• Corpus ID: 127539537

Diophantine Analysis on Moduli of Local Systems

@inproceedings{Whang2018DiophantineAO,
  title={Diophantine Analysis on Moduli of Local Systems},
  author={Junho Peter Whang},
  year={2018}
}
We develop a Diophantine analysis on moduli of special linear rank two local systems over surfaces with prescribed boundary traces. We first show that such a moduli space is a log Calabi-Yau variety if the surface has nonempty boundary, and relate this property to a symmetry of generating series for combinatorial counts of essential multicurves on surfaces. We establish the finiteness of “class numbers” for integral orbits of mapping class group dynamics on the moduli space, generalizing a… 

Figures from this paper

References

SHOWING 1-10 OF 134 REFERENCES
Arithmetic of curves on moduli of local systems
We study the Diophantine geometry of algebraic curves on relative moduli of special linear rank two local systems over surfaces. We prove that the set of integral points on any nondegenerately
Moduli spaces of local systems and higher Teichmüller theory
Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S
Canonical bases for cluster algebras
In [GHK11], Conjecture 0.6, the first three authors conjectured that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical
Short Loop Decompositions of Surfaces and the Geometry of Jacobians
Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different
The dual complex of Calabi–Yau pairs
A log Calabi–Yau pair consists of a proper variety X and a divisor D on it such that $$K_X+D$$KX+D is numerically trivial. A folklore conjecture predicts that the dual complex of D is homeomorphic to
Integral points on subvarieties of semiabelian varieties, I
This paper proves a finiteness result for families of integral points on a semiabelian variety minus a divisor, generalizing the corresponding result of Faltings for abelian varieties. Combined with
Diophantine Problems and Linear Groups
In this lecture we describe and exploit the relation between analytic Diophantine problems on homogeneous varieties and harmonic analysis on the corresponding groups. For the case G = SL(2) this
Monodromy of certain Painlevé–VI transcendents and reflection groups
Abstract.We study the global analytic properties of the solutions of a particular family of Painlevé VI equations with the parameters β=γ=0, δ=1/2 and 2α=(2μ-1)2 with arbitrary μ, 2μ≠∈ℤ. We introduce
Trace Coordinates on Fricke spaces of some simple hyperbolic surfaces
The conjugacy class of a generic unimodular 2 by 2 complex matrix is determined by its trace, which may be an arbitrary complex number. In the nineteenth century, it was known that a generic pair
On skein algebras and Sl2(C)-character varieties
...
...