The Orbit Method In Geometry And Physics

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The Orbit Method in Geometry and Physics

Author : Christian Duval
Publisher : Springer Science & Business Media
ISBN 13 : 1461200296
Total Pages : 478 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Orbit Method in Geometry and Physics by : Christian Duval

Download or read book The Orbit Method in Geometry and Physics written by Christian Duval and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses.

Lectures on the Orbit Method

Author : Aleksandr Aleksandrovich Kirillov
Publisher : American Mathematical Soc.
ISBN 13 : 0821835300
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lectures on the Orbit Method by : Aleksandr Aleksandrovich Kirillov

Download or read book Lectures on the Orbit Method written by Aleksandr Aleksandrovich Kirillov and published by American Mathematical Soc.. This book was released on 2004 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the essence of the orbit method for non-experts and gives a detailed exposition of the method. This work can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.

Lectures on the Orbit Method

Author : Aleksandr Aleksandrovich Kirillov
Publisher :
ISBN 13 : 9781470417994
Total Pages : 408 pages
Book Rating : 4.4/5 (179 download)

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Book Synopsis Lectures on the Orbit Method by : Aleksandr Aleksandrovich Kirillov

Download or read book Lectures on the Orbit Method written by Aleksandr Aleksandrovich Kirillov and published by . This book was released on 1900 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Isaac Newton encrypted his discoveries in analysis in the form of an anagram, which deciphers to the sentence ``It is worthwhile to solve differential equations''. Accordingly, one can express the main idea behind the Orbit Method by saying "It is worthwhile to study coadjoint orbits". The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for non-experts and gives the first systematic, detailed, and self-contained exposition of the method. It starts with a convenient ``User's Guide'' and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.

Lectures on Geometric Methods in Mathematical Physics

Author : Jerrold E. Marsden
Publisher : SIAM
ISBN 13 : 0898711703
Total Pages : 103 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Lectures on Geometric Methods in Mathematical Physics by : Jerrold E. Marsden

Download or read book Lectures on Geometric Methods in Mathematical Physics written by Jerrold E. Marsden and published by SIAM. This book was released on 1981-01-01 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.

Theory of Orbits

Author : Dino Boccaletti
Publisher : Springer Science & Business Media
ISBN 13 : 3662033194
Total Pages : 402 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Theory of Orbits by : Dino Boccaletti

Download or read book Theory of Orbits written by Dino Boccaletti and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Half a century ago, S. Chandrasekhar wrote these words in the preface to his l celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ ... J Indeed, several of the problems of modern stellar dy namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con sidered from the point of view of celestial mechanics (the N-body problem with N » 1), fluid mechanics (the system is represented by a material con tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).

Theory of Orbits

Author : Dino Boccaletti
Publisher : Springer Science & Business Media
ISBN 13 : 3662092409
Total Pages : 430 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Theory of Orbits by : Dino Boccaletti

Download or read book Theory of Orbits written by Dino Boccaletti and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Half a century ago, S. Chandrasekhar wrote these words in the preface to his 1 celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ ... ] Indeed, several of the problems of modern stellar dy namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con sidered from the point of view of celestial mechanics (the N-body problem with N» 1), fluid mechanics (the system is represented by a material con tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).

Commutative Algebra

Author : Irena Peeva
Publisher : Springer Nature
ISBN 13 : 3030896943
Total Pages : 898 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Commutative Algebra by : Irena Peeva

Download or read book Commutative Algebra written by Irena Peeva and published by Springer Nature. This book was released on 2022-02-18 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume is a follow-up to the 2013 volume of the same title, published in honor of noted Algebraist David Eisenbud's 65th birthday. It brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Category Theory, Combinatorics, Computational Algebra, Homological Algebra, Hyperplane Arrangements, and Non-commutative Algebra. The book aims to showcase the area and aid junior mathematicians and researchers who are new to the field in broadening their background and gaining a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

Coxeter Matroids

Author : Alexandre V. Borovik
Publisher : Springer Science & Business Media
ISBN 13 : 1461220661
Total Pages : 282 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Coxeter Matroids by : Alexandre V. Borovik

Download or read book Coxeter Matroids written by Alexandre V. Borovik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.

Polynomial Convexity

Author : Edgar Lee Stout
Publisher : Springer Science & Business Media
ISBN 13 : 0817645381
Total Pages : 454 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Polynomial Convexity by : Edgar Lee Stout

Download or read book Polynomial Convexity written by Edgar Lee Stout and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive monograph details polynomially convex sets. It presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. Coverage examines in considerable detail questions of uniform approximation for the most part on compact sets but with some attention to questions of global approximation on noncompact sets. The book also discusses important applications and motivates the reader with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries.

