Algebraic Geometry Seminar: Arc spaces and equivariant cohomology II

Let G be an algebraic group acting on a smooth complex variety X. In joint work with Alan Stapledon, we present a new perspective on the G-equivariant cohomology of X, which replaces the action of G on X with the induced action of the respective arc spaces. I will explain how this point of view allows one to interpret the cup product of classes of subvarieties geometrically via contact loci in the arc space, at least under suitable hypotheses on the singularities. As an explicit example, I'll discuss GL_n acting on the space of matrices.