# Moduli of relative stable maps to $\mathbf{P}^1$: cut-and-paste invariants

### Siddarth Kannan (Brown University)

Fri Apr 1, 19:00-20:00 (6 months ago)

Abstract: 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.

algebraic geometry

Audience: researchers in the topic

( slides | video )

Comments: The synchronous discussion for Siddarth Kannan’s talk is taking place not in zoom-chat, but at tinyurl.com/2022-04-01-sk (and will be deleted after ~3-7 days).