Research interests

Applied Mathematics in the broad sense: Deterministic and Stochastic Partial Differential Equations, Inverse Problems, Probability, Homogenization, Numerical Analysis, with applications to:

Wave propagation in random media, inverse problems and imaging

• Time reversal

• Stochastic partial differential equations, limit theorems (existence/regularity of solutions, asymptotics)

• Multiscale analysis, derivation and numerical simulation of asymptotic models for high frequency wave propagation in random media (e.g. transport and diffusion)

• Applications to inverse problems and imaging (e.g. localization of inclusions in clutter)

Quantum sciences

• Entropy minimization, quantum hydrodynamics

• Analysis of quantum transport models

• Derivation of multiscale numerical schemes

• Applications to nanodevice modeling

Editor for SIAM Multiscale Modeling and Simulation

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Support from the NSF greatly acknowledged.