The celebrated ELSV formula expresses Hurwitz numbers in terms of intersection theory of the moduli space of stable curves. Hurwitz numbers enumerate branched covers of the Riemann sphere with prescribed ramification profiles.
Since the original ELSV was found, many more ELSV-type formulae appeared in the literature, especially in connection with Eynard-Orantin topological recursion theory. They connect different conditions on the ramification profiles of the Hurwitz problem with the integration of different cohomological classes which have been studied independently.
We will go through this interplay, focusing on a conjecture proposed by Zvonkine and a conjecture of Goulden, Jackson, and Vakil. In both these conjectures, classes introduced by Chiodo play a key role. | 
