Constructing Equivariant Enumerative Invariants

In the second lecture, I will discuss the homotopy-theoretic techniques underlying the construction of these invariants. Specifically, I will introduce the Euler number in (derived) equivariant motivic homotopy theory, joint with C. Ravi, which is an algebro-geometric analogue of the topological equivariant Euler numbers of T. Brazelton and Bethea—Wickelgren. This construction leads to refined counts valued in the representation ring of a finite group. I will end by sketching how these constructions are used to produce equivariant enumerative results like those discussed in the first lecture.