This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.
This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of man...
The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations. These two types of computation coexist in mathematics yet are separated in traditional research of mathematical computation. This book presents 27 research articles on the integration and interaction of symbolic and numeric computation.
The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and nu...
Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.
Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical ph...
The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential & integral equations, harmonic, complex & stochas- tic analysis, and analytic number theory during more than half a century. Yet, the extent of his contributions has not always been fully recognized in the mathematics community. For example, the horseshoe mapping constructed by Stephen Smale in 1960 played a central role in the development of the modern theory of dynami- cal systems and chaos. The horseshoe map was directly stimulated by Levinson's research on forced periodic...
The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential & integral equations, harmonic, complex ...
This volume explores multiscale methods as applied to various areas of physics and to the relative developments in mathematics. In the last few years, multiscale methods have lead to spectacular progress in our understanding of complex physical systems and have stimulated the development of very refined mathematical techniques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics.
This volume explores multiscale methods as applied to various areas of physics and to the relative developments in mathematics. In the last few yea...
This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developping new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.
This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dort...
High dimensional probability, in the sense that encompasses the topics rep- resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es- sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values...
High dimensional probability, in the sense that encompasses the topics rep- resented in this volume, began about thirty years ago with research in two...
Ring theory provides the algebraic underpinnings for many areas of mathematics, computer science, and physics. For example, ring theory appears in: functional analysis; algebraic topology; algebraic number theory; coding theory; and in the study of quantum theory. This volume is a collection of research papers, many presented at the 3rd Korea-China-Japan International Symposium on Ring Theory held jointly with the 2nd Korea-Japan Ring Theory Seminar, in Korea, The articles examine wide-ranging developments and methodologies in various areas, including classical Hopf algebras and quantum...
Ring theory provides the algebraic underpinnings for many areas of mathematics, computer science, and physics. For example, ring theory appears in: fu...
During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related...
During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, incl...
Affine flag manifolds are infinite dimensional versions of familiar objects such as Gramann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory of symmetric polynomials), arithmetic geometry (e.g., the fundamental lemma in the Langlands program), and algebraic geometry (e.g., affine flag manifolds as parameter spaces for principal bundles). Novel...
Affine flag manifolds are infinite dimensional versions of familiar objects such as Gramann varieties. The book features lecture notes, survey article...
