Research

Metric entropy has been studied extensively in a variety of literature and disciplines. It plays a central role in different areas of information theory and statistics, including nonparametric function estimation, density information, empirical processes and machine learning.

My research focuses on finding sharp estimates for the metric entropy of classes of bounded total generalized variation functions and using these results to measure the set of solutions of certain nonlinear partial differential equations, where it could provide a measure of the order of “resolution” and “complexity” of a numerical scheme.

This work is being done under the supervision of Dr. Khai T. Nguyen, within the Nonlinear Analysis Thematic Group at North Carolina State University.