I study mathematical models, generally in the context of kinetic theory. At the discrete level, I work on applications of interacting particle models and agent-based models; thus far, I have applied them to fish migration, human gang rivalries and gang territorial development, and I am now developing models in the context of medicine. I am very interested in the kinetic and hydrodynamic limits of these models, especially in models that undergo phase transitions as one or more of the parameters are varied. I have studied these phase transition at the microscopic, mesoscopic, and macroscopic scales.
Abdulaziz Alsenafi (advisor), PhD in Applied Mathematics, expected August 2016
Douglas Brubaker (co-advisor), PhD in Proteomics and Bioinformatics, expected May 2016