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Author : Pierre Schapira
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.F/5 ( download)
Download or read book Index Theorem for Elliptic Pairs written by Pierre Schapira and published by . This book was released on 1994 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stephan Rempel
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311270715X
Total Pages : 396 pages
Book Rating : 4.1/5 (127 download)
Download or read book Index Theory of Elliptic Boundary Problems written by Stephan Rempel and published by Walter de Gruyter GmbH & Co KG. This book was released on 1982-12-31 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Index Theory of Elliptic Boundary Problems".
Author : Peter B. Gilkey
Publisher : CRC Press
ISBN 13 : 9780849378744
Total Pages : 534 pages
Book Rating : 4.3/5 (787 download)
Download or read book Invariance Theory written by Peter B. Gilkey and published by CRC Press. This book was released on 1994-12-22 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.
Author : Michael Francis Atiyah
Publisher : Princeton University Press
ISBN 13 : 9780691080314
Total Pages : 384 pages
Book Rating : 4.0/5 (83 download)
Download or read book Seminar on the Atiyah-Singer Index Theorem written by Michael Francis Atiyah and published by Princeton University Press. This book was released on 1965-09-21 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic treatment of the Atiyah-Singer index theorem from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Author : M. Furuta
Publisher : American Mathematical Soc.
ISBN 13 : 9780821820971
Total Pages : 230 pages
Book Rating : 4.8/5 (29 download)
Download or read book Index Theorem. 1 written by M. Furuta and published by American Mathematical Soc.. This book was released on 2007 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Atiyah-Singer index theorem is a remarkable result that allows one to compute the space of solutions of a linear elliptic partial differential operator on a manifold in terms of purely topological data related to the manifold and the symbol of the operator. First proved by Atiyah and Singer in 1963, it marked the beginning of a completely new direction of research in mathematics with relations to differential geometry, partial differential equations, differential topology, K-theory, physics, and other areas.
Author : Richard Melrose
Publisher : CRC Press
ISBN 13 : 1439864608
Total Pages : 392 pages
Book Rating : 4.4/5 (398 download)
Download or read book The Atiyah-Patodi-Singer Index Theorem written by Richard Melrose and published by CRC Press. This book was released on 1993-03-31 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.
Author : John Roe
Publisher : Longman Scientific and Technical
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.3/5 (91 download)
Download or read book Elliptic Operators, Topology, and Asymptotic Methods written by John Roe and published by Longman Scientific and Technical. This book was released on 1988 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joachim Cuntz
Publisher : Springer Science & Business Media
ISBN 13 : 3662064448
Total Pages : 147 pages
Book Rating : 4.6/5 (62 download)
Download or read book Cyclic Homology in Non-Commutative Geometry written by Joachim Cuntz and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.
Author : Katrin Tent
Publisher : Cambridge University Press
ISBN 13 : 0521717884
Total Pages : 327 pages
Book Rating : 4.5/5 (217 download)
Download or read book Groups and Analysis written by Katrin Tent and published by Cambridge University Press. This book was released on 2008-10-16 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many areas of mathematics were deeply influenced or even founded by Hermann Weyl, including geometric foundations of manifolds and physics, topological groups, Lie groups and representation theory, harmonic analysis and analytic number theory as well as foundations of mathematics. In this volume, leading experts present his lasting influence on current mathematics, often connecting Weyl's theorems with cutting edge research in dynamical systems, invariant theory, and partial differential equations. In a broad and accessible presentation, survey chapters describe the historical development of each area alongside up-to-the-minute results, focussing on the mathematical roots evident within Weyl's work.
Author : Henri Moscovici
Publisher : American Mathematical Soc.
ISBN 13 : 0821849441
Total Pages : 337 pages
Book Rating : 4.8/5 (218 download)
Download or read book Noncommutative Geometry and Global Analysis written by Henri Moscovici and published by American Mathematical Soc.. This book was released on 2011 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Author : Neculai S. Teleman
Publisher : Springer Nature
ISBN 13 : 3030284336
Total Pages : 406 pages
Book Rating : 4.0/5 (32 download)
Download or read book From Differential Geometry to Non-commutative Geometry and Topology written by Neculai S. Teleman and published by Springer Nature. This book was released on 2019-11-10 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.
Author : Michael Hitrik
Publisher : Springer
ISBN 13 : 3030015882
Total Pages : 660 pages
Book Rating : 4.0/5 (3 download)
Download or read book Algebraic and Analytic Microlocal Analysis written by Michael Hitrik and published by Springer. This book was released on 2018-12-19 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University. Featured papers expand on mini-courses and talks ranging from foundational material to advanced research-level papers, and new applications in symplectic geometry, mathematical physics, partial differential equations, and complex analysis are discussed in detail. Topics include Procesi bundles and symplectic reflection algebras, microlocal condition for non-displaceability, polarized complex manifolds, nodal sets of Laplace eigenfunctions, geodesics in the space of Kӓhler metrics, and partial Bergman kernels. This volume is a valuable resource for graduate students and researchers in mathematics interested in understanding microlocal analysis and learning about recent research in the area.
Author : Eric Grinberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821811487
Total Pages : 524 pages
Book Rating : 4.8/5 (218 download)
Download or read book Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis written by Eric Grinberg and published by American Mathematical Soc.. This book was released on 2000 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the conference honoring the work of Leon Ehrenpreis. Professor Ehrenpreis worked in many different areas of mathematics and found connections among all of them. For example, one can find his analytic ideas in the context of number theory, geometric thinking within analysis, transcendental number theory applied to partial differential equations, and more. The conference brought together the communities of mathematicians working in the areas of interest to Professor Ehrenpreis and allowed them to share the research inspired by his work. The collection of articles here presents current research on PDEs, several complex variables, analytic number theory, integral geometry, and tomography. The work of Professor Ehrenpreis has contributed to basic definitions in these areas and has motivated a wealth of research results. This volume offers a survey of the fundamental principles that unified the conference and influenced the mathematics of Leon Ehrenpreis.
Author : Bernhelm Booß-Bavnbek
Publisher : Springer Science & Business Media
ISBN 13 : 1461203376
Total Pages : 322 pages
Book Rating : 4.4/5 (612 download)
Download or read book Elliptic Boundary Problems for Dirac Operators written by Bernhelm Booß-Bavnbek and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic boundary problems have enjoyed interest recently, espe cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.
Author : Rufus Willett
Publisher : Cambridge University Press
ISBN 13 : 1108853110
Total Pages : 595 pages
Book Rating : 4.1/5 (88 download)
Download or read book Higher Index Theory written by Rufus Willett and published by Cambridge University Press. This book was released on 2020-07-02 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
Author : Ryoshi Hotta
Publisher : Springer Science & Business Media
ISBN 13 : 081764363X
Total Pages : 408 pages
Book Rating : 4.8/5 (176 download)
Download or read book D-Modules, Perverse Sheaves, and Representation Theory written by Ryoshi Hotta and published by Springer Science & Business Media. This book was released on 2007-11-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
Author : Jörg Schürmann
Publisher : Birkhäuser
ISBN 13 : 3034880618
Total Pages : 461 pages
Book Rating : 4.0/5 (348 download)
Download or read book Topology of Singular Spaces and Constructible Sheaves written by Jörg Schürmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.
