Philip Tosteson: Representation stability and Deligne–Mumford compactifications

The space \(\overline{M}_{g,n}\) is a compactification of the moduli space of algebraic curves with marked points, obtained by allowing smooth curves to degenerate to nodal ones. We will talk about how the asymptotic behavior of its homology, \(H_i(\overline{M}_{g,n})\), for \(n\gg 0\) can be studied using the representation theory of the category of finite sets and surjections.