**AMS/IP Studies in Advanced Mathematics**

Volume: 38;
2006;
576 pp;
Softcover

MSC: Primary 14; 11; 32; 81;

Print ISBN: 978-0-8218-4251-5

Product Code: AMSIP/38

List Price: $118.00

Individual Member Price: $94.40

**Electronic ISBN: 978-1-4704-3827-2
Product Code: AMSIP/38.E**

List Price: $118.00

Individual Member Price: $94.40

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# Mirror Symmetry V

Share this page *Edited by *
*Noriko Yui; Shing-Tung Yau; James D. Lewis*

A co-publication of the AMS and International Press of Boston, Inc.

Since its discovery in the early 1990s, mirror symmetry, or more generally, string theory, has exploded onto the mathematical landscape. This topic touches upon many branches of mathematics and mathematical physics, and has revealed deep connections between subjects previously considered unrelated. The papers in this volume treat mirror symmetry from the perspectives of both mathematics and physics. The articles can be roughly grouped into four sub-categories within the topic of mirror symmetry: arithmetic aspects, geometric aspects, differential geometric and mathematical physics aspects, and geometric analytic aspects. In these works, the reader will find mathematics addressing, and in some cases solving, problems inspired and influenced by string theory.

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

#### Table of Contents

# Table of Contents

## Mirror Symmetry V

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- Arithmetic aspects 112
- Mahler’s measure and 𝐿-series of 𝐾3 hypersurfaces 314
- On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces Appendix A. A Modularity Criterion for Integral Galois Representations and Calabi-Yau Threefolds 1930
- Arithmetic mirror symmetry for a two-parameter family of Calabi-Yau manifolds 3546
- A rational map between two threefolds 8798
- A modular non-rigid Calabi-Yau threefold 89100
- Arithmetic of algebraic curves and the affine algebra 𝐴₁⁽¹⁾ 123134
- Mahler measure variations, Eisenstein series and instanton expansions 139150
- Mahler measure, Eisenstein series and dimers 151162
- Mirror symmetry for zeta functions with appendix 159170
- The 𝐿-series of Calabi-Yau orbifolds of CM type Appendix B. The 𝐿-series of Cubic Hypersurface Fourfolds 185196
- Geometric aspects 253264
- Integral cohomology and mirror symmetry for Calabi-Yau 3-folds 255266
- The real regulator for a product of 𝐾3 surfaces 271282
- Derived equivalence for stratified Mukai flop on 𝐺(2,4) 285296
- A survey of transcendental methods in the study of Chow groups of zero-cycles 295306
- Geometry and arithmetic of non-rigid families of Calabi-Yau 3-folds; Questions and examples 351362
- Some results on families of Calabi-Yau varieties 361372
- Differential geometric and mathematical physical aspects 379390
- Boundary RG flows of 𝒩=2 minimal models 381392
- Central charges, symplectic forms, and hypergeometric series in local mirror symmetry 405416
- Extracting Gromov-Witten invariants of a conifold from semi-stable reduction and relative GW-invariants of pairs 441452
- Generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric varieties II 457468
- Geometric analytic aspects: Picard-Fuchs equations 479490
- Differential equations, mirror maps and zeta values 481492
- Mirror symmetry and integral variations of Hodge structure underlying one-parameter families of Calabi-Yau threefolds 517528
- Monodromy calculations of fourth order equations of Calabi-Yau type 539550
- Open string mirror maps from Picard-Fuchs equations 561572
- Problems 571582
- Other titles in this series 577588
- Back Cover Back Cover1590

#### Readership

Graduate students and research mathematicians interested in theoretical physics and mathematical areas such as geometry and modular forms.