A bstract Compactification of M-theory and of IIB string theory on threefold canonical
singularities gives rise to superconformal field theories (SCFTs) in 5d and 4d, respectively …

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 …

In Chapter 1, we have seen how the algebra of the polynomial rings k [x1,..., xn] and the
geometry of affine algebraic varieties are linked. In this chapter, we will study the method of …

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 …

The book starts with a thorough introduction to connections and holonomy groups, and to
Riemannian, complex and Kähler geometry. Then the Calabi conjecture is proved and used …

The world is continuous, but the mind is discrete. David Mumford We seek to bridge some
critical gaps between various? elds of mathematics by studying the interplay between the …

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 …

Certain Feynman integrals are associated to Calabi-Yau geometries. We demonstrate how
these integrals can be computed with the method of differential equations. The four-loop …