An introduction to the gauged linear sigma model

A Landau—Ginzburg model (Y, w) consists of a smooth complex variety Y together with a function w: Y—> C. Curve counting invariants have recently been defined for a large class Landau—Ginzburg models. The theory goes by the name of the gauged linear sigma model, and generalizes, among other things, the Gromov—Witten theory of hypersurfaces. In this talk I will give a gentle introduction to the theory, focusing on examples.