I am an applied mathematician whose research lies at the intersection of partial differential equations, spectral theory, and mathematical physics.
I am interested in developing and analyzing mathematical models which can be used to study physical phenomena such as wave propagation, dispersion, localization, scattering, and the formation of bound or edge states. Much of my work concerns Schrödinger and Dirac operators, quantum-optical models, waves in periodic or random media, and the effective equations that emerge from more complicated microscopic dynamics.
My work combines operator theory, spectral and scattering methods, dispersive estimates, ordinary and partial differential equations, as well as asymptotic analysis. I am particularly interested in the use of analytically tractable models as a tool for isolating important mechanisms. Exactly or partially solvable models can provide insight into phenomena that may be intractable in more general settings, while retaining the essential mathematical and physical features of the problem.
I also enjoy working on research projects with undergraduate students. These projects are designed to introduce students to modern questions in mathematical physics through problems that admit a meaningful combination of analysis and computation.