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 (Brown University)

Abstract

This talk will be a friendly introduction to using topological invariants in enumerative geometry. I will talk about how one might use equivariant homotopy theory to answer enumerative questions under the presence of a finite group action and give examples. Finally, I will discuss recent work joint with Kirsten Wickelgren on an equivariant count of 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.