From Quantum Cohomology to Integrable Systems

Hardcover | March 19, 2008

byMartin A. Guest

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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 ofmathematics 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 discussedwithin 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.

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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 ofmathematics as well as its appearance in new ...

Martin Guest is a Professor in the Department of Mathematics and Information Sciences at Tokyo Metropolitan University.

other books by Martin A. Guest

Format:HardcoverDimensions:304 pages, 9.21 × 6.14 × 0.91 inPublished:March 19, 2008Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198565992

ISBN - 13:9780198565994

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Table of Contents

1. The many faces of cohomology2. Quantum cohomology3. Quantum differential equations4. Linear differential equations in general5. The quantum D-module6. Abstract quantum cohomology7. Integrable systems8. Solving integrable systems9. Quantum cohomology as an integrable system10. Integrable systems and quantum cohomologyReferences