Surveys In Noncommutative Geometry
DOWNLOAD
Download Surveys In Noncommutative Geometry PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Surveys In Noncommutative Geometry book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Surveys In Noncommutative Geometry
DOWNLOAD
Author : Nigel Higson
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Surveys In Noncommutative Geometry written by Nigel Higson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
In June 2000, the Clay Mathematics Institute organized an Instructional Symposium on Noncommutative Geometry in conjunction with the AMS-IMS-SIAM Joint Summer Research Conference. These events were held at Mount Holyoke College in Massachusetts from June 18 to 29, 2000. The Instructional Symposium consisted of several series of expository lectures which were intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Those expository lectures have been edited and are reproduced in this volume. The lectures of Rosenberg and Weinberger discuss various applications of noncommutative geometry to problems in ordinary geometry and topology. The lectures of Lagarias and Tretkoff discuss the Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory. Higson gives an account of the residue index theorem of Connes and Moscovici. Noncommutative geometry is to an unusual extent the creation of a single mathematician, Alain Connes. The present volume gives an extended introduction to several aspects of Connes' work in this fascinating area.
Noncommutative Geometry
DOWNLOAD
Author : Alain Connes
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-08
Noncommutative Geometry written by Alain Connes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-08 with Mathematics categories.
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Basic Noncommutative Geometry
DOWNLOAD
Author : Masoud Khalkhali
language : en
Publisher: European Mathematical Society
Release Date : 2009
Basic Noncommutative Geometry written by Masoud Khalkhali and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
"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.
Noncommutative Geometry
DOWNLOAD
Author : Igor V. Nikolaev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-11-07
Noncommutative Geometry written by Igor V. Nikolaev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with Mathematics categories.
This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field. Contents Part I: Basics Model examples Categories and functors C∗-algebras Part II: Noncommutative invariants Topology Algebraic geometry Number theory Part III: Brief survey of NCG Finite geometries Continuous geometries Connes geometries Index theory Jones polynomials Quantum groups Noncommutative algebraic geometry Trends in noncommutative geometry
Advances In Noncommutative Geometry
DOWNLOAD
Author : Ali Chamseddine
language : en
Publisher: Springer
Release Date : 2021-08-26
Advances In Noncommutative Geometry written by Ali Chamseddine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-26 with Mathematics categories.
This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.
From Differential Geometry To Non Commutative Geometry And Topology
DOWNLOAD
Author : Neculai S. Teleman
language : en
Publisher: Springer Nature
Release Date : 2019-11-10
From Differential Geometry To Non Commutative Geometry And Topology written by Neculai S. Teleman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-10 with Mathematics categories.
This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.
Index Theory For Locally Compact Noncommutative Geometries
DOWNLOAD
Author : A. L. Carey
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-08-12
Index Theory For Locally Compact Noncommutative Geometries written by A. L. Carey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-12 with Mathematics categories.
Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
An Invitation To Noncommutative Geometry
DOWNLOAD
Author : Matilde Marcolli
language : en
Publisher: World Scientific
Release Date : 2008-02-11
An Invitation To Noncommutative Geometry written by Matilde Marcolli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-11 with Science categories.
This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory.
An Introduction To Noncommutative Geometry
DOWNLOAD
Author : Joseph C. Várilly
language : en
Publisher: European Mathematical Society
Release Date : 2006
An Introduction To Noncommutative Geometry written by Joseph C. Várilly and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Noncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples. This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the conditions on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples. The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples.
Noncommutative Geometry And Number Theory
DOWNLOAD
Author : Caterina Consani
language : en
Publisher: Vieweg+Teubner Verlag
Release Date : 2014-12-02
Noncommutative Geometry And Number Theory written by Caterina Consani and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-02 with Mathematics categories.
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.