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.
Rezensionen / Stimmen
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. * Mathematical Association of America * This book is written in the style of lecture notes, which, in the reviewers opinion, is quite nice. It begins with basic materials, followed by separate discussions on the main topics, and eventually puts them all together. This makes the book quite accessible to readers with little or no experience in the subject. * American Mathematical Society *
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Maße
Höhe: 239 mm
Breite: 163 mm
Dicke: 25 mm
Gewicht
ISBN-13
978-0-19-856599-4 (9780198565994)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Tokyo Metropolitan University
1. The many faces of cohomology ; 2. Quantum cohomology ; 3. Quantum differential equations ; 4. Linear differential equations in general ; 5. The quantum D-module ; 6. Abstract quantum cohomology ; 7. Integrable systems ; 8. Solving integrable systems ; 9. Quantum cohomology as an integrable system ; 10. Integrable systems and quantum cohomology ; References
