Overview | Research | Grants/Awards | Teaching | Publications | Recent Talks
I am currently working in the following areas
- Nonlinear PDEs
One focus of my research is the qualitative behavior of
nonlinear partial differential equations, including issues of well
posedness and existence and stability of equilibrium solutions.
interested in the application of techniques from mathematical analysis,
including dispersive estimates and calculus of variations, to help elucidate the behavior of physical systems.
Many important physical
systems exhibit phenomena that evolve on
multiple scales, and asymptotic and numerical methods
are indispensable tools for studying such systems. A
particular area of interest to me is the development of averaging
theories for both deterministic and stochastic PDEs.
- Waves in
inhomogenous media, including random media
Much of my work has focused on the study of
optical pulse propagation in
spatially periodic or random media. I am particularly interested
in the interplay
between nonlinearity and randomness.
- Applications to
optics and biology
An important goal of my research is the integration of information from experiments, physical modeling, simulation, and mathematical analysis to gain insight into problems of significance in the physical world. The applications have ranged from pulse propagation in inhomogenous optical fibers, slab waveguides, and discrete waveguide arrays to supercontinuum generation in photonic crystal fibers and chemical reaction kinetics for signal transduction pathways.