Assistant Professor, Department of Mathematics, Brigham Young University
My group currently has ongoing projects in these general areas:
We are exploring the relationship between statistical properties of the data (modeled as random graphs) and the performance of graph neural networks on that data. This includes theoretical work and simulation. We are also exploring combining graph neural networks with equation-free modeling to perform rapid simulation of complex problems such as disease spread and protein action.
We are working with psychologists, psychiatrists, neuroscientists, and social scientists to build (a) mathematical models and (b) machine learning solutions for key questions in psychology and psychotherapy.
Recent events have highlighted the need for enhanced robustness and resilience of the global supply chain infrastructure. We are collecting data, building theory, and performing simulations to understand what vulnerabilities exist and optimal solutions to mitigate them.
I have a small number of (very cool) projects in graph theory and dynamics. These include community detection, metrics on random graphs, and influence maximization on graphs, as well as a broad interest in dealing with weighted graphs and graphs that are incomplete in interesting ways.
Genealogical networks are "family tree" networks linking parents to children and spouses to each other (and possibly other relationships). We are modeling the structure of these networks and using random graph theory to help people more efficiently understand the human family and their place in it.