Title: Counting rational curves equivariantly
Abstract: This talk will be a friendly introduction to using topological invariants in enumerative geometry and how one might use equivariant homotopy theory to answer enumerative questions under the presence of a finite group action. Recent work with Kirsten Wickelgren (Duke) defines a global and local degree in stable equivariant homotopy theory that can be used to compute the equivariant Euler characteristic and Euler number. I will discuss an application to counting orbits of rational plane cubics through an invariant set of 8 points in general position under a finite group action on CP^2, valued in the representation ring and Burnside ring. This recovers a signed count of real rational cubics when Z/2 acts on CP^2 by complex conjugation.