The Do-Karev conjecture is true: monotone orbifold Hurwitz numbers obey the Chekhov-Eynard-Orantin topological recursion.
Loop equations and a proof of Zvonkine's $qr$-ELSV formula
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abstract
We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called $r$-ELSV formula, as well as its orbifold generalization, the $qr$-ELSV formula, proposed recently in [KLPS17].
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Topological recursion for monotone orbifold Hurwitz numbers: a proof of the Do-Karev conjecture
The Do-Karev conjecture is true: monotone orbifold Hurwitz numbers obey the Chekhov-Eynard-Orantin topological recursion.