Tropical Jucys covers

Abstract

We study monotone and strictly monotone Hurwitz numbers from a bosonic Fock space perspective. This yields to an interpretation in terms of tropical geometry involving local multiplicities given by Gromov-Witten invariants. Furthermore, this enables us to prove that a main result of Cavalieri-Johnson-Markwig-Ranganathan is actually equivalent to the Gromov-Witten/Hurwitz correspondence by Okounkov-Pandharipande for the equivariant Riemann sphere.