An Invitation to Noncommutative Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to Noncommutative Geometry write by Masoud Khalkhali. This book was released on 2008. An Invitation to Noncommutative Geometry available in PDF, EPUB and Kindle. A walk in the noncommutative garden / A. Connes and M. Marcolli -- Renormalization of noncommutative quantum field theory / H. Grosse and R. Wulkenhaar -- Lectures on noncommutative geometry / M. Khalkhali -- Noncommutative bundles and instantons in Tehran / G. Landi and W. D. van Suijlekom -- Lecture notes on noncommutative algebraic geometry and noncommutative tori / S. Mahanta -- Lectures on derived and triangulated categories / B. Noohi -- Examples of noncommutative manifolds: complex tori and spherical manifolds / J. Plazas -- D-branes in noncommutative field theory / R. J. Szabo.
Noncommutative Geometry
Noncommutative Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Noncommutative Geometry write by Alain Connes. This book was released on 2003-12-15. Noncommutative Geometry available in PDF, EPUB and Kindle. 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.
Spectral Action in Noncommutative Geometry
Spectral Action in Noncommutative Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spectral Action in Noncommutative Geometry write by Michał Eckstein. This book was released on 2018-12-18. Spectral Action in Noncommutative Geometry available in PDF, EPUB and Kindle. What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given. Chapter 2 is designed to serve as a toolkit for computations. The third chapter offers an in-depth view into the subtle links between the asymptotic expansions of traces of heat operators and meromorphic extensions of the associated spectral zeta functions. Chapter 4 studies the behaviour of the spectral action under fluctuations by gauge potentials. A subjective list of open problems in the field is spelled out in the fifth Chapter. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries. The book serves both as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts.
An Introduction to Noncommutative Geometry
An Introduction to Noncommutative Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Noncommutative Geometry write by Joseph C. Várilly. This book was released on 2006. An Introduction to Noncommutative Geometry available in PDF, EPUB and Kindle. 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.
Basic Noncommutative Geometry
Basic Noncommutative Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Basic Noncommutative Geometry write by Masoud Khalkhali. This book was released on 2009. Basic Noncommutative Geometry available in PDF, EPUB and Kindle. "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.
