Title: From Hurwitz numbers to log Chow
Abstract: Double Hurwitz numbers count ramified covers of the projective line with prescribed profiles over 0 and ∞. In this talk I will review work that, on the one hand, develops a combinatorial framework to compute Hurwitz numbers in terms of a sum of weighted graphs, and on the other it connects these enumerative invariants to the tautological intersection theory of the logarithmic DR cycle. This perspective then opens up a path to new enumerative geometric problems. This is based on joint work with H. Markwig, D. Ranganathan and J. Schmitt.