• Corpus ID: 229923630

Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type

@inproceedings{Bychkov2020TopologicalRF,
  title={Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type},
  author={Boris Bychkov and Petr Dunin-Barkowski and Maxim Kazarian and Sergey Viktorovich Shadrin},
  year={2020}
}
We study the n-point differentials corresponding to Kadomtsev–Petviashvili tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions), with an emphasis on their ~-deformations and expansions. Under the naturally required analytic assumptions, we prove certain higher loop equations that, in particular, contain the standard linear and quadratic loop equations, and thus imply the blobbed topological recursion. We also distinguish two large families of the Orlov… 

Tables from this paper

Topological recursion for Orlov-Scherbin tau functions, and constellations with internal faces
We study the correlators W g,n arising from Orlov–Sherbin 2-Toda tau functions with rational content-weight G ( z ) , at arbitrary values of the two sets of time parameters. Combinatorially, they
Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture
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 construct the weighed
Enumeration of non-oriented maps via integrability
ABSTRACT. In this note, we examine how the BKP structure of the generating series of several models of maps on non-oriented surfaces can be used to obtain explicit and/or efficient recurrence
Higher genera Catalan numbers and Hirota equations for extended nonlinear Schrödinger hierarchy
We consider the Dubrovin–Frobenius manifold of rank 2 whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the
Symplectic duality for topological recursion
. 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
A new spin on Hurwitz theory and ELSV via theta characteristics
We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. These numbers are known to be related to Gromov-Witten theory of
KP hierarchy for Hurwitz-type cohomological field theories
Abstract. We generalise a result of Kazarian regarding Kadomtsev-Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting
Integrality in the Matching-Jack conjecture and the Farahat-Higman algebra
. Using Jack polynomials, Goulden and Jackson have introduced a b -deformation τ b of the generating series of bipartite maps. The Matching-Jack conjecture suggests that the coefficients c λµ , ν of
On the $x$-$y$ Symmetry of Correlators in Topological Recursion via Loop Insertion Operator
Topological Recursion generates a family of symmetric differential forms (correlators) from some initial data (Σ, x, y, B). We give a functional relation between the correlators of genus g = 0
Explicit closed algebraic formulas for Orlov-Scherbin $n$-point functions
We derive a new explicit formula in terms of sums over graphs for the npoint correlation functions of general formal weighted double Hurwitz numbers coming from the Orlov–Scherbin partition
...
...

References

SHOWING 1-10 OF 134 REFERENCES
Blobbed Topological Recursion of the Quartic Kontsevich Model I: Loop Equations and Conjectures
We provide strong evidence for the conjecture that the analogue of Kontsevich’s matrix Airy function, with the cubic potential $$\mathrm {Tr}(\Phi ^3)$$ Tr ( Φ 3 ) replaced by a quartic
Combinatorial structure of colored HOMFLY-PT polynomials for torus knots
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 very similar to the
Weighted Hurwitz numbers and topological recursion: An overview
Multiparametric families of hypergeometric $\tau$-functions of KP or Toda type serve as generating functions for weighted Hurwitz numbers, providing weighted enumerations of branched covers of the
Polynomiality of orbifold Hurwitz numbers, spectral curve, and a new proof of the Johnson–Pandharipande–Tseng formula
TLDR
For orbifold Hurwitz numbers, a new proof of the spectral curve topological recursion is given in the sense of Chekhov, Eynard and Orantin, where the main new step compared to the existing proofs is a direct combinatorial proof of their quasi-polynomiality.
Quantum curves for the enumeration of ribbon graphs and hypermaps
The topological recursion of Eynard and Orantin governs a variety of problems in enumerative geometry and mathematical physics. The recursion uses the data of a spectral curve to define an infinite
Weighted Hurwitz Numbers and Topological Recursion
The KP and 2D Toda $$\tau $$ τ -functions of hypergeometric type that serve as generating functions for weighted single and double Hurwitz numbers are related to the topological recursion programme.
Topological Recursion for the extended Ooguri-Vafa partition function of colored HOMFLY-PT polynomials of torus knots
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 function called the
Blobbed topological recursion: properties and applications
  • G. Borot, S. Shadrin
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2016
Abstract We study the set of solutions (ωg,n ) g⩾0,n⩾1 of abstract loop equations. We prove that ω g,n is determined by its purely holomorphic part: this results in a decomposition that we call
Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfants
We prove quasi-polynomiality for monotone and strictly monotone orbifold Hurwitz numbers. The second enumerative problem is also known as enumeration of a special kind of Grothendieck's dessins
...
...