Topology Seminar: Stability patterns in the rational homology of (ordered) Hurwitz spaces

Abstract: I will give an introduction to Hurwitz spaces, which are certain covers of unordered configuration spaces of the plane. I will talk about a pattern called homological stability that these spaces have, due to work of Ellenberg--Venkatesh--Westerland. I will also talk about joint work with Anh Hoang, Jeremy Miller, and Jennifer Wilson, concerning ordered Hurwitz spaces and a pattern that these spaces have called representation stability. This talk will be accessible to a broad audience in topology and related fields.