10 papers
A new spin on polynomial relations among kappa classes
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algeb…
KP integrability of non-perturbative differentials
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We prove the KP integrability of non-perturbative topological recursion, which can be considered as a formal -deformation of the Krichever construction of algebro-geometric…
Any topological recursion on a rational spectral curve is KP integrable
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We prove that for any initial data on a genus zero spectral curve the corresponding correlation differentials of topological recursion are KP integrable. As an application we prove…
A new family of weighted double Hurwitz numbers and a new ELSV-type formula with -classes
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We analyze a new family of weighted double Hurwitz numbers that was introduced as a notable example in the context of the duality for logarithmic topological recursion. We us…
Degenerate and irregular topological recursion
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We use the theory of duality to propose a new definition / construction for the correlation differentials of topological recursion; we call it "generalized topological recurs…
KP integrability through the swap relation
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We discuss a universal relation that we call the swap relation, which plays a prominent role in the theory of topological recursion, Hurwitz theory, and free probability theo…