Advances in Noncommutative Geometry: On the Occasion of Alain Connes` 70th Birthday, Chamseddine Ali, Consani Caterina, Higson Nigel
Автор: Alain Connes Название: Noncommutative Geometry, ISBN: 012185860X ISBN-13(EAN): 9780121858605 Издательство: Elsevier Science Рейтинг: Цена: 59500.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Reveals what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields. This work presents an approach to measure theory, geometry, and mathematical physics. It includes features such as: space of Penrose tilings; space of leaves of a foliation; and more.
Автор: Alain Connes, Matilde Marcolli Название: Noncommutative Geometry, Quantum Fields and Motives ISBN: 1470450453 ISBN-13(EAN): 9781470450458 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 82770.00 T Наличие на складе: Нет в наличии. Описание: The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces.The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adele class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
Автор: Ali Chamseddine; Caterina Consani; Nigel Higson; M Название: Advances in Noncommutative Geometry ISBN: 3030295966 ISBN-13(EAN): 9783030295967 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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.
Автор: Eisenbud Название: Commutative Algebra and Noncommutative Algebraic Geometry ISBN: 110714972X ISBN-13(EAN): 9781107149724 Издательство: Cambridge Academ Рейтинг: Цена: 121440.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In recent years there have been many significant developments in these two fields; furthermore, the boundary between them has become increasingly blurred. Based on a series of successful lectures, this two-volume series contains survey articles and research papers by experts in the field which emphasise the connections between them. Volume 2 focuses on the most recent research.
Автор: Igor V. Nikolaev Название: Noncommutative Geometry: A Functorial Approach ISBN: 3110543176 ISBN-13(EAN): 9783110543179 Издательство: Walter de Gruyter Цена: 123910.00 T Наличие на складе: Невозможна поставка. Описание:
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
Автор: Yoshiaki Maeda; Hitoshi Moriyoshi; Hideki Omori; D Название: Noncommutative Differential Geometry and Its Applications to Physics ISBN: 9401038295 ISBN-13(EAN): 9789401038294 Издательство: Springer Рейтинг: Цена: 121890.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Proceedings of the Workshop at Shonan, Japan, June 1999
Автор: Wim Beenakker; Thijs van den Broek; Walter D. Suij Название: Supersymmetry and Noncommutative Geometry ISBN: 3319247964 ISBN-13(EAN): 9783319247960 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed.
Автор: Jose M. Gracia-Bondia; Joseph C. Varilly; Hector F Название: Elements of Noncommutative Geometry ISBN: 146126569X ISBN-13(EAN): 9781461265696 Издательство: Springer Рейтинг: Цена: 83850.00 T Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Caterina Consani; Klas Diederich; Matilde Marcolli Название: Noncommutative Geometry and Number Theory ISBN: 3834826731 ISBN-13(EAN): 9783834826732 Издательство: Springer Рейтинг: Цена: 74010.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. Research across these ?elds has now reached an imp- tant turning point, as shows the increasing interest with which the mathematical community approaches these topics. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new c- nections between the ?elds of number theory, algebraic geometry and noncom- tative geometry. Thecontributionstothisvolumepartlyre?ectthetwoworkshops"Noncom- tative Geometry and Number Theory" that took place at the Max-Planck-Institut f] ur Mathematik in Bonn, in August 2003 and June 2004. The two workshops were the ?rst activity entirely dedicated to the interplay between these two ?elds of mathematics. An important part of the activities, which is also re?ected in this volume, came from the hindsight of physics which often provides new perspectives onnumber theoretic problems that make it possible to employ the tools of nonc- mutative geometry, well designed to describe the quantum world.
Автор: Pierre Martinetti, Jean-Christophe Wallet Название: Noncommutative Geometry and Optimal Transport ISBN: 1470422972 ISBN-13(EAN): 9781470422974 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 108110.00 T Наличие на складе: Невозможна поставка. Описание: Contains the proceedings of the Workshop on Noncommutative Geometry and Optimal Transport, held in November 2014. This volume contains several review papers that will give the reader an extensive introduction to the metric aspect of noncommutative geometry and its possible interpretation as a Wasserstein distance on a quantum space, as well as several topic papers.
