Project description: Discrete and computational geometry studies the combinatorial and computational properties of points, lines, polygons, etc. as embedded in Euclidean spaces. Problems in this area are often very hands-on as we can draw explicit examples. The first example that one often learns are both the theoretical properties of the convex hull of a set of points in the plane as well as efficient algorithms for explicitly computing this convex hull.

Project 1: One application of this field involves "data depth." Data depth combines discrete and computational geometry with statistics to develop a nonparametric generalization of the median in high dimensions. More explicitly, data depth functions quantify centrality of a point in a data cloud using only the geometry of the data. There are many data depth functions whose theoretical properties have not been explored or do not yet have efficient algorithms for implementation. The goal of this project would be to study and develop the theory of some of these functions.

Project 2: Many papers in this active field are very approachable and can be read without too much background study. It is common in this area to end papers with a list of open problems. This project is a bit more free-form and we would read a few papers together and attempt to solve some of the posed open problems.

Prerequisites:  High-school geometry skills necessary, computer science skills are a plus.

Project faculty:
Prof. Michael Burr
Email: burr2 at clemson.edu (change "at" to "@")
Office hours: TBA
Bio: coming soon