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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].
Forward citations
Cited by 3 Pith papers
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Universal Correlators on Exponentially Ramified Spectral Curves
Generalized topological recursion extends to spectral curves with essential singularities by replacing residues at the essential point with residues at ordinary meromorphic points.
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Quantum spectral curve operators for arbitrary base points can be derived by applying x-y and symplectic duality transformations to simpler spectral curves.
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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.
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