38 citations · 217 across the 12 of their papers we have counts for
5 papers · 1 filter
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…
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…
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…