Introduction to homological geometry: part II

Abstract

Although this article can be read independently, it is a continuation of the introduction to integrable systems aspects of quantum cohomology given in part 1 (math.DG/0104274). In the same elementary style, i.e. assuming basic properties of quantum cohomology and concentrating on the simplest nontrivial examples, the quantum differential equations of Givental are studied in some detail. The solutions are described first as generating functions for certain Gromov-Witten invariants, then as generalizations of hypergeometric functions, as predicted by the Mirror Theorem.