We define and study a structure that can be associated to supersymmetric gauge theories in two or more spacetime dimensions. This is a generalization of the two dimensional A-model, which is used to study gauged linear sigma models, and defines the equivariant quantum cohomology ring on the low-energy target spaces. The three- and four-dimensional generalizations give rise, respectively, to a trigonometric and elliptic generalization of this construction. These rings naturally describe the fusion of Wilson loop operators in three dimensional theories, generalizing the Verlinde algebra in Chern-Simons theory, and surface operators in four dimensional theories. Using this structure one may also construct the partition function on general three and four dimensional Seifert manifolds. All of these structures obey interesting relations under supersymmetric dualities, and have connections to the integrable systems through the gauge-Bethe correspondence. Speaker(s): Brian Willett (KITP-Santa Babara)