Relations in the tautological ring of the moduli space of curves

Aaron Pixton, October 1st, 2013

The tautological ring of the moduli space of smooth curves of genus g is the subring of
its Chow ring generated by the kappa classes. The Faber-Zagier relations are an explicit
algebraic description of a large number of relations in this ring, conjectured to span all
the relations. I will discuss an extension of these relations to the moduli space of stable
curves with marked points and explain how this gives a new perspective on the
Faber-Zagier relations. Part of this talk presents joint work with R. Pandharipande and
D. Zvonkine.