Title:  Motivic Hilbert Zeta Functions of Curves

 

Abstract:  The Grothendieck ring of varieties is a beautiful and intricate object which bears witness to an interplay between arithmetic, geometry, and topology. I will discuss in particular the behavior of Hilbert schemes of points on singular curves and the associated "motivic zeta function". After surveying work in this area, I will report on joint work in progress with Dori Bejleri and Ravi Vakil, in which we prove that the motivic Hilbert zeta function of an arbitrary curve is rational, in the spirit of the Weil conjectures.