38 citations · 217 across the 12 of their papers we have counts for
12 papers
Topological recursion for monotone orbifold Hurwitz numbers: a proof of the Do-Karev conjecture
Reinier Kramer, Alexandr Popolitov, Sergey Shadrin
We prove the conjecture of Do and Karev that the monotone orbifold Hurwitz numbers satisfy the Chekhov-Eynard-Orantin topological recursion.
Loop equations and a proof of Zvonkine's -ELSV formula
Petr Dunin-Barkowski, Reinier Kramer, Alexandr Popolitov +1
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 -ELSV formu…
Cut-and-join equation for monotone Hurwitz numbers revisited
Petr Dunin-Barkowski, Reinier Kramer, Alexandr Popolitov +1
We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. Our proof in particular uses a combinatorial te…
Towards an orbifold generalization of Zvonkine's -ELSV formula
Reinier Kramer, Danilo Lewanski, Alexandr Popolitov +1
We perform a key step towards the proof of Zvonkine's conjectural -ELSV formula that relates Hurwitz numbers with completed -cycles to the geometry of the moduli spaces o…
Primary invariants of Hurwitz Frobenius manifolds
Petr Dunin-Barkowski, Paul Norbury, Nicolas Orantin +2
Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifold…
Dubrovin's superpotential as a global spectral curve
Petr Dunin-Barkowski, Paul Norbury, Nicolas Orantin +2
We apply the spectral curve topological recursion to Dubrovin's universal Landau-Ginzburg superpotential associated to a semi-simple point of any conformal Frobenius manifold. We s…
Polynomiality of orbifold Hurwitz numbers, spectral curve, and a new proof of the Johnson-Pandharipande-Tseng formula
Petr Dunin-Barkowski, Danilo Lewanski, Alexandr Popolitov +1
In this paper we present an example of a derivation of an ELSV-type formula using the methods of topological recursion. Namely, for orbifold Hurwitz numbers we give a new proof of…
Chiodo formulas for the r-th roots and topological recursion
Danilo Lewanski, Alexandr Popolitov, Sergey Shadrin +1
We analyze Chiodo's formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The inters…
Combinatorics of loop equations for branched covers of sphere
P. Dunin-Barkowski, N. Orantin, A. Popolitov +1
We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which are dual objects to dessins d'enfant. Fur…
Quantum spectral curve for the Gromov-Witten theory of the complex projective line
Petr Dunin-Barkowski, Motohico Mulase, Paul Norbury +2
We construct the quantum curve for the Gromov-Witten theory of the complex projective line.
On the Homology of Certain Smooth Covers of Moduli Spaces of Algebraic Curves
Petr Dunin-Barkowski, Alexander Popolitov, George Shabat +1
We suggest a general method of computation of the homology of certain smooth covers of moduli spaces $\mathcal{M}_{g,1}\br{\mathbb{C}}$ of poi…
On coincidence of Alday-Maldacena-regularized -model and Nambu-Goto areas of minimal surfaces
A. Popolitov
For the -model and Nambu-Goto actions, values of the Alday-Maldacena-regularized actions are calculated on solutions of the equations of motion with constant non-regularized Lag…