Noncommutative Geometry And Physics 3 - Proceedings Of The Noncommutative Geometry And Physics 2008, On K-theory And D-branes & Proceedings Of The Rims Thematic Year 2010 On Perspectives In Deformation Quantization And Noncommutative Geometry

Noncommutative Geometry And Physics 3 - Proceedings Of The Noncommutative Geometry And Physics 2008, On K-theory And D-branes & Proceedings Of The Rims Thematic Year 2010 On Perspectives In Deformation Quantization And Noncommutative Geometry

Author: Giuseppe Dito

Publisher: World Scientific

Published: 2013-01-11

Total Pages: 537

ISBN-13: 9814425028

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Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field. It is an important topic both for mathematics and physics.


Noncommutative Geometry and Physics 3

Noncommutative Geometry and Physics 3

Author: Giuseppe Dito

Publisher: World Scientific

Published: 2013

Total Pages: 537

ISBN-13: 981442501X

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Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.


Noncommutative Geometry and Physics, 3

Noncommutative Geometry and Physics, 3

Author: Giuseppe Dito

Publisher: World Scientific Publishing Company Incorporated

Published: 2013

Total Pages: 528

ISBN-13: 9789814425001

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Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field. It is an important topic both for mathematics and physics.


Quanta of Maths

Quanta of Maths

Author: Institut des hautes études scientifiques (Paris, France)

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 695

ISBN-13: 0821852035

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The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.


The Shape of Inner Space

The Shape of Inner Space

Author: Shing-Tung Yau

Publisher: Il Saggiatore

Published: 2010-09-07

Total Pages: 398

ISBN-13: 0465020232

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The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.


Lie Theory and Its Applications in Physics

Lie Theory and Its Applications in Physics

Author: Vladimir Dobrev

Publisher: Springer Science & Business Media

Published: 2013-04-09

Total Pages: 535

ISBN-13: 4431542701

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Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantum groups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples of these new trends are presented in this volume, based on contributions from the Workshop “Lie Theory and Its Applications in Physics” held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience of mathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theory.


Cohomological and Geometric Approaches to Rationality Problems

Cohomological and Geometric Approaches to Rationality Problems

Author: Fedor Bogomolov

Publisher: Springer Science & Business Media

Published: 2009-11-03

Total Pages: 316

ISBN-13: 0817649344

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Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov


Lagrangian Intersection Floer Theory

Lagrangian Intersection Floer Theory

Author: Kenji Fukaya

Publisher: American Mathematical Soc.

Published: 2010-06-21

Total Pages: 426

ISBN-13: 0821852507

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This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered $A_\infty$-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered $A_\infty$ algebras and $A_\infty$ bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.


Focus on Quantum Field Theory

Focus on Quantum Field Theory

Author: O. Kovras

Publisher: Nova Publishers

Published: 2005

Total Pages: 258

ISBN-13: 9781594541261

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Gang activity in the United States has been traced to the early 19th century when youth gangs emerged from some immigrant populations. Now, as then, gangs provide identity and social relationships for some young people who feel marginalised by the dominant social, economic and cultural environments in which they live. Gangs, however, are not simply a "street family" to some of the nation's disenfranchised. As distinguished by the U.S. Department of Justice, "a group must be involved in a pattern of criminal acts to be considered a youth gang." Between 1980 and 1996, the U.S. experienced significant growth in youth gangs, when the number of cities and jurisdictions that reported gang problems rose from 2863 to approximately 4,800. From 1996 through 1998, the growth seemed to slow down, but according to the 1999 National Youth Gang Survey, the number of gang members is again on the rise.