C. H. Lam The regular representations and the $A_{n}(V)$-algebras by H. Li Linear dependencies among completely replicable functions by J. McKay Arithmetic semistable elliptic surfaces by J. McKay and A. Sebbar Modular invariance of trace functions on VOAs in many variables by M. Miyamoto The mirror map for a family of $K$3 surfaces induced from the simplest 3-dimensional reflexive polytope by N. Narumiya and H. Shiga From moonshine to the monster by S. Norton Hypergeometric functions and non-associative algebras by Y. Ohyama Extended affine root systems. V. Elliptic eta-products and their Dirichlet series by K. Saito Deflating infinite Coxeter groups to finite groups by C. S. Simons Genus two meromorphic conformal field theory by M. P. Tuite Picard-Fuchs equations of some families of elliptic curves by H. Verrill.
