160 citations · 1.4k across the 97 of their papers we have counts for
37 papers · 1 filter
Augmentation curve for torus knots
Alexander Hock, Sergey Shadrin
We prove a version of topological recursion for the correlation differentials of colored HOMFLY-PT polynomials of torus knots on the corresponding augmentation curves, following th…
Lifts of partial cohomological field theories and examples of bi-Hamiltonian structures in the non-semisimple case
Guido Carlet, Dimitrios Makris, Sergey Shadrin
We define the lift of a partial cohomological field theory with respect to a Frobenius algebra and the corresponding lift of local polyvector fields, extending the lift procedure p…
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…
Quantum Curves in the Context of Symplectic Duality
Alexander Hock, Sergey Shadrin
We discuss how to use the recent progress in understanding of the - duality and symplectic duality in the theory of topological recursion and its generalizations in order to…
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…
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…
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…
Symplectic duality via log topological recursion
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
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 c…
Structure of Dubrovin-Zhang free energy functions and universal identities
Sergey Shadrin, Zhe Wang
We prove a structural theorem relating the higher genera free energy functions of the Dubrovin-Zhang hierarchies to the Witten-Kontsevich free energy function of the Korteweg-de Vr…
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…
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…
Topological recursion, symplectic duality, and generalized fully simple maps
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the -point functions produced by the topol…
Miura-reciprocal transformations and localizable Poisson pencils
P. Lorenzoni, S. Shadrin, R. Vitolo
We show that the equivalence classes of deformations of localizable semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura-reciprocal group contain…
A universal formula for the swap in topological recursion
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
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…
Enumeration of hypermaps and Hirota equations for extended rationally constrained KP
G. Carlet, J. van de Leur, H. Posthuma +1
We consider the Hurwitz Dubrovin--Frobenius manifold structure on the space of meromorphic functions on the Riemann sphere with exactly two poles, one simple and one of arbitrary o…
Symplectic duality for topological recursion
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian +1
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 arbitrar…
Generalised ordinary vs fully simple duality for -point functions and a proof of the Borot--Garcia-Failde conjecture
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian +1
We study a duality for the -point functions in VEV formalism that we call the ordinary vs fully simple duality. It provides an ultimate generalisation and a proper context for t…
Bi-Hamiltonian recursion, Liu-Pandharipande relations, and vanishing terms of the second Dubrovin-Zhang bracket
Francisco Hernández Iglesias, Sergey Shadrin
The Dubrovin-Zhang hierarchy is a Hamiltonian infinite-dimensional integrable system associated to a semi-simple cohomological field theory or, alternatively, to a semi-simple Dubr…
Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture
Alexander Alexandrov, Sergey Shadrin
In this paper, we discuss the properties of the generating functions of spin Hurwitz numbers. In particular, for spin Hurwitz numbers with arbitrary ramification profiles, we const…
Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian +1
We study the -point differentials corresponding to Kadomtsev-Petviashvili tau functions of hypergeometric type (also known as Orlov-Scherbin partition functions), with an emphas…
Topological Recursion for the extended Ooguri-Vafa partition function of colored HOMFLY-PT polynomials of torus knots
Petr Dunin-Barkowski, Maxim Kazarian, Aleksandr Popolitov +2
We prove that topological recursion applied to the spectral curve of colored HOMFLY-PT polynomials of torus knots reproduces the n-point functions of a particular partition functio…
Towards a bihamiltonian structure for the double ramification hierarchy
Alexandr Buryak, Paolo Rossi, Sergey Shadrin
We propose a remarkably simple and explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy corresponding to an arbitrary homogeneous cohomol…
Ground states of Nicolai and Nicolai models
Ruben La, Kareljan Schoutens, Sergey Shadrin
We derive explicit recursions for the ground state generating functions of the one-dimensional Nicolai model and Nicolai model. Both are examples of lattice models w…
Combinatorial structure of colored HOMFLY-PT polynomials for torus knots
Petr Dunin-Barkowski, Aleksandr Popolitov, Sergey Shadrin +1
We rewrite the (extended) Ooguri-Vafa partition function for colored HOMFLY-PT polynomials for torus knots in terms of the free-fermion (semi-infinite wedge) formalism, making it v…