AMS/IP Studies in Advanced Mathematics 2002; 381 pp; hardcover Volume: 33 ISBN10: 0821833359 ISBN13: 9780821833353 List Price: US$76 Member Price: US$60.80 Order Code: AMSIP/33
 This book presents contributions of participants of a workshop held at the Centre de Recherches Mathématiques (CRM), University of Montréal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M and Dbranes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and 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 into this rapidly expanding area. Titles in this series are copublished with International Press, Cambridge, MA. Readership Graduate students and researchers in theoretical physics and mathematical areas such as geometry and modular forms. Table of Contents CalabiYau Manifolds, Mirror Symmetry, and Symplectic Geometry  B. H. Lian, K. Liu, and S.T. Yau  A survey of mirror principle
 B. R. Greene  Mirror symmetry: aspects of the first 10 years
 W.D. Ruan  Lagrangian torus fibrations of CalabiYau hypersurfaces in toric varieties and SYZ mirror symmetry conjecture
 G. Liu  Moduli space of stable maps
 F. Lalonde and D. McDuff  Cohomological properties of ruled symplectic structures
Supersymmetric gauge theories and integrable models  J. C. Hurtubise  Spectral Lax pairs and CalogeroMoser systems
 I. P. Ennes, C. Lozano, S. G. Naculich, H. Rhedin, and H. J. Schnitzer  Mtheory tested by \({\mathcal {N}}=2\) SeibergWitten theory
 I. P. Ennes, C. Lozano, S. G. Naculich, and H. J. Schnitzer  SeibergWitten curves for elliptic models
 I. Krichever and K. L. Vaninsky  The periodic and open Toda lattice
 J.L. Gervais  Exact integration methods for supersymmetric YangMills theory
Mtheory, Dbranes, and noncommutative geometry  R. C. Meyers  Nonabelian Dbranes and noncommutative geometry
 P. Pouliot  Evidence for winding states in noncommutative quantum field theory
 K. G. Savvidy  The discrete bound state spectrum of the rotating D0brane system, and its decay by emission of RamondRamond field radiation
 F. Denef  On the correspondence between Dbranes and stationary supergravity solutions of type II CalabiYau compactifications
 M. Faux, D. Lüst, and B. A. Ovrut  Phasetransitions and tensor dynamics in \(M\)theory
 N. A. Obers and B. Pioline  Duality, Eisenstein series and exact thresholds
Strings, gauge theories, and AdS/CFT correspondence  E. Witten and S.T. Yau  Connectedness of the boundary in the AdS/CFT correspondence
 S.T. Yau  A note on the topology of the boundary in the AdS/CFT correspondence
 M. Porrati and A. Starinets  Holographic duals of 4D field theories
 D. Kabat, G. Lifschytz, and D. A. Lowe  Black hole thermodynamics from calculations in stronglycoupled gauge theory
 O. Lunin and S. D. Mathur  Correlation functions for orbifolds of the type \(M^N/S^N\)
Elliptic genera and automorphic forms  L. A. Borisov and A. Libgober  Elliptic genera of singular varieties, orbifold elliptic genus and chiral de Rham complex
 K. Liu and X. Ma  On family rigidity theorems for Spin\(^{c}\) manifolds
 J. Jorgenson and A. Todorov  Aample divisors, automorphic forms and Shafarevich's conjecture
