EVENT DETAILS AND ABSTRACT

Title: Branched covers of the projective line and the Chow ring of the moduli space of curves
Speaker: Professor Ravi Vakil
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

Branched covers of the sphere have recnetly proved a powerful tool in understanding the Chow ring of the moduli space of pointed curves, $\overline{\mathcal{M}}_{g,n}$.

I will briefly describe the moduli space and its cohomlogy, Chow, and tautological rings. I will then define Hurwitz numbers (counting branched covers of $\mathbb{P}^1$), and describe their links to Gromov-Witten theory, and the connection discovered by Ekedahl et al to the tautological ring. I'll give several consequences, including a verfication of predictions of a remarkable question/conjecture of Hain/Looijenga/Faber/Pandharipande that the tautological ring ``should be a combinatorial object''. (This is joint work with T. Graber.)