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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 connectio

Homology theory. --- Quantum theory. --- Differential equations. --- Mappings (Mathematics) --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- 517.91 Differential equations --- Differential equations --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- 517.91. --- Homology theory --- Quantum theory --- 512.73 --- 512.73 Cohomology theory of algebraic varieties and schemes --- Cohomology theory of algebraic varieties and schemes --- Numerical solutions --- Homologie --- Théorie quantique --- Equations différentielles --- Applications (Mathématiques) --- 517.91