Fetching the paper…

Reading the bibliography…

2013

Quantum curves for the enumeration of ribbon graphs and hypermaps

Do, Norman, Manescu, David

Original
PDF
Post on X

Understand

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 family of multidifferentials.
It has been conjectured that, under certain conditions, the spectral curve possesses a non-commutative quantisation whose associated differential operator annihilates the partition function for the spectral curve.
In this paper, we determine the quantum curves and partition functions for an infinite sequence of enumerative problems involving generalisations of ribbon graphs known as hypermaps.

Quantum curves for the enumeration of ribbon graphs and hypermaps · Around

Built on

The number of ramified coverings of the sphere by the double torus, and a general form for higher genera
1999
Earlier work this paper cites.
Hurwitz numbers and intersections on moduli spaces of curves
2001
Earlier work this paper cites.
Graphs on surfaces and their applications
2004
Earlier work this paper cites.
The colored Jones function is
2005
Earlier work this paper cites.
Invariants of algebraic curves and topological expansion
2007
Earlier work this paper cites.

Similar

Hurwitz numbers, matrix models and enumerative geometry
2008
Cited alongside, same era.
Remodeling the B-model
2009
Cited alongside, same era.
A matrix model for simple Hurwitz numbers, and topological recursion
2011
Cited alongside, same era.
The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
2011
Cited alongside, same era.
All-order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials
Original
Cited in the paper.
Think globally, compute locally
Original
Cited in the paper.
Mirror symmetry for orbifold Hurwitz numbers
Original
Cited in the paper.
Orbifold Hurwitz numbers and Eynard–Orantin invariants
Original
Cited in the paper.
The spectral curve of the Eynard–Orantin recursion via the Laplace transform
Original
Cited in the paper.
Polynomiality of Hurwitz numbers, Bouchard–Mariño conjecture, and a new proof of the ELSV formula
Original
Cited in the paper.
Quantum spectral curve for the Gromov–Witten theory of the complex projective line
Original
Cited in the paper.
Identification of the Givental formula with the spectral curve topological recursion procedure
Original
Cited in the paper.

Then

Counting lattice points in compactified moduli spaces of curves
2011
Later among the works it cites.
The Laplace transform of the cut-and-join equation and the Bouchard-Mariño conjecture on Hurwitz numbers
2011
Later among the works it cites.
A-polynomial, B-model, and quantization
2012
Later among the works it cites.
String and dilaton equations for counting lattice points in the moduli space of curves
2013
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…