Introduction to Vertex Operator Algebras and Their Representations

Author : James Lepowsky
Publisher : Springer Science & Business Media
ISBN 13 : 0817681868
Total Pages : 330 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Introduction to Vertex Operator Algebras and Their Representations by : James Lepowsky

Download or read book Introduction to Vertex Operator Algebras and Their Representations written by James Lepowsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.

Momentum Maps and Hamiltonian Reduction

Author : Juan-Pablo Ortega
Publisher : Springer Science & Business Media
ISBN 13 : 1475738110
Total Pages : 526 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Momentum Maps and Hamiltonian Reduction by : Juan-Pablo Ortega

Download or read book Momentum Maps and Hamiltonian Reduction written by Juan-Pablo Ortega and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. * Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.

Extended Abstracts February 2016

Author : Maria Alberich-Carramiñana
Publisher : Springer
ISBN 13 : 3030000273
Total Pages : 118 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Extended Abstracts February 2016 by : Maria Alberich-Carramiñana

Download or read book Extended Abstracts February 2016 written by Maria Alberich-Carramiñana and published by Springer. This book was released on 2018-11-03 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains extended abstracts outlining selected talks and other selected presentations given by participants of the workshop "Positivity and Valuations", held at the Centre de Recerca Matemàtica (CRM) in Barcelona from February 22nd to 26th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and the outcome of work in groups initiated during the workshop. The general subject is the application of valuation theory to positivity questions in algebraic geometry. The topics covered range from purely algebraic problems like finite generation of semigroups and algebras defined by valuations, and properties of the associated Poincaré series, to more geometric questions like resolution of singularities and properties of Newton-Okounkov bodies, linked with non-archimedean geometry and tropical geometry. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

Studies in Lie Theory

Author : Anthony Joseph
Publisher : Springer Science & Business Media
ISBN 13 : 9780817643423
Total Pages : 526 pages
Book Rating : 4.6/5 (434 download)

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Book Synopsis Studies in Lie Theory by : Anthony Joseph

Download or read book Studies in Lie Theory written by Anthony Joseph and published by Springer Science & Business Media. This book was released on 2006-01-26 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains new results on different aspects of Lie theory, including Lie superalgebras, quantum groups, crystal bases, representations of reductive groups in finite characteristic, and the geometric Langlands program

Parabolic Quasilinear Equations Minimizing Linear Growth Functionals

Author : Fuensanta Andreu-Vaillo
Publisher : Birkhäuser
ISBN 13 : 3034879288
Total Pages : 351 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Parabolic Quasilinear Equations Minimizing Linear Growth Functionals by : Fuensanta Andreu-Vaillo

Download or read book Parabolic Quasilinear Equations Minimizing Linear Growth Functionals written by Fuensanta Andreu-Vaillo and published by Birkhäuser. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details the mathematical developments in total variation based image restauration. From the reviews: "This book is devoted to PDE's of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters....The book is written with great care, paying also a lot of attention to the bibliographical and historical notes."-- ZENTRALBLATT MATH

The Problem of Time

Author : Edward Anderson
Publisher : Springer
ISBN 13 : 3319588486
Total Pages : 917 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis The Problem of Time by : Edward Anderson

Download or read book The Problem of Time written by Edward Anderson and published by Springer. This book was released on 2017-09-18 with total page 917 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics. By this development, and interpreting shape theory as modelling background independence, this book further establishes background independence as a field of study. Background independent mechanics, as well as minisuperspace (spatially homogeneous) models of GR and perturbations thereabout are used to illustrate these points. As hitherto formulated, the different facets of the Problem of Time greatly interfere with each others' attempted resolutions. This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation. Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and what background independence entails at the topological level and beyond.

Geometry and Physics

Author : Jørgen Ellegaard Andersen
Publisher : Oxford University Press, USA
ISBN 13 : 0198802021
Total Pages : 347 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis Geometry and Physics by : Jørgen Ellegaard Andersen

Download or read book Geometry and Physics written by Jørgen Ellegaard Andersen and published by Oxford University Press, USA. This book was released on 2018 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.

In Search of the Riemann Zeros

Author : Michel Laurent Lapidus
Publisher : American Mathematical Soc.
ISBN 13 : 9780821842225
Total Pages : 594 pages
Book Rating : 4.8/5 (422 download)

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Book Synopsis In Search of the Riemann Zeros by : Michel Laurent Lapidus

Download or read book In Search of the Riemann Zeros written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2008 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possible--or, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line.