Mirror Symmetry V

by Yui, Noriko; Yau, Shing-Tung; Lewis, James D.

• ISBN13: 9780821842515
• ISBN10: 082184251X
• Format: Paperback
• Copyright: 2007-01-01
• Publisher: Amer Mathematical Society

Summary

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 ofmirror 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. Information for ourdistributors: Titles in this series are copublished with International Press, Cambridge, MA.

Table of Contents

Arithmetic aspects: Mahler's measure and $L$-series of $K$3 hypersurfaces

On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces

A Modularity Criterion for Integral Galois Representations and Calabi-Yau Threefolds

Arithmetic mirror symmetry for a two-parameter family of Calabi-Yau manifolds

A rational map between two threefolds

A modular non-rigid Calabi-Yau threefold

Arithmetic of algebraic curves and the affine algebra $A_1^{(1)}$

Mahler measure variations, Eisenstein series and instanton expansions

Mahler measure, Eisenstein series and dimers

Mirror symmetry for zeta functions with appendix

The $L$-series of Calabi-Yau orbifolds of CM type

The $L$-series of Cubic Hypersurface Fourfolds

Geometric aspects: Integral cohomology and mirror symmetry for Calabi-Yau 3-folds

The real regulator for a product of $K$3 surfaces

Derived equivalence for stratified Mukai flop on $G(2,4)$

A survey of transcendental methods in the study of Chow groups of zero-cycles

Geometry and arithmetic of non-rigid families of Calabi-Yau 3-folds; Questions and examples

Some results on families of Calabi-Yau varieties

Differential geometric and mathematical physical aspects: Boundary RG flows of $\mathcal{N}=2$ minimal models

Central charges, symplectic forms, and hypergeometric series in local mirror symmetry

Extracting Gromov-Witten invariants of a conifold from semi-stable reduction and relative GW-invariants of pairs

Generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric varieties II

Geometric analytic aspects: Picard-Fuchs equations: Differential equations, mirror maps and zeta values

Mirror symmetry and integral variations of Hodge structure underlying one-parameter families of Calabi-Yau threefolds

Monodromy calculations of fourth order equations of Calabi-Yau type

Open string mirror maps from Picard-Fuchs equations

Problems

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