• Corpus ID: 211010614

On discrete surfaces: Enumerative geometry, matrix models and universality classes via topological recursion

@article{GarciaFailde2020OnDS,
  title={On discrete surfaces: Enumerative geometry, matrix models and universality classes via topological recursion},
  author={Elba Garcia-Failde},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. Our problems have a powerful relatively recent tool in common, the so-called topological recursion (TR) introduced by Chekhov, Eynard and Orantin. We call a map fully simple if it has non self-intersecting disjoint boundaries, and ordinary if such a restriction is not imposed. We study the combinatorial relation between fully simple and ordinary maps with the topology of a disk… 
4 Citations
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
Topological recursion for fully simple maps from ciliated maps
Ordinary maps satisfy topological recursion for a certain spectral curve (x,y). We solve a conjecture from [5] that claims that fully simple maps, which are maps with non selfintersecting disjoint
Ju n 20 21 T OPOLOGICAL RECURSION FOR FULLY SIMPLE MAPS FROM CILIATED MAPS
Ordinary maps satisfy topological recursion for a certain spectral curve (x,y). We solve a conjecture from [5] that claims that fully simple maps, which are maps with non selfintersecting disjoint
On the Hodge-BGW correspondence
We establish an explicit relationship between the partition function of certain special cubic Hodge integrals and the generalized Brézin–Gross–Witten (BGW) partition function, which we refer to as

References

SHOWING 1-10 OF 119 REFERENCES
A Generalized Topological Recursion for Arbitrary Ramification
The Eynard–Orantin topological recursion relies on the geometry of a Riemann surface S and two meromorphic functions x and y on S. To formulate the recursion, one must assume that x has only simple
The topological structure of scaling limits of large planar maps
We discuss scaling limits of large bipartite planar maps. If p≥2 is a fixed integer, we consider, for every integer n≥2, a random planar map Mn which is uniformly distributed over the set of all
Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies
We compute the generating functions of an model (loop gas model) on a random lattice of any topology. On the disc and the cylinder, the topologies were already known, and here we compute all the
Topological recursion for Gaussian means and cohomological field theories
We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich–Penner matrix model (KPMM), which is the
Monotone Hurwitz Numbers and the HCIZ Integral
In this article, we study the topological expansion of the Harish-Chandra-Itzykson-Zuber matrix model. We prove three types of results concerning the free energy of the HCIZ model. First, at 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
Conformal loop ensembles: the Markovian characterization and the loop-soup construction
For random collections of self-avoiding loops in two-dimensional domains, we dene a simple and natural conformal restriction property that is conjecturally satised by the scaling limits of interfaces
...
1
2
3
4
5
...