Research

Since completing my PhD, I have been fortunate to work with some amazingly gifted applied scientists and mathematicians on interesting problems within a variety of research areas:

Partial Differential Equations and Kinetic Theory

A large portion of my previous and ongoing research deals with the modeling, analysis, and simulation of PDEs, especially those which arise within the kinetic theory of plasma dynamics. Physically, these systems model phenomena like the Solar Wind, a stream of charged particles continuously ejected from the sun which interact with the earth's magnetic field and generally engulf our solar system. Additional projects in this area concern the instability of steady states of nonlinear diffusion equations, increased parabolic regularity for nonlinear Fokker-Planck equations, global sensitivity metrics to understand Landau Damping, and chemical reaction dynamics within imperfectly-mixed fluids.

Mathematical Biology, Computational Biophysics, and Multiscale Analysis

My research in these fields can be categorized into three distinct areas:

1. Computational Virology

These projects represent a joint venture with the Center for Cell and Virus Theory at Indiana University.  The overarching goal is to create a dynamical software system which can be used to predict the influence of host media (such as a vaccine or antiviral therapeutic molecules) on the structural stability of a virus.  Associated tools include models from statistical mechanics and thermodynamics, multi-scale analysis, and simulation of generalized Langevin equations.

2. in-host HIV dynamics

These projects have generally focused on developing new population models and analytic tools to capture the time course of all three stages of HIV as it battles the immune system within a host. Additionally, our group efforts have concentrated on better representing the acute stage and studying the effects of anti-retroviral therapy.

3. Mathematical and Computational Epidemiology

Projects in this area use computational means to study recent outbreaks of disease throughout the world.  Tools include the development of new deterministic and stochastic SIR, SEIR, and vector-borne disease models and statistical methods, such as Approximate Bayesian Computation, to estimate the spread of infection, latent periods, reporting rates, and the efficacy of mitigation strategies to inhibit or eliminate epidemics.