Siddarth Kannan (Apr. 1, 2022):  Moduli of relative stable maps to P^1: cut-and-paste invariants
Channel: Algebraic Geometry at Stanford
Date: 2022-04-02

I will give an introduction to the moduli space of genus zero rubber stable maps to $\mathbf{P}^1$, relative to 0 and infinity, with fixed ramification profiles. Then I will discuss two recent results on the topology of these moduli spaces. The first concerns a chamber structure for the classes of these moduli spaces in the Grothendieck ring of varieties. The second gives a recursive algorithm for the calculation of the Euler characteristic, in the case where the maps are fully ramified over zero, and unramified over infinity. If time permits, I will also discuss some potential future directions.