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My research focuses on inverse problems for partial differential equations, especially problems involving unknown coefficients, source terms, and initial data. The mathematical models I study include elliptic, parabolic, hyperbolic, elasticity, radiative transfer, Hamilton-Jacobi, Maxwell, Navier-Stokes, and nonlinear diffusive coagulation-fragmentation equations. Much of my recent work concerns inverse scattering and related problems, as well as the development of globally convergent numerical methods based on Carleman estimates and time-dimensional reduction techniques.

These inverse problems arise in applications such as medical imaging, geophysical exploration, non-destructive testing, remote sensing, wave propagation, and the detection of hidden or buried objects. My goal is to develop methods that are both mathematically rigorous and computationally effective for recovering unknown information from indirect and noisy data.

I am a co-organizer of the Computational and Applied Mathematics Seminar.