Corpus ID: 235446834

Generalised ordinary vs fully simple duality for $n$-point functions and a proof of the Borot--Garcia-Failde conjecture

@inproceedings{Bychkov2021GeneralisedOV,
  title={Generalised ordinary vs fully simple duality for \$n\$-point functions and a proof of the Borot--Garcia-Failde conjecture},
  author={B. Bychkov and P. Dunin-Barkowski and M. Kazarian and S. Shadrin},
  year={2021}
}
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 Garcia-Failde. Our approach allows to transfer the algebraicity properties between the systems of n-point functions related by this duality, and gives direct tools for the analysis of singularities. As an application, we give a proof of a recent… Expand
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References

SHOWING 1-10 OF 27 REFERENCES
Relating Ordinary and Fully Simple Maps via Monotone Hurwitz Numbers
TLDR
The goal of this paper is to present two independent proofs that are purely combinatorial and generalise in various directions, such as to the setting of stuffed maps and hypermaps. Expand
Simple maps, Hurwitz numbers, and Topological Recursion.
We introduce the notion of fully simple maps, which are maps with non self-intersecting disjoint boundaries. In contrast, maps where such a restriction is not imposed are called ordinary. We study inExpand
Combinatorics of loop equations for branched covers of sphere
We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which in a certain way generalize the notion of dessins d'enfant.Expand
Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion
TLDR
A structural quasi-polynomiality property for the Bousquet-Melou-Schaeffer numbers is proved in a purely combinatorial way from the existing correspondence between the topological recursion and Givental's theory for cohomological field theories. Expand
Think globally, compute locally
A bstractWe introduce a new formulation of the so-called topological recursion, that is defined globally on a compact Riemann surface. We prove that it is equivalent to the generalized recursion forExpand
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.Expand
Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
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 theirExpand
Formal multidimensional integrals, stuffed maps, and topological recursion
We show that the large N expansion in the multi-trace 1 formal hermitian matrix model is governed by the topological recursion of [Eynard and Orantin, 2007] with initial conditions. In terms of a 1dExpand
Invariants of algebraic curves and topological expansion
For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties.Expand
The KP hierarchy, branched covers, and triangulations
The KP hierarchy is a completely integrable system of quadratic, partial differential equations that generalizes the KdV hierarchy. A linear combination of Schur functions is a solution to the KPExpand
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