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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