Melvin Leok

Melvin Leok is a Professor of Mathematics at the University of California, San Diego (UCSD). He directs the Computational Geometric Mechanics group, affiliated with the Center for Computational Mathematics and the Computational Science, Mathematics, and Engineering (CSME) Program. His research focuses on computational geometric mechanics, combining differential geometry and numerical analysis to develop stable and robust methods for modeling and controlling engineering systems.

Leok holds a Ph.D. in Control and Dynamical Systems from Caltech (2004). Before joining UCSD in 2009, he was an assistant professor at Purdue University and a visiting researcher at Caltech and the University of Michigan. He has received prestigious awards, including the Simons Fellowship, DoD Newton Award, and NSF CAREER Award.

His research interests include numerical differential equations, geometric control theory, and computational methods for interconnected systems. He has authored over 100 publications and serves on editorial boards for journals like Journal of Nonlinear Science. Leok teaches advanced courses such as optimization on manifolds and numerical analysis, emphasizing geometric principles.

Key achievements include co-authoring the monograph Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds, developing variational integrators for mechanical systems, and leading projects in geometric uncertainty propagation and structure-preserving algorithms for plasma physics. He actively collaborates on NSF-funded initiatives like the TILOS AI Research Institute.

Leok advises doctoral students, including Brian Tran, who won the Chancellor's Dissertation Medal. He also mentors postdoctoral researchers through the Alexander von Humboldt Foundation's Feodor Lynen Program.