# Low degree Hurwitz stacks in the Grothendieck ring

#### ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

Date: Thursday, June 9, 2022 16:00 - 17:00
Speaker: Aaron Landesman (Harvard University)
Location: https://mathseminars.org/seminar/AGNTISTA
Series: Mathematics and CS Seminar
Host: Tim Browning

For $2 \leq d \leq 5$, we show that the class of the Hurwitz space of smooth degree $d$, genus $g$ covers of $\mathbb P^1$ stabilizes in the Grothendieck ring of stacks as $g \to \infty$. We will survey the connections between this result and related stabilizations occuring in algebraic geometry, number theory, and topology. This is based on joint work with Ravi Vakil and Melanie Matchett Wood.