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Noncommutative Geometry and Number Theory

Where Arithmetic Meets Geometry and Physics (Aspects of Mathematics)
  • 372 Pages
  • 3.54 MB
  • 9856 Downloads
  • English

Verlag Vieweg
The Physical Object
FormatHardcover
ID Numbers
Open LibraryOL9788608M
ISBN 103834801704
ISBN 139783834801708

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 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 Lfactors of arithmetic varieties.

The subject of noncommutative geometry has recently made its way into theoretical physics, and so a perusal of this book would be of interest to individuals working in string theory or quantum field theory.

The main idea of this book is to generalize measure and operator theory to /5(10). noncommutative geometry to address questions in a new way and to reinterpret results and constructions from number theory and arithmetic algebraic geometry.

This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at. Noncommutative Geometry and Number Theory Paula B. Cohen Introduction In almost every branch of mathematics we use the ring of rational integers, yet in looking beyond the formal structure of this ring we often encounter great gaps in our understanding.

Developed by Alain Connes since the late s, 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. The theory, called noncommutative geometry, rests on two essential points: 1. The existence of many natural spaces for which the classical set-theoretic tools of analysis, such as measure theory, topology, calculus, and metric ideas lose their pertinence, but which correspond very naturally to a noncommutative algebra.

Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry.

This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of. 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.

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.

$ This book covers the basics of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. A brief survey of the main parts of noncommutative geometry with historical remarks, bibliography, and a list of exercises is : Igor V.

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Nikolaev. applications of noncommutative geometry to problems in “ordinary” topology, and the lectures of Lagarias and Tretkoff discussed the Riemann hypothesis and the possible application of the methods of noncommutative geometry in number the-ory.

This book also contains an account by Higson of the “residue index theorem” of Connes and Moscovici. 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 Format: Hardcover. 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.

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.

( views) Noncommutative Geometry by Alain Connes - Academic Press, The definitive treatment of the. commutative Geometry", Princeton Univ. Press, Finally, a more spe-cialized \Noncommutative Geometry, Quantum Fields and Motives", AMS Colloquium Publications, by A. Connes and M. Marcolli is devoted to the links to physics and number theory.

None of these books treat the NCG as a functor [63]. I thank the organizers, participants and. Hello, Sign in.

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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.

Dear Colleagues, There is a growing evidence that noncommutative geometry may have a lasting impact on the unsolved classical problems of number theory; see the work of Bost and Connes on the Riemann Hypothesis, Cuntz's generalization of the Bost–Connes systems, and.

Download Noncommutative Geometry And Global Analysis books, This volume represents the proceedings of the conference on Noncommutative Geometric Methods in Global Analysis, held in honor of Henri Moscovici, from June July 4,in Bonn, Germany.

Henri Moscovici has made a number of major contributions to noncommutative geometry, global. 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 : Springer-Verlag Berlin Heidelberg.

This is the first and so far the only book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. Although the book provides important results, which are in a sense definitive, on the above-mentioned topic, it contains all the necessary preliminary material.

Caterina Consani is the author of Noncommutative Geometry and Number Theory ( avg rating, 0 ratings, 0 reviews), Noncommutative Geometry and Number Th 4/5(1).

Description Noncommutative Geometry and Number Theory EPUB

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. Download Arithmetic Noncommutative Geometry books, Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry.

This general philosophy is applied to the. Quantum Field Theory And Noncommutative Geometry Quantum Field Theory And Noncommutative Geometry by Ursula Carow-Watamura.

Download it Quantum Field Theory And Noncommutative Geometry books also available in PDF, EPUB, and Mobi Format for read it on your Kindle device, PC, phones or tablets.

This volume reflects the growing collaboration between mathematicians and. Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in some generalized sense).

A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which does. Buy Quantum Field Theory and Noncommutative Geometry (Lecture Notes in Physics ()) on FREE SHIPPING on qualified orders Quantum Field Theory and Noncommutative Geometry (Lecture Notes in Physics ()): Carow-Watamura, Ursula, Maeda, Yoshiaki, Watamura, Satoshi: : Books.

Noncommutative Geometry and Applications to Number Theory The Ohio State University Aprilcyclic homology and symplectic topology, November, Palo Alto, California Noncommutative Geometry, September 6th th,Oberwolfach, Germany.

Purchase Noncommutative Geometry - 1st Edition. Print Book & E-Book. ISBN. Other instances of noncommutative spaces that arise in the context of number theory and arithmetic geometry can be found in the non-commutative compacti cation of modular curves of [25], [70].

This noncommutative space is again related to the noncommutative geom-etry of Q-lattices. In fact, it can be seen as a stratum in the com-pacti cation of.Part of the Lecture Notes in Physics book series (LNP, volume ) Chapters Table of contents (15 of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry.

A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum.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/5(3).