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Product Code:  AMSIP/38 
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Electronic ISBN:  9781470438272 
Product Code:  AMSIP/38.E 
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Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 38; 2006; 576 ppMSC: Primary 14; 11; 32; 81;
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.
ReadershipGraduate students and research mathematicians interested in theoretical physics and mathematical areas such as geometry and modular forms.

Table of Contents

Arithmetic aspects

Mahler’s measure and $L$series of $K$3 hypersurfaces

On the modularity of CalabiYau threefolds containing elliptic ruled surfaces Appendix A. A Modularity Criterion for Integral Galois Representations and CalabiYau Threefolds

Arithmetic mirror symmetry for a twoparameter family of CalabiYau manifolds

A rational map between two threefolds

A modular nonrigid CalabiYau 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 CalabiYau orbifolds of CM type Appendix B. The $L$series of Cubic Hypersurface Fourfolds

Geometric aspects

Integral cohomology and mirror symmetry for CalabiYau 3folds

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 zerocycles

Geometry and arithmetic of nonrigid families of CalabiYau 3folds; Questions and examples

Some results on families of CalabiYau 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 GromovWitten invariants of a conifold from semistable reduction and relative GWinvariants of pairs

Generalized special Lagrangian torus fibrations for CalabiYau hypersurfaces in toric varieties II

Geometric analytic aspects: PicardFuchs equations

Differential equations, mirror maps and zeta values

Mirror symmetry and integral variations of Hodge structure underlying oneparameter families of CalabiYau threefolds

Monodromy calculations of fourth order equations of CalabiYau type

Open string mirror maps from PicardFuchs equations

Problems


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

Arithmetic aspects

Mahler’s measure and $L$series of $K$3 hypersurfaces

On the modularity of CalabiYau threefolds containing elliptic ruled surfaces Appendix A. A Modularity Criterion for Integral Galois Representations and CalabiYau Threefolds

Arithmetic mirror symmetry for a twoparameter family of CalabiYau manifolds

A rational map between two threefolds

A modular nonrigid CalabiYau 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 CalabiYau orbifolds of CM type Appendix B. The $L$series of Cubic Hypersurface Fourfolds

Geometric aspects

Integral cohomology and mirror symmetry for CalabiYau 3folds

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 zerocycles

Geometry and arithmetic of nonrigid families of CalabiYau 3folds; Questions and examples

Some results on families of CalabiYau 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 GromovWitten invariants of a conifold from semistable reduction and relative GWinvariants of pairs

Generalized special Lagrangian torus fibrations for CalabiYau hypersurfaces in toric varieties II

Geometric analytic aspects: PicardFuchs equations

Differential equations, mirror maps and zeta values

Mirror symmetry and integral variations of Hodge structure underlying oneparameter families of CalabiYau threefolds

Monodromy calculations of fourth order equations of CalabiYau type

Open string mirror maps from PicardFuchs equations

Problems