Online Talk 

The rational Chow ring of the moduli space M_g of curves of genus g is known for g up to 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by earlier work of Faber.

In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).