Student AG Seminar: Equivariant Intersection Theory and the Chow Ring of the Stack of Smooth Plane Cubics

Equivariant intersection theory, developed by Totaro, Edidin-Graham and others, is an algebraic analogue of Borel-equivariant cohomology. The equivariant Chow groups record how algebraic cycles intersect with respect to a group action on a scheme and provide a way of defining cohomological invariants for quotient stacks. In this talk, we will motivate these definitions through the classical Borel construction. After calculating basic examples, we will sketch the determination of the Chow ring of the stack of smooth plane cubic curves following Fulghesu-Vistoli 2018.