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Mirror Symmetry IV
Edited by: Eric D'Hoker, University of California, Los Angeles, CA, Duong Phong, Columbia University, New York, NY, and Shing-Tung Yau, Harvard University, Cambridge, MA
A co-publication of the AMS and International Press of Boston, Inc..

AMS/IP Studies in Advanced Mathematics
2002; 381 pp; hardcover
Volume: 33
ISBN-10: 0-8218-3335-9
ISBN-13: 978-0-8218-3335-3
List Price: US$80
Member Price: US$64
Order Code: AMSIP/33
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See also:

Mirror symmetry II - B Greene and S-T Yau

Mirror Symmetry I - Shing-Tung Yau

Mirror Symmetry III - Duong H Phong, Luc Vinet and Shing-Tung Yau

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 D-branes 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 co-published with International Press of Boston, Inc., Cambridge, MA.


Graduate students and researchers in theoretical physics and mathematical areas such as geometry and modular forms.

Table of Contents

Calabi-Yau 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 Calabi-Yau 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 Calogero-Moser systems
  • I. P. Ennes, C. Lozano, S. G. Naculich, H. Rhedin, and H. J. Schnitzer -- M-theory tested by \({\mathcal {N}}=2\) Seiberg-Witten theory
  • I. P. Ennes, C. Lozano, S. G. Naculich, and H. J. Schnitzer -- Seiberg-Witten curves for elliptic models
  • I. Krichever and K. L. Vaninsky -- The periodic and open Toda lattice
  • J.-L. Gervais -- Exact integration methods for supersymmetric Yang-Mills theory
M-theory, D-branes, and non-commutative geometry
  • R. C. Meyers -- Nonabelian D-branes 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 D0-brane system, and its decay by emission of Ramond-Ramond field radiation
  • F. Denef -- On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications
  • M. Faux, D. Lüst, and B. A. Ovrut -- Phase-transitions 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 strongly-coupled 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
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