AMS/IP Studies in Advanced Mathematics 2006; 576 pp; softcover Volume: 38 ISBN10: 082184251X ISBN13: 9780821842515 List Price: US$112 Member Price: US$89.60 Order Code: AMSIP/38
 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 subcategories 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 copublished with International Press, Cambridge, MA. Readership Graduate students and research mathematicians interested in theoretical physics and mathematical areas such as geometry and modular forms. Table of Contents Arithmetic aspects  M. J. Bertin  Mahler's measure and \(L\)series of \(K\)3 hypersurfaces
 K. Hulek, H. Verrill, and L. V. Dieulefait  On the modularity of CalabiYau threefolds containing elliptic ruled surfaces Appendix A. A Modularity Criterion for Integral Galois Representations and CalabiYau Threefolds
 S. Kadir  Arithmetic mirror symmetry for a twoparameter family of CalabiYau manifolds
 K. Kimura  A rational map between two threefolds
 E. Lee  A modular nonrigid CalabiYau threefold
 M. Lynker and R. Schimmrigk  Arithmetic of algebraic curves and the affine algebra \(A_1^{(1)}\)
 J. Stienstra  Mahler measure variations, Eisenstein series and instanton expansions
 J. Stienstra  Mahler measure, Eisenstein series and dimers
 D. Wan and C. D. Haessig  Mirror symmetry for zeta functions with appendix
 N. Yui and Y. Goto  The \(L\)series of CalabiYau orbifolds of CM type Appendix B. The \(L\)series of Cubic Hypersurface Fourfolds
Geometric aspects  V. Batyrev and M. Kreuzer  Integral cohomology and mirror symmetry for CalabiYau 3folds
 X. Chen and J. D. Lewis  The real regulator for a product of \(K\)3 surfaces
 Y. Kawamata  Derived equivalence for stratified Mukai flop on \(G(2,4)\)
 M. Kerr  A survey of transcendental methods in the study of Chow groups of zerocycles
 E. Viehweg and K. Zuo  Geometry and arithmetic of nonrigid families of CalabiYau 3folds; Questions and examples
 Y. Zhang  Some results on families of CalabiYau varieties
Differential geometric and mathematical physical aspects  K. Hori  Boundary RG flows of \(\mathcal{N}=2\) minimal models
 S. Hosono  Central charges, symplectic forms, and hypergeometric series in local mirror symmetry
 C.H. Liu and S.T. Yau  Extracting GromovWitten invariants of a conifold from semistable reduction and relative GWinvariants of pairs
 W.D. Ruan  Generalized special Lagrangian torus fibrations for CalabiYau hypersurfaces in toric varieties II
Geometric analytic aspects: PicardFuchs equations  G. Almkvist and W. Zudilin  Differential equations, mirror maps and zeta values
 C. F. Doran and J. W. Morgan  Mirror symmetry and integral variations of Hodge structure underlying oneparameter families of CalabiYau threefolds
 C. van Enckevort and D. van Straten  Monodromy calculations of fourth order equations of CalabiYau type
 B. Forbes  Open string mirror maps from PicardFuchs equations
 N. Yui, S.T. Yau, and J. D. Lewis  Problems
