Product details:
| ISBN13: | 9780198565994 |
| ISBN10: | 0198565992 |
| Binding: | Hardback |
| No. of pages: | 322 pages |
| Size: | 242x164x22 mm |
| Weight: | 646 g |
| Language: | English |
| 0 |
Category:
From Quantum Cohomology to Integrable Systems
Series:
Oxford Graduate Texts in Mathematics;
15;
Publisher: OUP Oxford
Date of Publication: 13 March 2008
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Short description:
This text focuses on the extraordinary success of quantum cohomology and its connections with many existing areas of traditional mathematics and new areas such as mirror symmetry. Aimed at graduate students in mathematics as well as theoretical physicists, the text assumes basic familiarity with differential equations and cohomology.
Long description:
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.
Well-written and reasonably paced, From Quantum Cohomology to Integrable Systems is a good introduction to a rich and fascinating subject that is still in its early stages of evolution. The book is indispensable for mathematicians interested in pursuing these ideas and themes.
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.
Well-written and reasonably paced, From Quantum Cohomology to Integrable Systems is a good introduction to a rich and fascinating subject that is still in its early stages of evolution. The book is indispensable for mathematicians interested in pursuing these ideas and themes.
Table of Contents:
The many faces of cohomology
Quantum cohomology
Quantum differential equations
Linear differential equations in general
The quantum D-module
Abstract quantum cohomology
Integrable systems
Solving integrable systems
Quantum cohomology as an integrable system
Integrable systems and quantum cohomology
References
Quantum cohomology
Quantum differential equations
Linear differential equations in general
The quantum D-module
Abstract quantum cohomology
Integrable systems
Solving integrable systems
Quantum cohomology as an integrable system
Integrable systems and quantum cohomology
References
