Olof Bergvall: Relations in the Tautological Ring of the Universal Curve

We formulate a few conjectures about the structure of the tautological ring of the universal curve, analogous to the so-called "Faber conjectures", and describe how existing techniques has been modified to verify these conjectures for genera between 2 and 9. We also study some matrices associated to the conjectures and find a relationship between these matrices and the corresponding matrices on the moduli space of curves.