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Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfants
We prove quasi-polynomiality for monotone and strictly monotone orbifold Hurwitz numbers. The second enumerative problem is also known as enumeration of a special kind of Grothendieck's dessinsExpand
Wall-crossing formulae and strong piecewise polynomiality for mixed Grothendieck dessins d'enfant, monotone, and simple double Hurwitz numbers
We derive explicit formulae for the generating series of mixed Grothendieck dessins d'enfant/monotone/simple Hurwitz numbers, via the semi-infinite wedge formalism. This reveals the strong piecewiseExpand
Central invariants revisited
We use refined spectral sequence arguments to calculate known and previously unknown bi-Hamiltonian cohomology groups, which govern the deformation theory of semi-simple bi-Hamiltonian pencils ofExpand
Loop equations and a proof of Zvonkine's $qr$-ELSV formula
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 itsExpand
Towards an orbifold generalization of Zvonkine's r-ELSV formula
We perform a key step towards the proof of Zvonkine’s conjectural r-ELSV formula that relates Hurwitz numbers with completed (r + 1)-cycles to the geometry of the moduli spaces of the r-spinExpand
The tautological ring of Mg,n via Pandharipande-Pixton-Zvonkine r-spin relations
We use relations in the tautological ring of the moduli spaces Mg,n derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the r-spin Witten class in order to obtain someExpand
UvA-DARE ( Digital Academic Repository ) Central invariants revisited
— We use refined spectral sequence arguments to calculate known and previously unknown bi-Hamiltonian cohomology groups, which govern the deformation theory of semisimple bi-Hamiltonian pencils ofExpand
Cut-and-join equation for monotone Hurwitz numbers revisited
Abstract We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. The main interest in this particular equation is itsExpand
KP hierarchy for Hurwitz-type cohomological field theories
We generalise a result of Kazarian regarding Kadomtsev-Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting problems orExpand
Half-spin tautological relations and Faber's proportionalities of kappa classes
We employ the $1/2$-spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Faber's formula for proportionalities ofExpand
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