Number Theory Seminar
Adrian Diaconu
University of Minnesota
Equivariant Euler characteristics of $\overline{\mathscr{M}}_{g, n}$
Abstract: Let $\overline{\mathscr{M}}_{g, n}$ be the moduli space of $n$-pointed stable genus
$g$ curves, and let $\mathscr{M}_{g, n}$ be the moduli space of $n$-pointed smooth curves of genus $g.$ In this talk, I will discuss an asymptotic expansion for the characteristic of the free modular operad $\mathbb{M}\mathcal{V}$ generated by a stable $\mathbb{S}$-module $\mathcal{V},$ allowing to effectively compute $\mathbb{S}_{n}$-equivariant Euler characteristics of $\overline{\mathscr{M}}_{g, n}$ in terms of $\mathbb{S}_{n'}$-equivariant Euler characteristics of $\mathscr{M}_{g'\!, n'}$ with $0\le g' \le g,$ $\textrm{max}\{0, 3 - 2g' \} \le n' \le 2(g - g') + n.$ This answers a question posed by Getzler and Kapranov by making their integral representation
of the characteristic of the modular operad $\mathbb{M}\mathcal{V}$ effective. I will also discuss some applications.
Adrian Diaconu will also speak in the Departmental Colloquium on April 27, 2018.
Friday April 27, 2018 at 11:00 AM in SEO 612