CRM Proceedings & Lecture Notes 2004; 258 pp; softcover Volume: 38 ISBN10: 0821835688 ISBN13: 9780821835685 List Price: US$87 Member Price: US$69.60 Order Code: CRMP/38
 This book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties. Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kōta Yoshioka, explains their recent work on the moduli space of instantons over \({\mathbb R}^4\). The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics. Table of Contents  M. Lehn  Lectures on Hilbert schemes
 H. Nakajima and K. Yoshioka  Lectures on instanton counting
 C. Bartocci and M. Jardim  HyperKähler Nahm transforms
 A. Braverman  Instanton counting via affine Lie algebras. I. Equivariant \(J\)functions of (affine) flag manifolds and Whittaker vectors
 M. A. A. de Cataldo and L. Migliorini  The Gysin map is compatible with mixed Hodge structures
 N.K. Ho and L. C. Jeffrey  Representations of fundamental groups of nonorientable 2manifolds
 Y. Namikawa  Mukai flops and derived categories. II
 S. Hosono, B. H. Lian, K. Oguiso, and S.T. Yau  FourierMukai number of a K3 surface
 J. Sawon  Derived equivalence of holomorphic symplectic manifolds
 M. Roth and R. Vakil  The affine stratification number and the moduli space of curves
 M. Verbitsky  Coherent sheaves on generic compact tori
 W.P. Li, Z. Qin, and W. Wang  The cohomology rings of Hilbert schemes via Jack polynomials
