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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 original curve.
“Hermitian matrix model free energy: Feynman graph technique for all genera”
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“Matrix eigenvalue model: Feynman graph technique for all genera”
Leonid Chekhov and Bertrand Eynard · 2006
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“Invariants of algebraic curves and topological expansion”
B. Eynard and N. Orantin · 2007
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“Topological recursion in enumerative geometry and random matrices”
Bertrand Eynard and Nicolas Orantin · 2009
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“Think globally, compute locally”
Vincent Bouchard and Bertrand Eynard · 2013
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“An overview of the topological recursion”
Bertrand Eynard · 2014
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“Blobbed topological recursion: properties and applications”
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“Relating ordinary and fully simple maps via monotone Hurwitz numbers”
Ga\"etan Borot, S\’everin Charbonnier, Norman Do and Elba Garcia-Failde · 2019
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“Simple maps, Hurwitz numbers, and topological recursion”
Ga\"etan Borot and Elba Garcia-Failde · 2020
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Gaëtan Borot, Séverin Charbonnier and Elba Garcia-Failde · 2021
Cited alongside, same era.
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian and Sergey Shadrin · 2022
Cited alongside, same era.
“Symplectic duality for topological recursion”, 2022
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian and Sergey Shadrin · 2022
Later among the works it cites.
“Topological recursion for the extended Ooguri-Vafa partition function of colored HOMFLY-PT polynomials of torus knots”
Petr Dunin-Barkowski, Maxim Kazarian, Aleksandr Popolitov, Sergey Shadrin and Alexey Sleptsov · 2022
Later among the works it cites.
“Taking limits in topological recursion”, 2023
G. Borot, V. Bouchard, N. Chidambaram, R. Kramer and S. Shadrin · 2023
Closest in time.
“Generalised ordinary vs fully simple duality for n n -point functions and a proof of the Borot–Garcia-Failde conjecture”
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian and Sergey Shadrin · 2023
Closest in time.
“Topological recursion for Orlov–Scherbin tau functions, and constellations with internal faces”
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“Explicit closed algebraic formulas for Orlov-Scherbin n n -point functions”
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian and Sergey Shadrin · 2022
Cited alongside, same era.
“A free probabilistic perspective on constellations” (tentative title, in preparation)
Gaëtan Borot, Séverin Charbonnier, Elba Garcia-Failde, Felix Leid and Sergey Shadrin
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Valentin Bonzom, Guillaume Chapuy, S\’everin Charbonnier and Elba Garcia-Failde · 2024
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“Topological recursion for Kadomtsev–Petviashvili tau functions of hypergeometric type”
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian and Sergey Shadrin · 2024
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