Tautological ring

In algebraic geometry, the tautological ring is (roughly) the subring of a Chow ring of the moduli space of curves generated by tautological classes.

See also

ELSV formula
Hodge bundle
Witten's conjecture

References

http://math.stanford.edu/~vakil/files/notices/ams4.pdf
T. Graber and R. Vakil, $\overline{\mathcal{M}}_{g, n}$ , in Proceedings of the Seventh Gǒkova Geometry-Topology Conference, International Press, 2000.