I am an applied mathematician and my principal research interests lie in Differential Equations, Dynamical Systems, and Mathematical Biology.
In Differential Equations and Dynamical Systems, my work to date has been primarily concerned with the study of stability of solutions to nonlinear evolution equations and the study of the spectrum of certain perturbed linear Schrodinger Equations. I have also studied the stability of solutions of discrete equations such as the nonlinear Klein-Gordon and Schrodinger equations.
In Mathematical Biology, I have been investigating the relation between the thermal denaturation profiles of DNA sequences and the location of promoters -- regions of DNA providing a control point for regulated gene transcription -- and other significant regulatory regions. I am also working on models that describe DNA configurations and dynamics.
I am working on disease models for Daphnia (waterflea) with Carla Caceres and the BIOMATH students. We are investigating how community ecology, such as competitors and predators, shape the epidemics.
I am also working with Juma Muturi on the modeling of mosquito-borne diseases.
I have also recently finished projects on the quantification and analysis of bumble bee color patterns and the modeling and analysis of gene regulatory networks in mammalian limb development.