In this talk, a mathematical definition is given of the topological correlation functions of a (0,2) gauged linear sigma model in the geometric phase of a neighborhood of the (2,2) locus in moduli. The geometric data determining the model is a smooth toric variety X and a deformation E of its tangent bundle TX. This definition is consistent with the known results of physics and leads to a proof of the existence of a quantum cohomology ring in complete generality, extending known results of physics. This is joint work with Ron Donagi, Josh Guffin, and Eric Sharpe.