Download or read book From Quantum Cohomology to Integrable Systems written by Martin A. Guest and published by OUP Oxford. This book was released on 2008-03-13 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry. Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework. Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.
Download or read book Frobenius Manifolds written by Claus Hertling and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems are flourishing areas since the early 90's. An activity was organized at the Max-Planck-Institute for Mathematics in Bonn, with the purpose of bringing together the main experts in these areas. This volume originates from this activity and presents the state of the art in the subject.
Download or read book Integrable Systems Geometry and Topology written by Chuu-lian Terng and published by American Mathematical Soc.. This book was released on 2006 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and theirrelations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu,and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of Yang-Mills-Higgs equations on Riemann surfaces. The article by Terng and Uhlenbeck explains the gauge equivalence of the matrix non-linear Schrödinger equation, the Schrödinger flow on Grassmanian, and the Heisenberg Feromagnetic model. The bookprovides an introduction to integrable systems and their relation to differential geometry. It is suitable for advanced graduate students and research mathematicians. Information for our distributors: Titles in this series are copublished with International Press, Cambridge, MA.
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.
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.
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.
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.
Download or read book Quantum Integrable Systems written by Asesh Roy Chowdhury and published by CRC Press. This book was released on 2004-01-28 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m
Download or read book Geometric and Topological Methods for Quantum Field Theory written by Hernan Ocampo and published by Cambridge University Press. This book was released on 2010-04-29 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.
Download or read book Classical and Quantum Nonlinear Integrable Systems written by A Kundu and published by CRC Press. This book was released on 2019-04-23 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories
Download or read book Elliptic Quantum Groups written by Hitoshi Konno and published by Springer Nature. This book was released on 2020-09-14 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on elliptic quantum groups, i.e., quantum groups associated to elliptic solutions of the Yang-Baxter equation. Based on research by the author and his collaborators, the book presents a comprehensive survey on the subject including a brief history of formulations and applications, a detailed formulation of the elliptic quantum group in the Drinfeld realization, explicit construction of both finite and infinite-dimensional representations, and a construction of the vertex operators as intertwining operators of these representations. The vertex operators are important objects in representation theory of quantum groups. In this book, they are used to derive the elliptic q-KZ equations and their elliptic hypergeometric integral solutions. In particular, the so-called elliptic weight functions appear in such solutions. The author’s recent study showed that these elliptic weight functions are identified with Okounkov’s elliptic stable envelopes for certain equivariant elliptic cohomology and play an important role to construct geometric representations of elliptic quantum groups. Okounkov’s geometric approach to quantum integrable systems is a rapidly growing topic in mathematical physics related to the Bethe ansatz, the Alday-Gaiotto-Tachikawa correspondence between 4D SUSY gauge theories and the CFT’s, and the Nekrasov-Shatashvili correspondences between quantum integrable systems and quantum cohomology. To invite the reader to such topics is one of the aims of this book.
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.
Download or read book Integrable Systems And Quantum Groups written by Mauro Carfora and published by World Scientific. This book was released on 1992-04-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures on recent advances in the theory of integrable systems and quantum groups. It introduces the reader to attractive areas of current research.
Download or read book Quantum Cohomology written by K. Behrend and published by Springer. This book was released on 2004-10-12 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gathers the lectures given at the C.I.M.E. summer school "Quantum Cohomology" held in Cetraro (Italy) from June 30th to July 8th, 1997. The lectures and the subsequent updating cover a large spectrum of the subject on the field, from the algebro-geometric point of view, to the symplectic approach, including recent developments of string-branes theories and q-hypergeometric functions.
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 408 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.
Download or read book Hilbert Schemes of Points and Infinite Dimensional Lie Algebras written by Zhenbo Qin and published by American Mathematical Soc.. This book was released on 2018-02-26 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes of collections of points (zero-dimensional subschemes) in a smooth algebraic surface . Schemes turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of , including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of and the Gromov–Witten correspondence. The last part of the book presents results about quantum cohomology of and related questions. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, combinatorics, topology, number theory, and theoretical physics.
Download or read book Integrable Systems and Quantum Groups written by Ron Donagi and published by Springer. This book was released on 2006-11-14 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this CIME Session was to review the state of the art in the recent development of the theory of integrable systems and their relations with quantum groups. The purpose was to gather geometers and mathematical physicists to allow a broader and more complete view of these attractive and rapidly developing fields. The papers contained in this volume have at the same time the character of survey articles and of research papers, since they contain both a survey of current problems and a number of original contributions to the subject.
