Dr. Li studies nonlinear problems and their applications in physics, geometry, and biomedical research. He has worked on new ways to study the conformal scalar curvature equations in differential geometry and Matukuma’s equation in astrophysics. While working on bioluminescence tomography, Li with G. Wang invented the computational optical biopsy modality. Li has also worked in the area of traveling fronts, a fundamental problem related in population dynamics, genetics, and flame propagation. In particular, he solved an open problem left by Berestycki and Nirenberg on the uniqueness and asymptotic behavior of such solutions for a semi-degenerated nonlinearity. He and his co-authors also settled another long-standing open problem on the stability of marginal speed traveling fronts for this semi-degenerated nonlinearity. His work has been published in more than 70 peer-reviewed publications, and supported by NSF and NIH.