From Quantum Cohomology to Integrable Systems

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 mat…