Edited by S.T. Yau

Surveys in Differential Geometry, Vol V

Vol. 5 Table of Contents:

Introduction, S.-T. Yau
K3 Surfaces and String Duality, Paul S. Aspinwall
Symplectic Geometry and Velinde Formulas, Jean-Michel Bismut and Francois Labourie
Counting curves on irrational surfaces, Jim Bryan and Naichung Conan Leung
Special Lagrangian Firbrations II:
Geometry. A Survey of Techniques in the Study of Special Lagrangian Fibrations Mark Gross
Mirror Principle I, Bong H. Lian, Kegeng Liu, and S.T. Yau
Mirror Principle II, Bong H. Lian, Kegeng Liu, and S.T. Yau
Differential Equations from Mirror Symmetry, Bong H. Lian and S.T. Yau
Heat Kernels, Symplectic Geometry, Moduli Spaces, and Finite Groups Kefeng Liu
A Brief Tour of GW Invariants, Gang Tian and Jun Li

Edited by Claude LeBrun and McKenzie Wang

Surveys in Differential Geometry, Vol VI

Vol. 6 Table of Contents:

Introduction,
Claude LeBrun and McKenzie Wang

PART I
Einstein Manifolds and Special Holonomy
Einstein Manifolds with Zero Ricci Curvature
S.T. Yau
Hyper-Kahler Manifolds
Andrew Dancer
Compact Riemannian Manifolds with Exceptional Holonomy
Dominic Joyce
Kahler-Einstein Manifolds of Positive Scalar Curvature
Gang Tian
Quarternion-Kahler Geometry
Simon Salamon
3-Sasakian Manifolds
Charles Boyer and Krzysztof Galicki

Part 2
Towards a General Theory of Einstein
Manifolds
Ricci Flow and Einstein Metrics in Low Dimensions
Ben Chow
Rigidity and Compactness of Einstein Metrics,
Peter Petersen
Einstein Deformations of Hyperbolic Metrics
Oliver Biquard
Four-Dimensional Einstein Manifolds, and Beyond
Claude LeBrun
Einstein Metrics from Symmetry and Bundle Constructions
McKenzie Wang

Part 3
Relativity Revisited
General Relativity
K. Tod
The Stability of Minkowski Space-Time
Demetrios Christodoulou
Einstein-Weyl Geometry
David Calderbank and Henrik Pedersen

Edited by S.T. Yau

Surveys in Differential Geometry, Vol VII

Dedicated to the Founders of Index Theory

The volume will include:

Geometry of Classical Particles, by Sir Michael Atiyah

Moduli Space of Abelian Varieties and the Singularities of the Theta Divisor, by Ciro
Ciliberto and Gerard van der Geer

Fix point theorems and Number theory by F. Hirzebruch

Morse Theory and Stokes' Theorem by Harvey and Lawson

Curvature and Function Theory by Peter Li

Non-Commutative Yang-Mills Theory by E. Witten

Misha Verbitsky and Dmitri Kaledin

Hyperkahler Manifolds

Verbitsky and Kaledin introduce Hyperkahler Manifolds to those who have not previously studied them and present new examples of Hyperkahler Manifolds extending the research knowledge in the field.

Table of Contents:

Part I. Hyperholomophic sheaves and new examples of hyperkahler manifolds M. Verbitsky
1.Introduction
2.Hyperkahler manifolds
3.Hyperholomorphic sheaves
4.Cohomology of hyperkahler manifolds
5.C -restricted complex structures on hyperkahler manifolds
6.Desingularization of hyperholomorphic sheaves
7.Twistor transform and quaternionic-Kahler geometry
8.C^*-equivalent twistor spaces
9.Moduli spaces of hyperholomorphic sheaves and bundles
10.New examples of hyperkahler manifolds
Part 2 Hyperkahler structures on total spaces of holomorphic cotangent bundles, by Dmitri Kaledin
1.Preliminary facts from linear algebra
2.Hodge bundles and quaternionic manifolds
3.Hodge manifolds
4.Regular Hodge manifolds
5.Tangent bundles as Hodge manifolds
6.Formal completions
7.Preliminaries on the Weil algebra
8.Classification of flat extended connections
9.Metrics
10.Convergence

Paul Frampton (Univ. of North Carolina, Chapel Hill, North Carolina)

Gauge Field Theories, 2nd Ed.

ISBN: 0-471-34783-3
Hardcover
Projected Pub Date: Aug 2000
Copyright: 2000

Quantum field theory remains a topic of great interest among physicists. This book provides a mathematical treatment of this topic that is key in particle physics and quantum mechanics/field theory.

Contents
Gauge Invariance.
Quantization.
Renormalization.
Electroweak Forces.
Renormalization Group.
Quantum Chromodynamics.
Model Buliding.
Index.

Dietrich Stauffer (Univ. of Cologne, Germany)
Debashish Chowdhury (Physics Department, Indian Institute of Technology)

Principles of Equilibrium Statistical Mechanics

ISBN: 3-527-40300-0
Hardcover

Pages: 564
Projected Pub Date: Sep 2000
Copyright: 2000
Imprint: A Wiley-VCH Publication

Thermodynamics and statistical physics are among the standard curriculum of physics courses in any university. This modern textbook is based on existing lectures and provides a complete survey on the broad field of statistical mechanics.
Due to its ambitious level and an extensive list of references for technical details on advanced topics, the book is also a must for