This book presents surveys from a workshop held during the theme year in geometry and topology at the Centre de recherches mathématiques (CRM, University of Montréal). The volume is in some sense a sequel to Mirror Symmetry I (1998) and Mirror Symmetry II (1996), copublished by the AMS and International Press.

Included are recent developments in the theory of mirror manifolds and the related areas of complex and symplectic geometry. The long introductory articles explain the key physical ideas and motivation, namely conformal field theory, supersymmetry, and string theory. Open problems are emphasized. Thus the book provides an efficient way for a very broad audience of mathematicians and physicists to reach the frontier of research in this fast expanding area.

Features:

• Crucial research pertaining to future developments in algebraic and symplectic geometry and to the physics of unified string theories
• Well-known authors who are leaders in the field
• Introductory article by Greene and Yau
• A solid and even blend of ideas and techniques from both mathematics and physics

Also available from the AMS is the related volume, Mirror Symmetry IV (2002).

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

Readership

Graduate students, research mathematicians and physicists working in mathematics and theoretical physics, especially in algebraic or complex geometry or conformal field theory.

Table of Contents

• B. R. Greene -- Aspects of quantum geometry
• S.-T. Yau -- Introduction to enumerative invariants
• T. H. Parker -- Compactified moduli spaces of pseudo-holomorphic curves
• M. Verbitsky -- Mirror symmetry for hyper-Kähler manifolds
• M. Gross -- Connecting the web: A prognosis
• A. Klemm and P. Mayr -- Strong coupling singularities and non-abelian gauge symmetries in $N = 2$ string theory
• S. Kachru -- Remarks on (0,2) Calabi-Yau models
• K. Liu -- Relations among fixed point
• J. Jorgenson and A. Todorov -- An analytic discriminant for polarized algebraic $K3$ surfaces
• D. R. Morrison -- Through the looking glass
• B. Siebert -- An update on (small) quantum cohomology