**Speaker**

Michele Pernice, KTH Royal Instititute of Technology

**Abstract**

The rational Chow ring of the moduli stack of stable curves is as interesting as it is hard to compute. In this talk, we will present a strategy for computing such invariant for the genus 3 case, in fact obtaining the Chow ring of $\overline{\mathcal{M}}_3$ with $\mathbb{Z}[1/6]$-coefficients. This extends the result of Faber which describes the rational Chow ring of $\overline{\mathcal{M}}_3$, and it does it in a completely independent way. To do so, we introduce a bigger moduli stack of curves (allowing worse-than-nodal singularities to appear), compute its Chow ring and then use localization sequence to finally get the Chow ring of $\overline{\mathcal{M}}_3$.