Mathematics faculty and graduate students are invited to attend the MS defense of Colin Jensen.

Date: Tuesday, April 5, 2022
Time: 1:00 p.m.
Location: Weber 201

Advisor: Dr. James Liu

Committee: Dr. Simon Tavener, Dr. Wen Zhou

Title: Optimal Transport: Algorithms and Applications

Abstract: Optimal Transport (OT) theory has seen a sharp increase in research interest as new applications to the field of data science have been discovered. This expository paper serves as a guide to data science researchers looking to break into the field of OT. We present the relevant mathematical background for the Monge and Kantorovich formulations of the OT problem. Then, we summarize some of the most important algorithms for solving the OT problem in the discrete and continuous settings. In the discrete setting, we cover linear program solvers and the use of the Sinkhorn-Knopp algorithm to solve the entropic-regularized version of the OT problem. In the continuous setting, we cover existing fluid mechanics and finite difference method approaches to solving the OT problem via the Monge-Ampere equation. We then propose further research into a novel finite element method. We conclude with a description of several major data science applications in computer vision and machine learning.