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I am primarily interested in applied mathematics involving partial differential equations, probability theory, and inverse problems. Right now I'm working on three projects. The first project is wave propagation in random media in the weak-coupling limit (small fluctuations). In this limit, wave energy propagation can be modeled by transport equations--which describe the average energy density. The question is, "is this deterministic equation indeed the correct limit as fluctuation size goes to zero?" The second project involves a combination of deterministic and probabilistic methods in inverse transport. The third involves the use of polynomial chaos expansions to model uncertainty propagation in very-large scale systems. This involves computation at the peta-scale. I am also interested in inverse problems and other applications of partial differential equations, functional analysis, differential geometry, probability, random processes, and statistical inference |