9 citations · 27 across the 3 of their papers we have counts for
4 papers
The Geometric Bogomolov Conjecture for Small Genus Curves
X. W. C. Faber
The Bogomolov Conjecture is a finiteness statement about algebraic points of small height on a smooth complete curve defined over a global field. We verify an effective form of the…
On the Finite Field Kakeya Problem in Two Dimensions
X. W. C. Faber
A two-dimensional Besicovitch set over a finite field is a subset of the finite plane containing a line in each direction. In this paper, we conjecture a sharp lower bound for the…
Spectral Convergence of the Discrete Laplacian on Models of a Metrized Graph
X. W. C. Faber
A metrized graph is a compact singular 1-manifold endowed with a metric. A given metrized graph can be modelled by a family of weighted combinatorial graphs. If one chooses a seque…
Metrized graphs, electrical networks, and Fourier analysis
Matthew Baker, Xander Faber
A metrized graph is a finite weighted graph whose edges are thought of as line segments. In this expository paper, we study the Laplacian operator on a metrized graph and some impo…