My education is in theoretical physics with a mathematical flavor, and for
two decades my research centered on quantum field theory in curved
space-time, helping to advance our understanding of black holes,
cosmology, and what is now called the dynamical Casimir effect. As a
natural evolution from that, I am mostly concerned now with the
interplay of asymptotics and spectral theory, with applications to
semiclassical approximation in quantum mechanics and to renormalization in
quantum field theory. Major themes in recent years have included (1)
using group theory, graph theory, and symbolic computation to clarify the
algebraic structure of the complicated heat kernel expansions that arise
in this work; (2) defining and using pseudodifferential operators (and
their physics cousins, Wigner distribution functions) in a manifestly
covariant way in the presence of gravitational and gauge fields. I have
side interests in literate programming and quantum
computation. I teach mostly upper-level undergraduate applied math
courses, and I'm very concerned with techniques for facilitating active
learning and using the computer network as a communications and
instructional tool in such courses.
