In these lecture notes I consider one remarkable system of differential equations that
appeared in the papers of physicists on two-dimensional topological field theory (TFT) in the …

This book is about the interplay of computational commutative algebra and the theory of
convex polytopes. It centres around a special class of ideals in a polynomial ring: the class …

This paper is a survey of new results and open problems connected with fundamental
combinatorial concepts, including polytopes, simplicial complexes, cubical complexes, and …

We consider families ${\cal F}(\Delta) $ consisting of complex $(n-1) $-dimensional
projective algebraic compactifications of $\Delta $-regular affine hypersurfaces $ Z_f …

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 …

Cox rings are significant global invariants of algebraic varieties, naturally generalizing
homogeneous coordinate rings of projective spaces. This book provides a largely self …

A Mirror Theorem for Toric Complete Intersections Page 1 A Mirror Theorem for Toric Complete
Intersections Alexander Givental * Abstract We prove a generalized mirror conjecture for …

Here, the study of torus actions on topological spaces is presented as a bridge connecting
combinatorial and convex geometry with commutative and homological algebra, algebraic …

Abstract Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa
couplings are discussed within the framework of toric geometry. It allows to establish mirror …