Loop equations and a proof of Zvonkine's qr-ELSV formula
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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