Zobrazeno 1 - 10
of 237
pro vyhledávání: '"Barkowski P"'
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
We prove the KP integrability of non-perturbative topological recursion, which can be considered as a formal $\hbar$-deformation of the Krichever construction. This property goes back to a 2011 conjecture of Borot and Eynard.
Comment: 21 pages
Comment: 21 pages
Externí odkaz:
http://arxiv.org/abs/2412.18592
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
We use the theory of $x-y$ duality to propose a new definition / construction for the correlation differentials of topological recursion; we call it "generalized topological recursion". This new definition coincides with the original topological recu
Externí odkaz:
http://arxiv.org/abs/2408.02608
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
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 KP integrability of partition functions associated via ELSV-type form
Externí odkaz:
http://arxiv.org/abs/2406.07391
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
Publikováno v:
Communications in Number Theory and Physics, Volume 18 (2024) Number 4, pp. 795-841
We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log topological
Externí odkaz:
http://arxiv.org/abs/2405.10720
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
Publikováno v:
Int. Math. Res. Not. IMRN 2024, no. 21, 13461--13487
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 definition satisfies the universal $x-y$ swap relation. This result pr
Externí odkaz:
http://arxiv.org/abs/2312.16950
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
We discuss a universal relation that we call the $x-y$ swap relation, which plays a prominent role in the theory of topological recursion, Hurwitz theory, and free probability theory. We describe in a very precise and detailed way the interaction of
Externí odkaz:
http://arxiv.org/abs/2309.12176
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
Publikováno v:
J. Geom. Phys. 206 (2024), 105329, 13 pp
For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions on the or
Externí odkaz:
http://arxiv.org/abs/2304.11687
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
We prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of $x$ and $y$ in the input data. We also show that this universal formul
Externí odkaz:
http://arxiv.org/abs/2212.00320
We consider weighted double Hurwitz numbers, with the weight given by arbitrary rational function times an exponent of the completed cycles. Both special singularities are arbitrary, with the lengths of cycles controlled by formal parameters (up to s
Externí odkaz:
http://arxiv.org/abs/2206.14792
Publikováno v:
Comm. Math. Phys. 402 (2023), no. 1, 665-694
We study a duality for the $n$-point functions in VEV formalism that we call the ordinary vs fully simple duality. It provides an ultimate generalisation and a proper context for the duality between maps and fully simple maps observed by Borot and Ga
Externí odkaz:
http://arxiv.org/abs/2106.08368