The papers in this volume are based on talks given at the 2001 Manchester Meeting of the London Mathematical Society, which was followed by an international workshop on Quantization, Deformations, and New Homological and Categorical Methods in Mathematical Physics. Focus is on the topics suggested by the title: quantization in its various aspects, Poisson brackets and generalizations, and structures beyond'' this, including symplectic supermanifolds, operads, Lie groupoids and Lie (bi)algebroids, and algebras with $n$-ary operations. The book offers accounts of up-to-date results as well as...

Swift progress and new applications characterize the area of solitons and the inverse scattering transform. There are rapid developments in current nonlinear optical technology: larger intensities are more available; pulse widths are smaller; relaxation times and damping rates are less significant. In keeping with these advancements, exactly integrable soliton equations, such as $3$-wave resonant interactions and second harmonic generation, are becoming more and more relevant in experimental applications. Techniques are now being developed for using these interactions to frequency convert...

An overview of the diversity of current trends in computational and statistical group theory. The book presents the latest research and a number of specific topics, such as growth, black box groups, measures on groups, product replacement algorithms and quantum automata. It includes contributions by speakers at AMS Special Sessions at the University of Nevada (Las Vegas) and the Stevens Institute of Technology (Hoboken, New Jersey). It is suitable for graduate students and research mathematicians interested in group theory.

The volume is from the proceedings of the international conference held in celebration of Stanley Osher's sixtieth birthday. It presents recent developments and exciting new directions in scientific computing and partial differential equations for time dependent problems and its interplay with other fields, such as image processing, computer vision and graphics. Over the past decade, there have been very rapid developments in the field. This volume emphasizes the strong interaction of advanced mathematics with real-world applications and algorithms. The book is suitable for graduate students...

This volume outlines current developments in model theory and combinatorial set theory and presents state-of-the-art research. Well-known researchers report on their work in model theory and set theory with applications to algebra.

This volume contains six detailed papers written by participants of the special session on value distribution theory and complex dynamics held in Hong Kong at the First Joint International Meeting of the AMS and the Hong Kong Mathematical Society in December 2000. It demonstrates the strong interconnections between the two fields and the progress of leading researchers from Asia. In the book, W. Bergweiler discusses proper analytic maps with one critical point and generalizes a previous result concerning Leau domains. W. Cherry and J. Wang discuss non-Archimedean analogues of Picard's...

This volume is derived from lectures presented at the 2001 John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville. The topic was computational mathematics, focusing on parallel numerical algorithms for partial differential equations, their implementation and applications in fluid mechanics and material science. Compiled here are articles from six of nine speakers. Each of them is a leading researcher in the field of computational mathematics and its applications. A vast area that has been coming into its own, computational mathematics has experienced major developments in...

This volume contains papers based on some of the talks given at the NSF-CBMS conference on The Geometrical Study of Differential Equations held at Howard University (Washington, DC). The collected papers present important recent developments in this area, including the treatment of nontransversal group actions in the theory of group invariant solutions of PDEs, a method for obtaining discrete symmetries of differential equations, the establishment of a group-invariant version of the variational complex based on a general moving frame construction, the introduction of a new variational complex...

This volume derives from the second Iberoamerican Congress on Geometry, held in 2001 in Mexico at the Centro de Investigacion en Matematicas AC, an internationally recognized programme of research in pure mathematics. The conference topics were chosen with an eye toward the presentation of new methods, recent results and the creation of more interconnections between the different research groups working in complex manifolds and hyperbolic geometry. This volume reflects both the unity and the diversity of these subjects. Researchers around the globe have been working on problems concerning...

This volume reflects the proceedings from an international conference on celestial mechanics held at Northwestern University (Evanston, Illinois) in celebration of Donald Saari's 60th birthday. Many leading experts and researchers presented their recent results. Don Saari's significant contribution to the field came in the late 1960s through a series of important works. His work revived the singularity theory in the $n$-body problem which was started by Poincare and Painleve. Saari's solution of the Littlewood conjecture, his work on singularities, collision and noncollision, on central...