The area of symplectic geometry has developed rapidly in the past ten years with major new discoveries that were motivated by and have provided links with many other subjects such as dynamical systems, topology, gauge theory, mathematical physics, and singularity theory. The contributions to this volume reflect the richness of the subject and include expository papers as well as original research.

This volume is comprised of the invited lectures given at the 14th British Combinatorial Conference. The lectures survey many topical areas of current research activity in combinatorics and its applications, and also provide a valuable overview of the subject, for both mathematicians and computer scientists.

The theory of blowup algebras--Rees algebras, associated graded rings, Hilbert functions, and birational morphisms--is undergoing a period of rapid development. One of the aims of this book is to provide an introduction to these developments. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this places limitations on the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra built on current understanding...

The subject of this book lies on the boundary between probability theory and the theory of function spaces. Here Professor Braverman investigates independent random variables in rearrangement invariant (r.i.) spaces. The significant feature of r.i. spaces is that the norm of an element depends on its distribution only, and this property allows the results and methods associated with r.i. spaces to be applied to problems in probability theory. On the other hand, probabilistic methods can also prove useful in the study of r.i. spaces. In this book new techniques are used and a number of...

This volume discusses results about quadratic forms that give rise to interconnections among number theory, algebra, algebraic geometry, and topology. The author deals with various topics including Hilbert's 17th problem, the Tsen-Lang theory of quasi-algebraically closed fields, the level of topological spaces, and systems of quadratic forms over arbitrary fields. Whenever possible, proofs are short and elegant, and the author has made this book as self-contained as possible. This book brings together thirty years' worth of results certain to interest anyone whose research touches on...

This monograph covers Poisson-Szego integrals on the ball, the Green's function for DEGREESD*D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. It also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Greens potentials. Applications of some of the results to Hp spaces, and...

The theory of these modules together with their bounded and unbounded operators is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebra. This book provides a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. Graduate students and researchers working in operator algebras will welcome this book as an excellent resource.

Stochastic partial differential equations can be used in many areas of science to model complex systems evolving over time. This book assembles together some of the world's best known authorities on stochastic partial differential equations. Subjects include the stochastic Navier-Stokes equation, critical branching systems, population models, statistical dynamics, and ergodic properties of Markov semigroups. For all workers on stochastic partial differential equations, this book will have much to offer.

Successive waves of migrant concepts, largely from mathematical physics, have stimulated the study of vector bundles over algebraic varieties in the past few years. But the subject has retained its roots in old questions concerning subvarieties of projective space. The 1993 Durham Symposium on vector bundles in algebraic geometry brought together some of the leading researchers in the field to further explore these interactions. This book is a collection of survey articles by the main speakers at the Symposium and presents to the mathematical world an overview of the key areas of research...

This study is concerned with computing the homotopy classes of maps algebraically and determining the law of composition for such maps. The problem is solved by introducing new algebraic models of a 4-manifold. Including a complete list of references for the text, the book appeals to researchers and graduate students in topology and algebra.