# Normal functions and the geometry of moduli spaces of curves

 Topology of Algebraic Varieties Topic: Normal functions and the geometry of moduli spaces of curves Speaker: Richard Hain Affiliation: Duke University; Member, School of Mathematics Date: Tuesday, January 13 Time/Room: 2:00pm - 3:30pm/S-101 Video Link: http://video.ias.edu/tav/2015/0113-RichardHain

In this talk, I will begin by recalling the classification of normal functions over $\mathcal M_{g,n}$, the moduli space of $n$-pointed smooth projective curves of genus $g$. I'll then explain how they can be used to resolve a question of Eliashberg, how they generate the tautological ring of $\mathcal M_{g,n}$, and how they can be used to strengthen slope inequalities of the type proved by Moriwaki.