This is the calendar of the Illinois' Math Department Topology Seminar. Talks are generally on Tuesdays at 11am, followed by an (optional) lunch with the speaker.
In Fall 2024 and Spring 2025, the seminar room is Altgeld Hall 241 (unless specified otherwise).
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.
Department of Mathematics
College of Liberal Arts & Sciences
273 Altgeld Hall
1409 W. Green Street (MC-382)
Urbana, IL 61801
Telephone: 217-333-3350
Email: math@illinois.edu