Edited by: Stephen S.-T. Yau, East China Normal University, Shanghai, People's Republic of China, and University of Illinois at Chicago, IL, and Zhijie Chen, Jianpan Wang, and Sheng-Li Tan, East China Normal University, Shanghai, People's Republic of China

Proceedings of the International Conference on Complex Geometry and Related Fields

AMS/IP Studies in Advanced Mathematics, Volume: 39
2007; 402 pp; softcover
ISBN-10: 0-8218-3949-7
ISBN-13: 978-0-8218-3949-2

In commemoration and celebration of the tenth anniversary of the Institute of Mathematics at East China Normal University, an International Conference on complex geometry and related fields recently convened. This collection presents some of the conference highlights, dealing with various and significant topics of differential and algebraic geometry, while exploring their connections to number theory and mathematical physics.

Titles in this series are co-published with International Press, Cambridge, MA.

Readership

Research mathematicians interested in complex differential geometry and complex algebraic geometry.

Table of Contents

Edited by: Andre Bandrauk, Universite de Sherbrooke, QC, Canada, Michel C. Delfour, Universite de Montreal, QC, Canada, and Claude Le Bris, Ecole Nationale des Ponts et Chausses, Marne La Vallee, France, and INRIA Rocquencourt, Le Chesnay, France

High-Dimensional Partial Differential Equations in Science and Engineering

CRM Proceedings & Lecture Notes, Volume: 41
2007; 194 pp; softcover
ISBN-10: 0-8218-3853-9
ISBN-13: 978-0-8218-3853-2
Expected publication date is July 14, 2007.

High-dimensional spatio-temporal partial differential equations are a major challenge to scientific computing of the future. Up to now deemed prohibitive, they have recently become manageable by combining recent developments in numerical techniques, appropriate computer implementations, and the use of computers with parallel and even massively parallel architectures. This opens new perspectives in many fields of applications. Kinetic plasma physics equations, the many body Schrodinger equation, Dirac and Maxwell equations for molecular electronic structures and nuclear dynamic computations, options pricing equations in mathematical finance, as well as Fokker-Planck and fluid dynamics equations for complex fluids, are examples of equations that can now be handled.

The objective of this volume is to bring together contributions by experts of international stature in that broad spectrum of areas to confront their approaches and possibly bring out common problem formulations and research directions in the numerical solutions of high-dimensional partial differential equations in various fields of science and engineering with special emphasis on chemistry and physics.

Titles in this series are co-published with the Centre de Recherches Mathematiques.

Readership

Graduate students and research mathematicians interested in numerical solutions of high-dimensional PDE's.

Table of Contents

Elisabetta Barletta and Sorin Dragomir, Universita degli Studi della Basilicata, Potenza, Italy, and Krishan L. Duggal, University of Windsor, Ontario, Canada

Foliations in Cauchy-Riemann Geometry

Mathematical Surveys and Monographs, Volume: 140
2007; 256 pp; hardcover
ISBN-10: 0-8218-4304-4
ISBN-13: 978-0-8218-4304-8
Expected publication date is July 22, 2007.

The authors study the relationship between foliation theory and differential geometry and analysis on Cauchy-Riemann (CR) manifolds. The main objects of study are transversally and tangentially CR foliations, Levi foliations of CR manifolds, solutions of the Yang-Mills equations, tangentially Monge-Ampere foliations, the transverse Beltrami equations, and CR orbifolds. The novelty of the authors' approach consists in the overall use of the methods of foliation theory and choice of specific applications. Examples of such applications are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's approximately commuting vector fields method for the study of global regularity of Neumann operators and Bergman projections in multi-dimensional complex analysis in several complex variables, as well as various applications to differential geometry. Many open problems proposed in the monograph may attract the mathematical community and lead to further applications of foliation theory in complex analysis and geometry of Cauchy-Riemann manifolds.

Readership

Graduate students and research mathematicians interested in foliation theory with applications to differential geometry and complex analysis.

Table of Contents

Edited by: Alexei Davydov, Michael Batanin, and Michael Johnson, Macquarie University, Sydney, Australia, Stephen Lack, University of Western Sydney, Penrith South, Australia, and Amnon Neeman, Australian National University, Canberra, Australia

Categories in Algebra, Geometry, and Mathematical Physics

Contemporary Mathematics, Volume: 431
2007; 467 pp; softcover
ISBN-10: 0-8218-3970-5
ISBN-13: 978-0-8218-3970-6
Expected publication date is July 1, 2007.

Category theory has become the universal language of modern mathematics. This book is a collection of articles applying methods of category theory to the areas of algebra, geometry, and mathematical physics. Among others, this book contains articles on higher categories and their applications and on homotopy theoretic methods. The reader can learn about the exciting new interactions of category theory with very traditional mathematical disciplines.

Readership

Graduate students and research mathematicians interested in category theory and its applications.

Table of Contents

Vladimir Maz'ya, University of Linkoping, Sweden, and University of Liverpool, United Kingdom, and Gunther Schmidt, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

Approximate Approximations

Mathematical Surveys and Monographs, Volume: 141
2007; approx. 356 pp; hardcover
ISBN-10: 0-8218-4203-X
ISBN-13: 978-0-8218-4203-4
Expected publication date is August 11, 2007.

In this book, a new approach to approximation procedures is developed. This new approach is characterized by the common feature that the procedures are accurate without being convergent as the mesh size tends to zero. This lack of convergence is compensated for by the flexibility in the choice of approximating functions, the simplicity of multi-dimensional generalizations, and the possibility of obtaining explicit formulas for the values of various integral and pseudodifferential operators applied to approximating functions.

The developed techniques allow the authors to design new classes of high-order quadrature formulas for integral and pseudodifferential operators, to introduce the concept of approximate wavelets, and to develop new efficient numerical and semi-numerical methods for solving boundary value problems of mathematical physics.

The book is intended for researchers interested in approximation theory and numerical methods for partial differential and integral equations.

Readership

Graduate students and research mathematicians interested in approximation theory and numerical methods.

Table of Contents

Quasi-interpolation
Error estimates for quasi-interpolation
Various basis functions--examples and constructions
Approximation of integral operators
Cubature of diffraction, elastic, and hydrodynamic potentials
Some other cubature problems
Approximation by Gaussians
Approximate wavelets
Cubature over bounded domains
More general grids
Scattered data approximate approximations
Numerical algorithms based upon approximate approximations--linear problems
Numerical algorithms based upon approximate approximations--non-linear problems
Bibliography
Index