8 papers · 1 filter
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…
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…
Blobbed topological recursion and KP integrability
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily adm…
Log topological recursion through the prism of swap
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We introduce a new concept of logarithmic topological recursion that provides a patch to topological recursion in the presence of logarithmic singularities and prove that this new…