ABSTRACT:
The moduli space of curves carries tautological cohomology
classes. I will discuss the study of relations amongst these classes
starting with ideas of Mumford in 1980s. The subject advanced in the 1990s
with conjectures of Faber and Faber-Zagier. I will explain the current state of affairs based on Pixton's conjectures related to cohomological field theories. The talk represents joint work with A. Pixton and D. Zvonkine.
