My research interests are
stochastic partial differential equations and uncertainty quantification:
proving existence, uniqueness, and smoothness of solutions,
developing numerical methods, and
multiscale problems (stochastic homogenization),
deterministic partial differential equations:
the Boltzmann transport equation and
multiscale problems (homogenization),
mathematical problems arising from applications in nanotechnology and metamaterials such as
stochastic aspects of nanopore senors,
stochastic aspects of nanowire sensors and nanoscale transistors, and
The research questions stem from the intersection of new mathematical problems and timely applications.
I believe that mathematical modeling and numerical simulations are an important contribution to the quantitative understanding of new technologies and their development.