GAAG seminar - An arithmetic Yau-Zaslow formula

Quadratically enriched enumerative geometry is a new area in which we take results in enumerative geometry over the complex numbers and refine them to give results over any base field. The “refinements” in question recover the classical results over algebraically closed fields but also include arithmetic information about the base field. In this talk, I’ll give an introduction to the field of quadratically enriched enumerative geometry, and then give an overview of a proof of an arithmetic refinement of the Yau-Zaslow formula for counting rational curves on K3 surfaces. This talk is based on joint work with Ambrus Pál.