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Mirror Symmetry V
Edited by: Noriko Yui, Queen's University, Kingston, ON, Canada, Shing-Tung Yau, Harvard University, Cambridge, MA, and James D. Lewis, University of Alberta, Edmonton, AB, Canada
A co-publication of the AMS and International Press.
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AMS/IP Studies in Advanced Mathematics
2006; 576 pp; softcover
Volume: 38
ISBN-10: 0-8218-4251-X
ISBN-13: 978-0-8218-4251-5
List Price: US$112
Member Price: US$89.60
Order Code: AMSIP/38
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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, 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 Calabi-Yau threefolds containing elliptic ruled surfaces Appendix A. A Modularity Criterion for Integral Galois Representations and Calabi-Yau Threefolds
  • S. Kadir -- Arithmetic mirror symmetry for a two-parameter family of Calabi-Yau manifolds
  • K. Kimura -- A rational map between two threefolds
  • E. Lee -- A modular non-rigid Calabi-Yau 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 Calabi-Yau 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 Calabi-Yau 3-folds
  • 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 zero-cycles
  • E. Viehweg and K. Zuo -- Geometry and arithmetic of non-rigid families of Calabi-Yau 3-folds; Questions and examples
  • Y. Zhang -- Some results on families of Calabi-Yau 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 Gromov-Witten invariants of a conifold from semi-stable reduction and relative GW-invariants of pairs
  • W.-D. Ruan -- Generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric varieties II
Geometric analytic aspects: Picard-Fuchs 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 one-parameter families of Calabi-Yau threefolds
  • C. van Enckevort and D. van Straten -- Monodromy calculations of fourth order equations of Calabi-Yau type
  • B. Forbes -- Open string mirror maps from Picard-Fuchs equations
  • N. Yui, S.-T. Yau, and J. D. Lewis -- Problems
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