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Mirror Symmetry IV

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Brand new. We distribute directly for the publisher. This book presents contributions of participants of a workshop held at the Centre de Recherches MathA©matiques (CRM), ... University of MontrA©al. 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. Read more Show Less

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Overview

The volume presents a broad survey of many noteworthy developments since the publication of the previous volume, Mirror Symmetry III (AMS and International Press, 1999). Included are recent advancements in the theory of mirror manifolds and the related areas of complex and symplectic geometry emphasizing the following topics: integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; elliptic genera and automorphic forms. Several introductory articles present an overview of geometric and of 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 in this rapidly expanding area.

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Product Details

Table of Contents

Introduction
A Survey of Mirror Principle 3
Mirror Symmetry: Aspects of the First 10 Years 11
Lagrangian torus fibrations of Calabi-Yau hypersurfaces in toric varieties and SYZ mirror symmetry conjecture 33
Moduli Space of Stable Maps 57
Cohomological properties of ruled symplectic structures 79
Spectral Lax pairs and Calogero-Moser systems 103
M-Theory tested by N = 2 Seiberg-Witten Theory 113
Seiberg-Witten curves for elliptic models 127
The periodic and open Toda lattice 139
Exact Integration Methods for Supersymmetric Yang-Mills Theory 159
Nonabelian D-branes and Noncommutative Geometry 169
Evidence for Winding States in Noncommutative Quantum Field Theory 187
The Discrete Bound State Spectrum of the Rotating DO-brane System, and its Decay by Emission of Ramond-Ramond Field Radiation 195
On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications 209
Phase-Transitions and Tensor Dynamics in M-theory 231
Duality, Eisenstein Series and Exact Thresholds 255
Connectedness of the Boundary in the AdS/CFT Correspondence 273
A note on the topology of the Boundary in the AdS/CFT Correspondence 289
Holographic duals of 4D field theories 291
Black Hole Thermodynamics from Calculations in Strongly-Coupled Gauge Theory 299
Correlation functions for orbifolds of the type M[superscript N] / S[superscript N] 311
Elliptic genera of singular varieties, orbifold elliptic genus and chiral de Rham complex 325
On Family Rigidity Theorems for Spin Manifolds 343
Ample Divisors, Automorphic Forms and Shafarevich's Conjecture 361
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