Stratified Noncommutative Geometry
Author: David Ayala
Publisher: American Mathematical Society
Published: 2024-06-07
Total Pages: 272
ISBN-13: 1470469626
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Noncommutative Geometry and Physics 2005
Author:
Publisher: World Scientific
Published: 2007
Total Pages: 333
ISBN-13: 9812779647
DOWNLOAD EBOOKThis book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems. Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings.
Surveys in Noncommutative Geometry
Author: Nigel Higson
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 212
ISBN-13: 9780821838464
DOWNLOAD EBOOKIn 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. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
Advances in Noncommutative Geometry
Author: Ali Chamseddine
Publisher: Springer Nature
Published: 2020-01-13
Total Pages: 753
ISBN-13: 3030295974
DOWNLOAD EBOOKThis 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.
Analytic and Geometric Study of Stratified Spaces
Author: Markus J. Pflaum
Publisher: Springer
Published: 2003-07-01
Total Pages: 233
ISBN-13: 3540454365
DOWNLOAD EBOOKThe book provides an introduction to stratification theory leading the reader up to modern research topics in the field. The first part presents the basics of stratification theory, in particular the Whitney conditions and Mather's control theory, and introduces the notion of a smooth structure. Moreover, it explains how one can use smooth structures to transfer differential geometric and analytic methods from the arena of manifolds to stratified spaces. In the second part the methods established in the first part are applied to particular classes of stratified spaces like for example orbit spaces. Then a new de Rham theory for stratified spaces is established and finally the Hochschild (co)homology theory of smooth functions on certain classes of stratified spaces is studied. The book should be accessible to readers acquainted with the basics of topology, analysis and differential geometry.
Cyclic Cohomology and Noncommutative Geometry
Author: Joachim J. R. Cuntz
Publisher: American Mathematical Soc.
Published: 1997
Total Pages: 199
ISBN-13: 0821808230
DOWNLOAD EBOOKNoncommutative geometry is a new field that is among the great challenges of present-day mathematics. Its methods allow one to treat noncommutative algebras - such as algebras of pseudodifferential operators, group algebras, or algebras arising from quantum field theory - on the same footing as commutative algebras, that is, as spaces. Applications range over many fields of mathematics and mathematical physics. This volume contains the proceedings of the workshop on "Cyclic Cohomology and Noncommutative Geometry" held at the Fields Institute in June 1995.
Noncommutative Coordinates for Symplectic Representations
Author: Daniele Alessandrini
Publisher: American Mathematical Society
Published: 2024-09-09
Total Pages: 130
ISBN-13: 1470471086
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Normed Amenability and Bounded Cohomology over Non-Archimedean Fields
Author: Francesco Fournier-Facio
Publisher: American Mathematical Society
Published: 2024-08-19
Total Pages: 116
ISBN-13: 1470470918
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Noncommutative Geometry and Global Analysis
Author: Henri Moscovici
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 337
ISBN-13: 0821849441
DOWNLOAD EBOOKThis volume represents the proceedings of the conference on Noncommutative Geometric Methods in Global Analysis, held in honor of Henri Moscovici, from June 29-July 4, 2009, in Bonn, Germany. Henri Moscovici has made a number of major contributions to noncommutative geometry, global analysis, and representation theory. This volume, which includes articles by some of the leading experts in these fields, provides a panoramic view of the interactions of noncommutative geometry with a variety of areas of mathematics. It focuses on geometry, analysis and topology of manifolds and singular spaces, index theory, group representation theory, connections of noncommutative geometry with number theory and arithmetic geometry, Hopf algebras and their cyclic cohomology.
Noncommutative Geometry
Author: Alain Connes
Publisher: Springer
Published: 2003-12-15
Total Pages: 364
ISBN-13: 3540397027
DOWNLOAD EBOOKNoncommutative 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.
