160 citations · 1.4k across the 97 of their papers we have counts for
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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…
Cohomological representations of quantum tau functions
Xavier Blot, Danilo Lewański, Sergey Shadrin
In 2016, Buryak and Rossi introduced the quantum Double Ramification (DR) hierarchies which associate a quantum integrable hierarchy to any Cohomological Field Theory (CohFT). Shor…
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…
Hidden structures behind ambient symmetries of the Maurer-Cartan equation
Vladimir Dotsenko, Sergey Shadrin
For every differential graded Lie algebra one can define two different group actions on the Maurer-Cartan elements: the ubiquitous gauge action and the action of $\m…
The master relation for polynomiality and equivalences of integrable systems
Xavier Blot, Adrien Sauvaget, Sergey Shadrin
We prove the so-called master relation in the tautological ring of the moduli space of curves that implies polynomial properties of the Dubrovin-Zhang hierarchies associated to dif…
Rooted trees with level structures, -classes and double ramification cycles
Xavier Blot, Danilo Lewański, Sergey Shadrin
We prove a new system of relations in the tautological ring of the moduli space of curves involving stable rooted trees with level structure decorated by the top Chern class of the…
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…
On the strong DR/DZ equivalence conjecture
Xavier Blot, Danilo Lewanski, Sergey Shadrin
We establish the Miura equivalence of two integrable systems associated to a semi-simple cohomological field theory: the double ramification hierarchy of Buryak and the Dubrovin-Zh…
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…