# Search Results for "introduction-to-the-baum-connes-conjecture-lectures-in-mathematics-eth-zÃƒÂ-rich"

## Operator Algebras, Quantization, and Noncommutative Geometry

*A Centennial Celebration Honoring John Von Neumann and Marshall H. Stone*

**Author**: Marshall Harvey Stone,Robert S. Doran,Richard V. Kadison**Publisher:**American Mathematical Soc.**ISBN:**0821834029**Category:**Mathematics**Page:**422**View:**5829

John von Neumann and Marshall Stone were two giants of Twentieth Century mathematics. In honor of the 100th anniversary of their births, a mathematical celebration was organized featuring developments in fields where both men were major influences. This volume contains articles from the AMS Special Session, Operator Algebras, Quantization and Noncommutative Geometry: A Centennial Celebration in Honor of John von Neumann and Marshall H. Stone.Papers range from expository and historical surveys to original research articles. All articles were carefully refereed and cover a broad range of mathematical topics reflecting the fundamental ideas of von Neumann and Stone. Most contributions are expanded versions of the talks and were written exclusively for this volume. Included, among others, are articles by George W. Mackey, Nigel Higson, and Marc Rieffel. Also featured is a reprint of P.R. Halmos' ""The Legend of John von Neumann"". The book is suitable for graduate students and researchers interested in operator algebras and applications, including noncommutative geometry.

## Topological and Bivariant K-Theory

**Author**: Joachim Cuntz,Jonathan Rosenberg**Publisher:**Springer Science & Business Media**ISBN:**3764383992**Category:**Mathematics**Page:**262**View:**9912

Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.

## Introduction to the Baum-Connes Conjecture

**Author**: Alain Valette**Publisher:**Springer Science & Business Media**ISBN:**9783764367060**Category:**Mathematics**Page:**104**View:**968

The Baum-Connes conjecture is part of A. Connes' non-commutative geometry programme. It can be viewed as a conjectural generalisation of the Atiyah-Singer index theorem, to the equivariant setting (the ambient manifold is not compact, but some compactness is restored by means of a proper, co-compact action of a group "gamma"). Like the Atiyah-Singer theorem, the Baum-Connes conjecture states that a purely topological object coincides with a purely analytical one. For a given group "gamma", the topological object is the equivariant K-homology of the classifying space for proper actions of "gamma", while the analytical object is the K-theory of the C*-algebra associated with "gamma" in its regular representation. The Baum-Connes conjecture implies several other classical conjectures, ranging from differential topology to pure algebra. It has also strong connections with geometric group theory, as the proof of the conjecture for a given group "gamma" usually depends heavily on geometric properties of "gamma". This book is intended for graduate students and researchers in geometry (commutative or not), group theory, algebraic topology, harmonic analysis, and operator algebras. It presents, for the first time in book form, an introduction to the Baum-Connes conjecture. It starts by defining carefully the objects in both sides of the conjecture, then the assembly map which connects them. Thereafter it illustrates the main tool to attack the conjecture (Kasparov's theory), and it concludes with a rough sketch of V. Lafforgue's proof of the conjecture for co-compact lattices in in Spn1, SL(3R), and SL(3C).

## Books in Print

**Author**: R.R. Bowker Company**Publisher:**N.A**ISBN:**N.A**Category:**American literature**Page:**N.A**View:**1294

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

## Basic Noncommutative Geometry

**Author**: Masoud Khalkhali**Publisher:**European Mathematical Society**ISBN:**9783037190616**Category:**Mathematics**Page:**223**View:**3987

"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.

## K-theory and Noncommutative Geometry

**Author**: Guillermo Cortiñas**Publisher:**European Mathematical Society**ISBN:**9783037190609**Category:**K-theory**Page:**440**View:**2179

"Contains the proceedings of VASBI, the ICM 2006 satellite on K-theory and Noncommutative Geometry which took place in Valladolid, Spain, from August 31 to September 6, 2006."--Pref.

## Proper Group Actions and the Baum-Connes Conjecture

**Author**: Guido Mislin,Alain Valette**Publisher:**Springer Science & Business Media**ISBN:**9783764304089**Category:**Mathematics**Page:**131**View:**5634

This book contains a concise introduction to the techniques used to prove the Baum-Connes conjecture. The approach is expository, but it contains proofs of many basic results on topological K-homology and the K-theory of C^*-algebras. It features a detailed discussion of naturality questions concerning the assembly map, a topic not well documented in the literature. The book is aimed at advanced graduate students and researchers in the area, leading to current research problems.

## 3-manifold Groups

**Author**: Matthias Aschenbrenner,Stefan Friedl,Henry Wilton**Publisher:**Erich Schmidt Verlag GmbH & Co. KG**ISBN:**9783037191545**Category:**Fundamental groups (Mathematics)**Page:**215**View:**3132

The field of 3-manifold topology has made great strides forward since 1982 when Thurston articulated his influential list of questions. Primary among these is Perelman's proof of the Geometrization Conjecture, but other highlights include the Tameness Theorem of Agol and Calegari-Gabai, the Surface Subgroup Theorem of Kahn-Markovic, the work of Wise and others on special cube complexes, and, finally, Agol's proof of the Virtual Haken Conjecture. This book summarizes all these developments and provides an exhaustive account of the current state of the art of 3-manifold topology, especially focusing on the consequences for fundamental groups of 3-manifolds. As the first book on 3-manifold topology that incorporates the exciting progress of the last two decades, it will be an invaluable resource for researchers in the field who need a reference for these developments. It also gives a fast-paced introduction to this material. Although some familiarity with the fundamental group is recommended, little other previous knowledge is assumed, and the book is accessible to graduate students. The book closes with an extensive list of open questions which will also be of interest to graduate students and established researchers.

