Twists, gorms, and antifields

I will discuss supersymmetry and localisation in the most general case where SUSY is realised up to homotopy using a version of the BV field-antifield formalism. This way, it is easy to generalise to «equivariant supersymmetry», and even extended equivariant supersymmetry. I will do so and discuss some physical examples, including a new equivariant version of the topological B-model.