Mirror Symmetry IV

The volume presents a broad survey of many noteworthy developments since the publication of the previous volume, Mirror Symmetry III (AMS and International Press, 1999). Included are recent advancements in the theory of mirror manifolds and the related areas of complex and symplectic geometry emphasizing the following topics: integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; elliptic genera and automorphic forms. Several introductory articles present an overview of geometric and of physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research in this rapidly expanding area.