Description
This text discusses the origins and connections of quantum cohomology, a mathematical concept that combines symplectic geometry, algebraic geometry, and differential equations. It explores the success of quantum cohomology and its relationship with other areas of mathematics, such as mirror symmetry. The book focuses on the links between quantum cohomology and traditional mathematics, specifically through certain types of differential equations. It is aimed at graduate students in mathematics and theoretical physicists who have a basic understanding of 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.
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