I am an applied mathematician. My training has been in developing and analyzing numerical methods for approximating solutions of time-dependent nonlinear PDEs. Over the years, I gradually shifted my interests to biological and medical applications. The list below summarizes my research interests. More specific information can be obtained by looking at my publications. Other places you might want to explore are the summaries of selected projects (under construction), the research photo gallery, and the photos of some of the conferences I participated in.
Applications
- Immunology and cancer dynamics (See the webpage of my collaborator Peter Lee, M.D. from the Division of Hematology, Stanford University)
- Radiation oncology (See the webpage of my collaborator Lei Xing from Radiation Oncology, Stanford University)
- Cell Motility (See the webpage of my collaborator Devaki Bhaya from the Department of Plant Biology, Stanford University)
- Environmental and atmospheric sciences
- Computational fluid dynamics
- Signal and image processing
- Nonlinear waves
Numerical Methods for Time-Dependent Problems
- Conservation laws
- Hamilton-Jacobi equations
- Balance laws
- Reaction-diffusion equations
Nonlinear phenomena
- Nonlinear time-dependent partial differential equations
- Hyperbolic conservation laws
- Hamilton-Jacobi equations
- Dispersive equations