From Quantum Cohomology to Integrable Systems [Hardcover]

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.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.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 This book is written in the style of lecture notes, which...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. --Mathematical Reviews

This text focuses on the extraordinary success of quantlS,