PhD Proposal: Computational Geometry in the Hilbert Metric

The Hilbert metric generalizes the Cayley-Klein (or Beltrami-Klein) model of hyperbolic geometry to arbitrary convex polygons. It has been used in a variety of fields, including graph embeddings, quantum information theory, machine learning, and convex geometry. As such, there has been interest in reproducing results from classical computational geometry on the Euclidean metric in the Hilbert metric. In this document we will present a description of work completed so far, a plan for proposed research with a timeline, and a survey of relevant literature.