Scattering problems are related to how obstacles interfere with the travel of acoustic or electromagnetic waves. I am interested in the opposite problem: given information about a wave which has interacted with some obstacles, what can we determine about those obstacles? With my Ph.D advisor, Dr. Fioralba Cakoni, I work to solve these inverse scattering problems. We specialize in so-called qualitative methods for inverse scattering, which are a relatively recent discovery and form an active area of research.

This research lives on the edges of pure and applied mathematics. We make use of functional analysis, the theory of partial differential equations, and numerical analysis and our results have immediate applications to non-destructive testing, materials science, medical imaging, and geophysics.