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In this talk, I shall outline some work with Sheldon Katz on generalizing the 2d topological field theories known as the A and B models, as relevant to both spacetime superpotentials as well as the conjectured (0,2) generalization of mirror symmetry. In the case of the A model generalization, the heterotic theory calculates curve-counting corrections to sheaf cohomology, generalizing the ordinary notion of a quantum cohomology ring. Understanding the B model generalization reveals that the ordinary B model can be consistently defined on very slightly more spaces than merely Calabi-Yau manifolds.