My research is in an area of mathematics called numerical analysis. In situations of practical interest, you are often faced with solving a particularly difficult equation in order to get the answer you want. Numerical analysis is the study of how to approximate the solution rather than compute it analytically. In particular, I study Galerkin methods for the solution of differential equations and integro-differential equations.
I am particularly interested in the radiative transport equation (RTE). The RTE governs the propagation of light through a biological medium. In some emerging medical imaging techniques (e.g. bioluminescence tomography, x-ray dark field tomography), a some light source is placed near or inside a biological medium. Measurements are taken using very sensitive cameras of the light emerging from the tissue. The goal is to figure out either some optical properties of the medium, or to find out where the source of the light was inside the tissue.
Here are the slides for a recent talk I gave as a very high level introduction to the area.