Advanced Studies in Pure Mathematics 1997; 418 pp; hardcover Volume: 25 ISBN10: 431410127X ISBN13: 9784314101271 List Price: US$76 Member Price: US$60.80 Order Code: ASPM/25
 This volume consists of survey articles and research papers on the most recent developments of CRgeometry and overdetermined systems. Some of the papers are based on the lectures delivered at a conference of the same title. The volume contains notes from three lectures on the invariant theory of the Bergman kernel, and on the deformation of CR structures with applications. Other papers, original or expository, are recent contributions on important problems in complex geometry of differential geometric aspects of analysis, and many of them are related to CRgeometry. This volume offers timely and useful information on the subject area. Volumes in this series are freely available electronically 5 years postpublication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students and research mathematicians interested in several complex variables and analytic spaces. Table of Contents  T. Akahori  Deformation theory of CRstructures and its application to deformations of isolated singularities I
 J. Bland and T. Duchamp  Deformation theory for the hyperplane line bundle on \(P^1\)
 D. DeTurck and H. Goldschmidt  Aspects of prescribing Ricci curvature
 C. L. Epstein  Deformations of singularities, complex manifolds and CRstructures
 T. Garrity and R. Mizner  Vectorvalued forms and CR geometry
 H. Gasqui and H. Goldschmidt  The infinitesimal spectral rigidity of the real Grassmannians of rank two
 J. F. Glazebrook and D. Sundararaman  On deformations of selfdual vector bundles over quaternionic manifolds
 C.K. Han and J.N. Yoo  A method of prolongation of tangential CauchyRiemann equations
 K. Hirachi and G. Komatsu  Invariant theory of the Bergman kernel
 L. Lempert  Spaces of CauchyRiemann manifolds
 H. S. Luk and S. S. T. Yau  Some remarks on compact strongly pseudoconvex CR manifolds
 K. Miyajima  Deformation theory of CRstructures and its application to deformations of isolated singularities II
 T. Ohsawa  A report on isolated singularities by transcendental methods
 D. H. Phong and R. Silvotti  The fusion matrix and the Verlinde loop operators in conformal field theory
 T. Sasaki, K. Yamaguchi, and M. Yoshida  On the rigidity of differential systems modelled on Hermitian symmetric spaces and disproofs of a conjecture concerning modular interpretations of configuration spaces
 N. K. Stanton  Infinitesimal CR automorphisms
 H. Umemura  LieDrachVessiot theoryInfinite dimensional differential Galois theory
 J. M. Veloso  Prolongation projection commutativity theorem
 S. M. Webster  A complex Frobenius problem
