53 citations · 390 across the 41 of their papers we have counts for
9 papers · 1 filter
Topological recursion for irregular spectral curves
Norman Do, Paul Norbury
We study topological recursion on the irregular spectral curve , which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recu…
Pruned Hurwitz numbers
Norman Do, Paul Norbury
We define a new Hurwitz problem which is essentially a small core of the simple Hurwitz problem. The corresponding Hurwitz numbers have simpler formulae, satisfy effective recursio…
Simple geodesics and Markoff quads
Yi Huang, Paul Norbury
The action of the mapping class group of the thrice-punctured projective plane on its character variety produces an algorithm for generating the simple…
Counting lattice points in compactified moduli spaces of curves
Norman Do, Paul Norbury
We define and count lattice points in the moduli space of stable genus g curves with n labeled points. This extends a construction of the second author for the uncompactified modul…
Cell decompositions of moduli space, lattice points and Hurwitz problems
Paul Norbury
In this article we describe cell decompositions of the moduli space of Riemann surfaces and their relationship to a Hurwitz problem. The cells possess natural linear structures and…
Lengths of geodesics on non-orientable hyperbolic surfaces
Paul Norbury
We give an identity involving sums of functions of lengths of simple closed geodesics, known as a McShane identity, on any non-orientable hyperbolic surface with boundary which gen…