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Integrable Systems Topology And Physics
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Book Synopsis Integrable Systems, Topology, and Physics by : Martin A. Guest
Download or read book Integrable Systems, Topology, and Physics written by Martin A. Guest and published by American Mathematical Soc.. This book was released on 2002 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the second of three collections of expository and research articles. This volume focuses on topology and physics. The role of zero curvature equations outside of the traditional context of differential geometry has been recognized relatively recently, but it has been an extraordinarily productive one, and most of the articles in this volume make some reference to it. Symplectic geometry, Floer homology, twistor theory, quantum cohomology, and the structure of special equations of mathematical physics, such as the Toda field equations--all of these areas have gained from the integrable systems point of view and contributed to it. Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The first volume from this conference also available from the AMS is Differential Geometry and Integrable Systems, Volume 308 CONM/308 in the Contemporary Mathematics series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the AMS in the Advanced Studies in Pure Mathematics series.
Book Synopsis Integrability, Quantization, and Geometry: I. Integrable Systems by : Sergey Novikov
Download or read book Integrability, Quantization, and Geometry: I. Integrable Systems written by Sergey Novikov and published by American Mathematical Soc.. This book was released on 2021-04-12 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Book Synopsis Representation Theory, Mathematical Physics, and Integrable Systems by : Anton Alekseev
Download or read book Representation Theory, Mathematical Physics, and Integrable Systems written by Anton Alekseev and published by Springer Nature. This book was released on 2022-02-05 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.
Book Synopsis Lectures on Integrable Systems by : Jens Hoppe
Download or read book Lectures on Integrable Systems written by Jens Hoppe and published by Springer Science & Business Media. This book was released on 2008-09-15 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.
Book Synopsis Differential Geometry and Integrable Systems by : Martin A. Guest
Download or read book Differential Geometry and Integrable Systems written by Martin A. Guest and published by American Mathematical Soc.. This book was released on 2002 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the first of three collections of expository and research articles. This volume focuses on differential geometry. It is remarkable that many classical objects in surface theory and submanifold theory are described as integrable systems. Having such a description generally reveals previously unnoticed symmetries and can lead to surprisingly explicit solutions.Surfaces of constant curvature in Euclidean space, harmonic maps from surfaces to symmetric spaces, and analogous structures on higher-dimensional manifolds are some of the examples that have broadened the horizons of differential geometry, bringing a rich supply of concrete examples into the theory of integrable systems. Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The second volume from this conference, also available from the 'AMS', is ""Integrable Systems, Topology, and Physics, Volume 309"" in the ""Contemporary Mathematics"" series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the 'AMS' in the ""Advanced Studies in Pure Mathematics"" series.
Book Synopsis Integrable Systems, Quantum Groups, and Quantum Field Theories by : Alberto Ibort
Download or read book Integrable Systems, Quantum Groups, and Quantum Field Theories written by Alberto Ibort and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.
Book Synopsis New Results in the Theory of Topological Classification of Integrable Systems by : A. T. Fomenko
Download or read book New Results in the Theory of Topological Classification of Integrable Systems written by A. T. Fomenko and published by American Mathematical Soc.. This book was released on 1995 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection contains new results in the topological classification of integrable Hamiltonian systems. Recently, this subject has been applied to interesting problems in geometry and topology, classical mechanics, mathematical physics, and computer geometry. This new stage of development of the theory is reflected in this collection. Among the topics covered are: classification of some types of singularities of the moment map (including non-Bott types), computation of topological invariants for integrable systems describing various problems in mechanics and mathematical physics, construction of a theory of bordisms of integrable systems, and solution of some problems of symplectic topology arising naturally within this theory. A list of unsolved problems allows young mathematicians to become quickly involved in this active area of research.
Book Synopsis Dynamical Systems VII by : V.I. Arnol'd
Download or read book Dynamical Systems VII written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.
Download or read book Spinning Tops written by M. Audin and published by Cambridge University Press. This book was released on 1999-11-13 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by classical mechanics. A modern view of the role played by algebraic geometry has been established iby many mathematicians. This book presents some of these techniques, which fall within the orbit of finite dimensional integrable systems. The main body of the text presents a rich assortment of methods and ideas from algebraic geometry prompted by classical mechanics, whilst in appendices the general, abstract theory is described. The methods are given a topological application to the study of Liouville tori and their bifurcations. The book is based on courses for graduate students given by the author at Strasbourg University but the wealth of original ideas will make it also appeal to researchers.
Book Synopsis Integrable Systems and Algebraic Geometry: Volume 1 by : Ron Donagi
Download or read book Integrable Systems and Algebraic Geometry: Volume 1 written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-04-02 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.
Book Synopsis Integrability, Quantization, and Geometry by : Sergeĭ Petrovich Novikov
Download or read book Integrability, Quantization, and Geometry written by Sergeĭ Petrovich Novikov and published by . This book was released on 2021 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.The contributions to this collection of papers are split into two parts: ""Integrable Systems"" and ""Quantum Theories and Algebraic Geometry"", reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, i.
Book Synopsis Topology, Geometry, Integrable Systems, and Mathematical Physics by : V. M. Buchstaber
Download or read book Topology, Geometry, Integrable Systems, and Mathematical Physics written by V. M. Buchstaber and published by American Mathematical Soc.. This book was released on 2014-11-18 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
Book Synopsis Integrable Systems: From Classical to Quantum by : John P. Harnad
Download or read book Integrable Systems: From Classical to Quantum written by John P. Harnad and published by American Mathematical Soc.. This book was released on 2000 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the papers based upon lectures given at the 1999 Séminaire de Mathémathiques Supérieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development throughout the past three decades, resulting in new motivation for study in r s3risingly different directions. Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the Seiberg-Witten approach to supersymmetric Yang-Mills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror symmetry, quantum cohomology, etc. This collection gives a nice cross-section of the current state of the work in the area of integrable systems which is presented by some of the leading active researchers in this field. The scope and quality of the articles in this volume make this a valuable resource for those interested in an up-to-date introduction and an overview of many of the main areas of study in the theory of integral systems.
Book Synopsis Integrable Systems by : N.J. Hitchin
Download or read book Integrable Systems written by N.J. Hitchin and published by Oxford University Press, USA. This book was released on 2013-03-14 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.
Book Synopsis Topology of Integrable Systems by : D. B. Zotev
Download or read book Topology of Integrable Systems written by D. B. Zotev and published by . This book was released on 2010 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topological theory of integrable Hamiltonian systems was created by Anatoly Fomenko and developed by his followers. In this article, It is briefly described on a level of strictness sufficient for self-dependent applications. Some new results, illustrating the theses of the theory and the loop molecule method by Alexey Bolsinov, are presented.
Book Synopsis Integrable Hamiltonian Systems by : A.V. Bolsinov
Download or read book Integrable Hamiltonian Systems written by A.V. Bolsinov and published by CRC Press. This book was released on 2004-02-25 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,
Book Synopsis Topology, Geometry, Integrable Systems, and Mathematical Physics by : Sergeĭ Petrovic Novikov
Download or read book Topology, Geometry, Integrable Systems, and Mathematical Physics written by Sergeĭ Petrovic Novikov and published by . This book was released on 2014 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