## Mathematical Analysis of Evolution, Information, and Complexity

**Author**: Wolfgang Arendt,Wolfgang P. Schleich**Publisher:**John Wiley & Sons**ISBN:**3527628037**Category:**Science**Page:**502**View:**5854

Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.

## Vertex Algebras for Beginners

**Author**: Victor G. Kac**Publisher:**American Mathematical Soc.**ISBN:**082181396X**Category:**Mathematics**Page:**201**View:**1476

This is a revised and expanded edition of Kac's original introduction to algebraic aspects of conformal field theory, which was published by the AMS in 1996. The volume serves as an introduction to algebraic aspects of conformal field theory, which in the past 15 years revealed a variety of unusual mathematical notions. Vertex algebra theory provides an effective tool to study them in a unified way. In the book, a mathematician encounters new algebraic structures that originated from Einstein's special relativity postulate and Heisenberg's uncertainty principle. A physicist will find familiar notions presented in a more rigorous and systematic way, possibly leading to a better understanding of foundations of quantum physics. This revised edition is based on courses given by the author at MIT and at Rome University in spring 1997. New material is added, including the foundations of a rapidly growing area of algebraic conformal theory. Also, in some places the exposition has been significantly simplified.

## The Porous Medium Equation

*Mathematical Theory*

**Author**: Juan Luis Vazquez**Publisher:**Oxford University Press**ISBN:**0198569033**Category:**Mathematics**Page:**624**View:**8340

Aimed at research students and academics in mathematics and engineering, as well as engineering specialists, this book provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation.

## Cohomology of Infinite-Dimensional Lie Algebras

**Author**: D.B. Fuks**Publisher:**Springer Science & Business Media**ISBN:**1468487655**Category:**Mathematics**Page:**352**View:**4681

There is no question that the cohomology of infinite dimensional Lie algebras deserves a brief and separate mono graph. This subject is not cover~d by any of the tradition al branches of mathematics and is characterized by relative ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to "recognize" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list. There are classifica tion theorems in the theory of infinite-dimensional Lie al gebras as well, but they are encumbered by strong restric tions of a technical character. These theorems are useful mainly because they yield a considerable supply of interest ing examples. We begin with a list of such examples, and further direct our main efforts to their study.

## Kac-Moody and Virasoro Algebras

*A Reprint Volume for Physicists*

**Author**: Peter Goddard,David Olive**Publisher:**World Scientific**ISBN:**9789971504205**Category:**Science**Page:**586**View:**503

This volume reviews the subject of Kac-Moody and Virasoro Algebras. It serves as a reference book for physicists with commentary notes and reprints.

## 18 Unconventional Essays on the Nature of Mathematics

**Author**: Reuben Hersh**Publisher:**Springer Science & Business Media**ISBN:**0387298312**Category:**Mathematics**Page:**326**View:**2072

Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines

## Analytic K-Homology

**Author**: Nigel Higson,John Roe**Publisher:**OUP Oxford**ISBN:**9780191589201**Category:**Mathematics**Page:**424**View:**4839

Analytic K-homology draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and it has been used with specacular success to discover remarkable theorems across a wide span of mathematics. The purpose of this book is to acquaint the reader with the essential ideas of analytic K-homology and develop some of its applications. It includes a detailed introduction to the necessary functional analysis, followed by an exploration of the connections between K-homology and operator theory, coarse geometry, index theory, and assembly maps, including a detailed treatment of the Atiyah-Singer Index Theorem. Beginning with the rudiments of C* - algebra theory, the book will lead the reader to some central notions of contemporary research in geometric functional analysis. Much of the material included here has never previously appeared in book form.

## Vertex Algebras and Algebraic Curves: Second Edition

**Author**: Edward Frenkel,David Ben-Zvi**Publisher:**American Mathematical Soc.**ISBN:**0821836749**Category:**Mathematics**Page:**400**View:**4338

Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.

## Trends in Representation Theory of Algebras and Related Topics

**Author**: Andrzej Skowroński**Publisher:**European Mathematical Society**ISBN:**9783037190623**Category:**Mathematics**Page:**710**View:**9373

This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatories, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development.

## Mathematical Understanding of Nature

*Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians*

**Author**: Vladimir Igorevich Arnolʹd**Publisher:**American Mathematical Soc.**ISBN:**1470418894**Category:**Mathematics**Page:**N.A**View:**4819

## Fourier-Mukai Transforms in Algebraic Geometry

**Author**: Daniel Huybrechts**Publisher:**Oxford University Press on Demand**ISBN:**0199296863**Category:**Mathematics**Page:**307**View:**3636

This work is based on a course given at the Institut de Mathematiques de Jussieu, on the derived category of coherent sheaves on a smooth projective variety. It is aimed at students with a basic knowledge of algebraic geometry and contains full proofs and exercises that aid the reader.