Dr. Kui Ren receives his Ph.D. with distinction from Columbia University in May 2006. His dissertation is entitled “Inverse Problems in Transport and Diffusion Theory with Applications in Optical Tomography”. He was advised by Professor Guillaume Bal of the Applied Mathematics Program within the Department of Applied Physics and Applied Mathematics. Dr. Ren’s area of research is the theoretical and numerical analysis of inverse transport problems. In addition to his work with Prof. Bal, Dr. Ren also worked closely with Prof. Andreas Hielscher in the Department of Biomedical Imaging where Ren learned about and solved important practical problems arising in medical imaging. In 2002, Kui Ren was awarded an Excellent Teaching Assistant Award from the Fu Foundation School or Engineering and Applied Science.

Dr. Ren’s contributions to the theoretical understanding of inverse transport were developed with regards to three important topics: reconstruction of gas concentration profiles in the atmosphere from satellite measurements, a generalized diffusion model that accounts for proton propagation in non-scattering “clear layers” as needed for accurate reconstructions of blood oxygenation in neonates, and a shape differentiation method to address the effect of clear layers on boundary measurements. In these areas, Dr. Ren both formulated the theoretical problem and developed numerical methodologies that showed the adequacy of the inverse solutions. Dr. Ren’s achievements in the application of inverse transport theory to medical imaging included the implementation of two and three dimensional algorithms and PDE-constrained optimization to the reconstruction of optical parameters in small animals.

Dr. Ren received his B.S. in Mathematics from Nanjing University in 1998 and his M.S. from Peking University in 2001 where he received the Proctor and Gamble (P&G) Award for Outstanding Graduate Student. Later in 2001, Ren entered Columbia University as a graduate student in Applied Physics and the following year started his thesis work in under the supervision of Prof. Bal. While at Columbia, Ren was first author on three articles in Optics Letters, Applied Optics, and SIAM J. Sci. Computing, and he was a contributing author on four other papers.

Dr. Ren will continue his research at Columbia University where he presently holds a postdoctoral position and is working in collaboration with Prof. Bal.