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Groupoids In Analysis Geometry And Physics
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Book Synopsis Groupoids in Analysis, Geometry, and Physics by : Arlan Ramsay
Download or read book Groupoids in Analysis, Geometry, and Physics written by Arlan Ramsay and published by American Mathematical Soc.. This book was released on 2001 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groupoids often occur when there is symmetry of a nature not expressible in terms of groups. Other uses of groupoids can involve something of a dynamical nature. Indeed, some of the main examples come from group actions. It should also be noted that in many situations where groupoids have been used, the main emphasis has not been on symmetry or dynamics issues. While the implicit symmetry and dynamics are relevant, the groupoid records mostly the structure of the space of leaves and the holonomy. More generally, the use of groupoids is very much related to various notions of orbit equivalance. This book presents the proceedings from the Joint Summer Research Conference on ``Groupoids in Analysis, Geometry, and Physics'' held in Boulder, CO. The book begins with an introduction to ways in which groupoids allow a more comprehensive view of symmetry than is seen via groups. Topics range from foliations, pseudo-differential operators, $KK$-theory, amenability, Fell bundles, and index theory to quantization of Poisson manifolds. Readers will find examples of important tools for working with groupoids. This book is geared to students and researchers. It is intended to improve their understanding of groupoids and to encourage them to look further while learning about the tools used.
Book Synopsis Symplectic Geometry, Groupoids, and Integrable Systems by : Pierre Dazord
Download or read book Symplectic Geometry, Groupoids, and Integrable Systems written by Pierre Dazord and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers, some of which are in English, the rest in French, in this volume are based on lectures given during the meeting of the Seminare Sud Rhodanien de Geometrie (SSRG) organized at the Mathematical Sciences Research Institute in 1989. The SSRG was established in 1982 by geometers and mathematical physicists with the aim of developing and coordinating research in symplectic geometry and its applications to analysis and mathematical physics. Among the subjects discussed at the meeting, a special role was given to the theory of symplectic groupoids, the subject of fruitful collaboration involving geometers from Berkeley, Lyon, and Montpellier.
Book Synopsis An Introduction to Groups, Groupoids and Their Representations by : Alberto Ibort
Download or read book An Introduction to Groups, Groupoids and Their Representations written by Alberto Ibort and published by CRC Press. This book was released on 2019-10-28 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject. Category theory is the natural language that is being used to develop the theory of groupoids. However, categorical presentations of mathematical subjects tend to become highly abstract very fast and out of reach of many potential users. To avoid this, foundations of the theory, starting with simple examples, have been developed and used to study the structure of finite groups and groupoids. The appropriate language and notions from category theory have been developed for students of mathematics and theoretical physics. The book presents the theory on the same level as the ordinary and elementary theories of finite groups and their representations, and provides a unified picture of the same. The structure of the algebra of finite groupoids is analysed, along with the classical theory of characters of their representations. Unnecessary complications in the formal presentation of the subject are avoided. The book offers an introduction to the language of category theory in the concrete setting of finite sets. It also shows how this perspective provides a common ground for various problems and applications, ranging from combinatorics, the topology of graphs, structure of databases and quantum physics.
Book Synopsis Lie Groupoids and Lie Algebroids in Differential Geometry by : K. Mackenzie
Download or read book Lie Groupoids and Lie Algebroids in Differential Geometry written by K. Mackenzie and published by Cambridge University Press. This book was released on 1987-06-25 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of Lie algebroid: in principal bundle terms this is the Atiyah sequence. The author's viewpoint is that certain deep problems in connection theory are best addressed by groupoid and Lie algebroid methods. After preliminary chapters on topological groupoids, the author gives the first unified and detailed account of the theory of Lie groupoids and Lie algebroids. He then applies this theory to the cohomology of Lie algebroids, re-interpreting connection theory in cohomological terms, and giving criteria for the existence of (not necessarily Riemannian) connections with prescribed curvature form. This material, presented in the last two chapters, is work of the author published here for the first time. This book will be of interest to differential geometers working in general connection theory and to researchers in theoretical physics and other fields who make use of connection theory.
Book Synopsis Groupoids, Inverse Semigroups, and their Operator Algebras by : Alan Paterson
Download or read book Groupoids, Inverse Semigroups, and their Operator Algebras written by Alan Paterson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, it has become increasingly clear that there are important connections relating three concepts -- groupoids, inverse semigroups, and operator algebras. There has been a great deal of progress in this area over the last two decades, and this book gives a careful, up-to-date and reasonably extensive account of the subject matter. After an introductory first chapter, the second chapter presents a self-contained account of inverse semigroups, locally compact and r-discrete groupoids, and Lie groupoids. The section on Lie groupoids in chapter 2 contains a detailed discussion of groupoids particularly important in noncommutative geometry, including the holonomy groupoids of a foliated manifold and the tangent groupoid of a manifold. The representation theories of locally compact and r-discrete groupoids are developed in the third chapter, and it is shown that the C*-algebras of r-discrete groupoids are the covariance C*-algebras for inverse semigroup actions on locally compact Hausdorff spaces. A final chapter associates a universal r-discrete groupoid with any inverse semigroup. Six subsequent appendices treat topics related to those covered in the text. The book should appeal to a wide variety of professional mathematicians and graduate students in fields such as operator algebras, analysis on groupoids, semigroup theory, and noncommutative geometry. It will also be of interest to mathematicians interested in tilings and theoretical physicists whose focus is modeling quasicrystals with tilings. An effort has been made to make the book lucid and 'user friendly"; thus it should be accessible to any reader with a basic background in measure theory and functional analysis.
