Calabi-Yau Varieties and Mirror Symmetry

Abstract

Geometric methods: Mixed toric residues and Calabi-Yau complete intersections by V. V. Batyrev and E. N. Materov Crepant resolutions of $\mathbb{C}^n/A_1(n)$ and flops of $n$-folders for $n=4,5$ by L. Chiang and S.-s. Roan Picard-Fuchs equations, integrable systems and higher algebraic K-theory by P. L. del Angel and S. Muller-Stach Counting BPS states via holomorphic anomaly equations by S. Hosono Regulators of Chow cycles on Calabi-Yau varieties by J. D. Lewis Arithmetic methods: Calabi-Yau manifolds over finite fields, II by P. Candelas, X. de la Ossa, and F. Rodriguez-Villegas Modularity of rigid Calabi-Yau threefolds over $\mathbb{Q}$ by L. Dieulefait and J. Manoharmayum $K3$ surfaces with symplectic group actions by Y. Goto Birational smooth minimal models have equal Hodge numbers in all dimensions by T. Ito The $n$th root of the mirror map by B. H. Lian and S.-T. Yau On a Shioda-Inose structure of a family of K3 surfaces by L. Long Black hole attractor varieties and complex multiplication by M. Lynker, V. Periwal, and R. Schimmrigk Hypergeometric families of Calabi-Yau manifolds by F. Rodriguez-Villegas Aspects of conformal field theory from Calabi-Yau arithmetic by R. Schimmrigk Ordinary Calabi-Yau-3 crystals by J. Stienstra The ordinary limit for varieties over $\mathbb{Z}[x_1,\ldots,x_r]$ by J. Stienstra Update on the modularity of Calabi-Yau varieties with appendix by Helena Verrill by N. Yui Problems by N. Yui and J. D. Lewis.