Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book
covers the standard topics in toric geometry; a novel feature is that each of the first nine …

A bstract We construct supersymmetric AdS 4 vacua of type IIB string theory in
compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit …

A bstract We provide a comprehensive summary of concepts from Calabi-Yau motives
relevant to the computation of multi-loop Feynman integrals. From this we derive several …

This thorough and detailed exposition is the result of an intensive month-long course on
mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry …

We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+ 1
dimensions. The proof involves establishing the equivalence of the gauged linear sigma …

Using the recent advances in our understanding of non-perturbative aspects of type 11
strings we show how non-trivial exact results for N= 2 quantum field theories can be reduced …

A bstract Using the Gelfand-Kapranov-Zelevinskĭ system for the primitive cohomology of an
infinite series of complete intersection Calabi-Yau manifolds, whose dimension is the loop …

During the last years we have generated a large number of data related to Calabi-Yau
hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified …

A bstract We use the GKZ description of periods and certain classes of relative periods on
families of Barth-Nieto Calabi-Yau (l− 1)-folds in order to solve the l-loop banana amplitudes …

Using geometric engineering in the context of type II strings, we obtain exact solutions for the
moduli space of the Coulomb branch of all N= 2 gauge theories in four dimensions involving …