The collection of articles in this volume are based on l ectures presented during the Winter School on Mirror Symmetry held at Harvard University. There are many new directions suggested by mirror symmetry which could potentially have very rich connections in physics and mathematics.

This book brings together the latest research in a major area of mathematical physics, including the recent progress in mirror manifolds and Lagrangian submanifolds. In particular, several articles describing homological approach and related topics are included.

Other AMS titles edited by S.-T Yau published in the AMS/IP Studies in Advanced Mathematics series include, Mirror Symmetry III, Volume 10, Mirror symmetry II, Volume 1, and Mirror Symmetry I, Volume 9.

Titles in this series are co-published with International Press, Cambridge, MA.

Readership

Graduate students and research mathematicians interested in algebraic geometry and its applications in mathematical physics.

Table of Contents

• B. S. Acharya -- Exceptional mirror symmetry
• K. Fukaya -- Floer homology and mirror symmetry I
• R. Gopakumar and C. Vafa -- On the gauge theory/geometry correspondence
• M. Gross -- Special Lagrangian fibrations I: Topology
• M. Gross -- Special Lagrangian fibrations II: Geometry. A survey of techniques in the study of special Lagrangian fibrations
• N. Hitchin -- Lectures on special Lagrangian submanifolds
• A. Klemm and E. Zaslow -- Local mirror symmetry at higher genus
• N. C. Leung, S.-T. Yau, and E. Zaslow -- From special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai transform
• P. Berglund and P. Mayr -- $N = 1$ heterotic string vacua from mirror symmetry
• A. Polishchuk -- Homological mirror symmetry with higher products
• D. Arinkin and A. Polishchuk -- Fukaya category and Fourier transform
• A. Polishchuk and E. Zaslow -- Categorical mirror symmetry in the eliptic curve
• W.-D. Ruan -- Lagrangian torus fibration of quintic hypersurfaces I: Fermat quintic case
• A. Strominger, S.-T. Yau, and E. Zaslow -- Mirror symmetry is T-duality
• R. P. Thomas -- Derived categories for the working mathematician
• R. P. Thomas -- Mirror symmetry and actions of braid groups on derived categories