Book Synopsis Poisson Geometry, Deformation Quantisation and Group Representations by : Simone Gutt
Download or read book Poisson Geometry, Deformation Quantisation and Group Representations written by Simone Gutt and published by Cambridge University Press. This book was released on 2005-06-21 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to Poisson geometry suitable for graduate students.
Book Synopsis Group Representations, Ergodic Theory, and Mathematical Physics by : Robert S. Doran
Download or read book Group Representations, Ergodic Theory, and Mathematical Physics written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 2008 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics.
Book Synopsis An Introduction to C*-Algebras and Noncommutative Geometry by : Heath Emerson
Download or read book An Introduction to C*-Algebras and Noncommutative Geometry written by Heath Emerson and published by Springer Nature. This book was released on with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Global Analysis by : Demeter Krupka
Download or read book Handbook of Global Analysis written by Demeter Krupka and published by Elsevier. This book was released on 2011-08-11 with total page 1243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents
Book Synopsis Geometric and Algebraic Topological Methods in Quantum Mechanics by : G. Giachetta
Download or read book Geometric and Algebraic Topological Methods in Quantum Mechanics written by G. Giachetta and published by World Scientific. This book was released on 2005 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
Book Synopsis Topology and Groupoids by : Ronald Brown
Download or read book Topology and Groupoids written by Ronald Brown and published by Booksurge Llc. This book was released on 2006 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation. The book is intended as a text for a two-semester course in topology and algebraic topology at the advanced undergraduate orbeginning graduate level. There are over 500 exercises, 114 figures, numerous diagrams. The general direction of the book is towardhomotopy theory with a geometric point of view. This book would providea more than adequate background for a standard algebraic topology coursethat begins with homology theory. For more information seewww.bangor.ac.uk/r.brown/topgpds.htmlThis version dated April 19, 2006, has a number of corrections made.
Book Synopsis Finite and Infinite Dimensional Analysis in Honor of Leonard Gross by : Hui-Hsiung Kuo
Download or read book Finite and Infinite Dimensional Analysis in Honor of Leonard Gross written by Hui-Hsiung Kuo and published by American Mathematical Soc.. This book was released on 2003 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the special session in honor of Leonard Gross held at the annual Joint Mathematics Meetings in New Orleans (LA). The speakers were specialists in a variety of fields, and many were Professor Gross's former Ph.D. students and their descendants. Papers in this volume present results from several areas of mathematics. They illustrate applications of powerful ideas that originated in Gross's work and permeate diverse fields. Topics include stochastic partial differential equations, white noise analysis, Brownian motion, Segal-Bargmann analysis, heat kernels, and some applications. The volume should be useful to graduate students and researchers. It provides perspective on current activity and on central ideas and techniques in the topics covered.
Book Synopsis Inverse Problems, Image Analysis, and Medical Imaging by : M. Zuhair Nashed
Download or read book Inverse Problems, Image Analysis, and Medical Imaging written by M. Zuhair Nashed and published by American Mathematical Soc.. This book was released on 2002 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Special Session, Interaction of Inverse Problems and Image Analysis, held at the January 2001 meeting of the AMS in New Orleans, LA. The common thread among inverse problems, signal analysis, and image analysis is a canonical problem: recovering an object (function, signal, picture) from partial or indirect information about the object. Both inverse problems and imaging science have emerged in recent years as interdisciplinary research fields with profound applications in many areas of science, engineering, technology, and medicine. Research in inverse problems and image processing shows rich interaction with several areas of mathematics and strong links to signal processing, variational problems, applied harmonic analysis, and computational mathematics. This volume contains carefully referred and edited original research papers and high-level survey papers that provide overview and perspective on the interaction of inverse problems, image analysis, and medical imaging. The book is suitable for graduate students and researchers interested in signal and image processing and medical imaging.
Book Synopsis Combinatorial and Geometric Group Theory by : Sean Cleary
Download or read book Combinatorial and Geometric Group Theory written by Sean Cleary and published by American Mathematical Soc.. This book was released on 2002 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compactRiemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.
Book Synopsis Advances in Noncommutative Geometry by : Ali Chamseddine
Download or read book Advances in Noncommutative Geometry written by Ali Chamseddine and published by Springer Nature. This book was released on 2020-01-13 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Number Theory and Algebraic Geometry by : S. V. Vostokov
Download or read book Algebraic Number Theory and Algebraic Geometry written by S. V. Vostokov and published by American Mathematical Soc.. This book was released on 2002 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: A. N. Parshin is a world-renowned mathematician who has made significant contributions to number theory through the use of algebraic geometry. Articles in this volume present new research and the latest developments in algebraic number theory and algebraic geometry and are dedicated to Parshin's sixtieth birthday. Well-known mathematicians contributed to this volume, including, among others, F. Bogomolov, C. Deninger, and G. Faltings. The book is intended for graduate students andresearch mathematicians interested in number theory, algebra, and algebraic geometry.
Book Synopsis Topics in Algebraic and Noncommutative Geometry by : Ruth Ingrid Michler
Download or read book Topics in Algebraic and Noncommutative Geometry written by Ruth Ingrid Michler and published by American Mathematical Soc.. This book was released on 2003 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of two conferences, Resolution des singularites et geometrie non commutative and the Annapolis algebraic geometry conference. Research articles in the volume cover various topics of algebraic geometry, including the theory of Jacobians, singularities, applications to cryptography, and more. The book is suitable for graduate students and research mathematicians interested in algebraic geometry.
