Modular Forms and String Duality

by Yui, Noriko; Verrill, Helena; Doran, Charles F.

• ISBN13: 9780821844847
• ISBN10: 0821844849
• Format: Hardcover
• Copyright: 2008-10-19
• Publisher: Amer Mathematical Society

Summary

"This book is a testimony to the BIRS Workshop, and it covers a wide range of topics at the interface of number theory and string theory, with special emphasis on modular forms and string duality. They include the recent advances as well as introductory expositions on various aspects of modular forms, motives, differential equations, conformal field theory, topological strings and Gromov-Witten invariants, mirror symmetry, and homological mirror symmetry. The contributions are roughly divided into three categories: arithmetic and modular forms, geometric and differential equations, and physics and string theory. The book is suitable for researchers working at the interface of number theory and string theory."--BOOK JACKET.

Table of Contents

Aspects of arithmetic and modular forms: Motives and mirror symmetry for Calabi-Yau orbifolds

String modular motives of mirrors of rigid Calabi-Yau varieties

Update on modular non-rigid Calabi-Yau threefolds

Finite index subgroups of the modular group and their modular forms

Aspects of geometric and differential equations: Apery limits of differential equations of order 4 and 5

Hypergeometric systems in two variables, quivers, dimers and dessins d'enfants

Some properties of hypergeometric series associated with mirror symmetry

Ramanujan-type formulae for $1/\pi$: A second wind?

Aspects of physics and string theory: Meet homological mirror symmetry

Orbifold Gromov-Witten invariants and topological strings

Conformal field theory and mapping class groups

$SL(2,\mathbb{C})$ Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial

Open strings and extended mirror symmetry

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