Email: abwatson@math.duke.edu

Office: 224 Physics Building

Office hours: (Spring 2020) Mondays 9-11AM


I am an applied mathematician working primarily in the field of partial differential equations (PDE). The overall goals of my research are to develop rigorous asymptotic analysis and accurate and efficient numerical methods for PDE which are important in applications. In my research career thus far, I have focused on the Schrödinger equations which model the wave-like dynamics of electrons in materials and the propagation of electromagnetic waves, motivated by problems arising in condensed matter physics and photonics respectively.

Two particular themes of my research have been understanding wave propagation: (1) in periodic structures beyond adiabaticity (spectral gap) assumptions (2) in non-periodic structures, such as structures with disorder or edges. These themes have been motivated by wanting to understand two families of materials which have attracted attention in recent years for their novel properties: (1) graphene and other semi-metallic materials (2) materials which conduct robustly at their physical edge known as topological insulators. For more details, see Research by theme.

My PhD advisor at Columbia was Michael I. Weinstein. I am currently William E. Elliott Assistant Research Professor at Duke working primarily with Jianfeng Lu.