Li-Tien Cheng

Li-Tien Cheng is a Professor in the Department of Mathematics at the University of California, San Diego. He obtained his Ph.D. from UCLA in 2000, following earlier MA and BS degrees from the same institution in 1996. His primary affiliation has been with UC San Diego where he maintains an active research program and teaches graduate-level courses in numerical analysis.

His research specializes in mathematical methods for scientific computing, with core expertise in level set methods, numerical partial differential equations, and image processing. These techniques are applied across diverse domains including biomolecular modeling, wave propagation, materials science, and computational geometry. Key application areas include:

• Implicit solvation models for biomolecules
• High-frequency wave propagation and geometric optics
• Dislocation dynamics in materials science
• Visibility optimization in computer vision

Professor Cheng's publications demonstrate consistent methodological innovation in level set techniques from 2001-2009. His most recent work (2007-2009) focuses on biomolecular applications, developing variational implicit solvent approaches for studying hydrophobic interactions and ligand binding. Earlier publications established fundamental algorithms for wavefront propagation, anisotropic media modeling, and materials defect simulations. The research consistently combines theoretical PDE analysis with practical computational implementations.