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From Quantum Cohomology to Integrable Systems

2008-03-13 Mathematics
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Release : 2008-03-13
Genre : Mathematics
Kind : eBook
Book Rating : 960/5 ( reviews)

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Book Synopsis From Quantum Cohomology to Integrable Systems by : Martin A. Guest

Download or read book From Quantum Cohomology to Integrable Systems written by Martin A. Guest. This book was released on 2008-03-13. 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.

Frobenius Manifolds

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 361/5 ( reviews)

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Book Synopsis Frobenius Manifolds by : Claus Hertling

Download or read book Frobenius Manifolds written by Claus Hertling. This book was released on 2012-12-06. 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.

Integrability, Quantization, and Geometry: I. Integrable Systems

2021-04-12 Education
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Release : 2021-04-12
Genre : Education
Kind : eBook
Book Rating : 919/5 ( reviews)

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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. This book was released on 2021-04-12. 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.

Integrable Systems, Geometry, and Topology

2006 Mathematics
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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 487/5 ( reviews)

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Book Synopsis Integrable Systems, Geometry, and Topology by : Chuu-lian Terng

Download or read book Integrable Systems, Geometry, and Topology written by Chuu-lian Terng. This book was released on 2006. 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.

Integrable Systems, Topology, and Physics

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 394/5 ( reviews)

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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. This book was released on 2002. 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.

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