| Every meromorphic function on a Riemann surface C has a divisor of zeros and poles. When is a divisor on C obtained from a meromorphic function? This question underlies much of the classical study of curves. A modern turn in the subject comes by viewing the answer as a cycle over the moduli space of curves. In 2014, Pixton proposed a complete formula for the class of the associated cycle. I will give an overview of the subject and a sketch of the very recent proof of Pixton's formula (joint work with Janda, Pixton, and Zvonkine). |