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Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfants

- R. Kramer, D. Lewa'nski, S. Shadrin
- Mathematics, Physics
- 26 October 2016

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 dessins… Expand

Wall-crossing formulae and strong piecewise polynomiality for mixed Grothendieck dessins d'enfant, monotone, and simple double Hurwitz numbers

- Marvin Anas Hahn, R. Kramer, D. Lewa'nski
- Mathematics
- 3 October 2017

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 piecewise… Expand

Central invariants revisited

- Guido Carlet, R. Kramer, S. Shadrin
- Mathematics, Physics
- 28 November 2016

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 of… Expand

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

- P. Dunin-Barkowski, R. Kramer, A. Popolitov, S. Shadrin
- Mathematics, Physics
- 11 May 2019

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… Expand

Towards an orbifold generalization of Zvonkine's r-ELSV formula

- R. Kramer, D. Lewa'nski, A. Popolitov, S. Shadrin
- Mathematics, Physics
- 20 March 2017

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-spin… Expand

The tautological ring of Mg,n via Pandharipande-Pixton-Zvonkine r-spin relations

- R. Kramer, Farrokh Labib, D. Lewa'nski, S. Shadrin
- Mathematics, Physics
- 2 March 2017

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 some… Expand

UvA-DARE ( Digital Academic Repository ) Central invariants revisited

- Guido Carlet, R. Kramer, S. Shadrin
- 2017

— 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 of… Expand

Cut-and-join equation for monotone Hurwitz numbers revisited

- P. Dunin-Barkowski, R. Kramer, A. Popolitov, S. Shadrin
- Mathematics
- 11 July 2018

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 its… Expand

KP hierarchy for Hurwitz-type cohomological field theories

- R. Kramer
- Mathematics, Physics
- 12 July 2021

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 or… Expand

Half-spin tautological relations and Faber's proportionalities of kappa classes

- Elba Garcia-Failde, R. Kramer, Danilo Lewa'nski, S. Shadrin
- Mathematics
- 7 February 2019

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 of… Expand

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