Department of Mathematics - Master Calendar

View Full Calendar

Candace Bethea (Brown): Counting rational curves equivariantly

Event Type
Seminar/Symposium
Sponsor
UIUC Math Department
Location
Altgeld
Date
Apr 1, 2025   11:00 am  
Views
73
Originating Calendar
Topology Seminar

 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.

link for robots only