Department of Mathematics,
University of California, Riverside
Dr. Moradifam's research interests include Partial Differential Equations, Inverse Problems, Medical Imaging, and Mathematical Biology. He uses techniques from Mathematical Analysis and PDEs to answer fundamental questions about real life problems. In particular, Dr. Moradifam's research has recently been focused on the analysis of two new medical imaging modalities: Current Density Impedance Imaging (CDII) and photoacoustic tomography. CDII in the inverse problem of recovering the conductivity inside an object from the magnitude of the induced current in the interior. Such interior measurements of interior current could be obtained by Magnetic Resonance Imaging (MRI). In his work on photoacoustic tomography, Dr. Moradifam has been working on simultaneous determination of both the source of a wave and its speed in a medium from the measurements of the solution of the wave equation on the boundary. Dr. Moradifam has also had important contributions to the theory of Elliptic Partial Differential Equations. His breakthrough work on the Sphere Covering Inequality provided a solution to a 30-year old conjecture of A. Change and P. Yang (1987) about Nirenberg's problem on prescribing the Gaussian curvature on the sphere.