Due to another flight cancellation, we have to move this talk to zoom. I will be setting up a laptop in the seminar room for those who wish to attend in person. The zoom meeting link is below, password is 123.
https://illinois.zoom.us/j/81880639335?pwd=Y7SNubyzAk7dHMcNFNKrpMfAcK2Iuz.1
Counting rational curves equivariantly
This talk will be a friendly introduction to 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 $\mathbb{CP}^2$, valued in the representation ring and Burnside ring. This recovers a signed count of real rational cubics when $\mathbb{Z}/2$ acts on $\mathbb{CP}2$ by complex conjugation.