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Mirror Symmetry V

Edited by: Noriko Yui Queen’s University, Kingston, ON, Canada
Shing-Tung Yau Harvard University, Cambridge, MA
James D. Lewis University of Alberta, Edmonton, AB, Canada
A co-publication of the AMS and International Press of Boston
Available Formats:
Softcover ISBN: 978-0-8218-4251-5
Product Code: AMSIP/38
List Price: $126.00 MAA Member Price:$113.40
AMS Member Price: $100.80 Electronic ISBN: 978-1-4704-3827-2 Product Code: AMSIP/38.E List Price:$118.00
MAA Member Price: $106.20 AMS Member Price:$94.40
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List Price: $189.00 MAA Member Price:$170.10
AMS Member Price: $151.20 Click above image for expanded view Mirror Symmetry V Edited by: Noriko Yui Queen’s University, Kingston, ON, Canada Shing-Tung Yau Harvard University, Cambridge, MA James D. Lewis University of Alberta, Edmonton, AB, Canada A co-publication of the AMS and International Press of Boston Available Formats:  Softcover ISBN: 978-0-8218-4251-5 Product Code: AMSIP/38  List Price:$126.00 MAA Member Price: $113.40 AMS Member Price:$100.80
 Electronic ISBN: 978-1-4704-3827-2 Product Code: AMSIP/38.E
 List Price: $118.00 MAA Member Price:$106.20 AMS Member Price: $94.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$189.00 MAA Member Price: $170.10 AMS Member Price:$151.20
• Book Details

Volume: 382006; 576 pp
MSC: 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 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.

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 Calabi-Yau threefolds containing elliptic ruled surfaces Appendix A. 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 Appendix B. 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

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 382006; 576 pp
MSC: 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 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.

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 Calabi-Yau threefolds containing elliptic ruled surfaces Appendix A. 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 Appendix B. 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
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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