**AMS/IP Studies in Advanced Mathematics**

Volume: 33;
2002;
381 pp;
Hardcover

MSC: Primary 14; 32; 81;

**Print ISBN: 978-0-8218-3335-3
Product Code: AMSIP/33**

List Price: $85.00

AMS Member Price: $68.00

MAA Member Price: $76.50

**Electronic ISBN: 978-1-4704-3822-7
Product Code: AMSIP/33.E**

List Price: $80.00

AMS Member Price: $64.00

MAA Member Price: $72.00

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# Mirror Symmetry IV

Share this page *Edited by *
*Eric D’Hoker; Duong Phong; Shing-Tung Yau*

A co-publication of the AMS and International Press of Boston

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.

#### Readership

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

# Table of Contents

## Mirror Symmetry IV

- Cover Cover11
- Half title page i2
- Title page iii4
- Contents v6
- Introduction vii8
- Calabi-Yau Manifolds, Mirror Symmetry, and Symplectic Geometry 112
- A survey of mirror principle 314
- Mirror symmetry: aspects of the first 10 years 1122
- Lagrangian torus fibrations of Calabi-Yau hypersurfaces in toric varieties and SYZ mirror symmetry conjecture 3344
- Moduli space of stable maps 5768
- Cohomological properties of ruled symplectic structures 7990
- Supersymmetric gauge theories and integrable models 101112
- Spectral Lax pairs and Calogero-Moser systems 103114
- M-theory tested by 𝒩=2 Seiberg-Witten theory 113124
- Seiberg-Witten curves for elliptic models 127138
- The periodic and open Toda lattice 139150
- Exact integration methods for supersymmetric Yang-Mills theory 159170
- M-theory, D-branes, and non-commutative geometry 167178
- Nonabelian D-branes and noncommutative geometry 169180
- Evidence for winding states in noncommutative quantum field theory 187198
- The discrete bound state spectrum of the rotating D0-brane system, and its decay by emission of Ramond-Ramond field radiation 195206
- On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications 209220
- Phase-transitions and tensor dynamics in 𝑀-theory 231242
- Duality, Eisenstein series and exact thresholds 255266
- Strings, gauge theories, and AdS/CFT correspondence 271282
- Connectedness of the boundary in the AdS/CFT correspondence 273284
- A note on the topology of the boundary in the AdS/CFT correspondence 289300
- Holographic duals of 4D field theories 291302
- Black hole thermodynamics from calculations in strongly-coupled gauge theory 299310
- Correlation functions for orbifolds of the type 𝑀^{𝑁}/𝑆^{𝑁} 311322
- Elliptic genera and automorphic forms 323334
- Elliptic genera of singular varieties, orbifold elliptic genus and chiral de Rham complex 325336
- On family rigidity theorems for Spin^{𝑐} manifolds 343354
- Ample divisors, automorphic forms and Shafarevich’s conjecture 361372
- Back Cover Back Cover1394