This book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the A-model half of the story remains much better-understood than the B-model. This book aims to address that imbalance. It begins with an overview of several methods by which mirrors have been constructed, and from there, gives a thorough account of the BCOV B-model theory from a physical perspective; this includes the appearance of such phenomena as the holomorphic anomaly equation and connections to number theory via modularity. Following a mathematical exposition of the subject of quantization, the remainder of the book is devoted to the B-model from a mathematician's point-of-view, including such topics as polyvector fields and primitive forms, Givental's ancestor potential, and integrablesystems.

Attempts to close the gap between the mathematical community's understanding of the B model and the A model Brings together mathematical and physical perspectives in one reference, providing a unique opportunity for the two communities to learn from one another Provides an overview of several methods by which mirrors have been constructed Details the BCOV B-model theory from a physical perspective

Inhalt
Mirror symmetry constructions.- The B-model approach to topological string theory on Calabi-Yau n-folds.- Geometric quantizations with applications to Gromov-Witten theory.- Some classical/quantum aspects of Calabi-Yau moduli.- The total ancestor potential in singularity theory.- Lecture notes on bihamiltonian structures and their central invariants.