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. Information for our distributors: Titles in this series are copublished with International Press, Cambridge, MA.
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Arithmetic aspects: Mahler's measure and $L$-series of $K$3 hypersurfaces by M. J. Bertin On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces Appendix A. A Modularity Criterion for Integral Galois Representations and Calabi-Yau Threefolds by K. Hulek, H. Verrill, and L. V. Dieulefait Arithmetic mirror symmetry for a two-parameter family of Calabi-Yau manifolds by S. Kadir A rational map between two threefolds by K. Kimura A modular non-rigid Calabi-Yau threefold by E. Lee Arithmetic of algebraic curves and the affine algebra $A_1^{(1)}$ by M. Lynker and R. Schimmrigk Mahler measure variations, Eisenstein series and instanton expansions by J. Stienstra Mahler measure, Eisenstein series and dimers by J. Stienstra Mirror symmetry for zeta functions with appendix by D. Wan and C. D. Haessig The $L$-series of Calabi-Yau orbifolds of CM type Appendix B. The $L$-series of Cubic Hypersurface Fourfolds by N. Yui and Y. Goto Geometric aspects: Integral cohomology and mirror symmetry for Calabi-Yau 3-folds by V. Batyrev and M. Kreuzer The real regulator for a product of $K$3 surfaces by X. Chen and J. D. Lewis Derived equivalence for stratified Mukai flop on $G(2,4)$ by Y. Kawamata A survey of transcendental methods in the study of Chow groups of zero-cycles by M. Kerr Geometry and arithmetic of non-rigid families of Calabi-Yau 3-folds; Questions and examples by E. Viehweg and K. Zuo Some results on families of Calabi-Yau varieties by Y. Zhang Differential geometric and mathematical physical aspects: Boundary RG flows of $\mathcal{N}=2$ minimal models by K. Hori Central charges, symplectic forms, and hypergeometric series in local mirror symmetry by S. Hosono Extracting Gromov-Witten invariants of a conifold from semi-stable reduction and relative GW-invariants of pairs by C.-H. Liu and S.-T. Yau Generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric varieties II by W.-D. Ruan Geometric analytic aspects: Picard-Fuchs equations: Differential equations, mirror maps and zeta values by G. Almkvist and W. Zudilin Mirror symmetry and integral variations of Hodge structure underlying one-parameter families of Calabi-Yau threefolds by C. F. Doran and J. W. Morgan Monodromy calculations of fourth order equations of Calabi-Yau type by C. van Enckevort and D. van Straten Open string mirror maps from Picard-Fuchs equations by B. Forbes Problems by N. Yui, S.-T. Yau, and J. D. Lewis.
