# Lie group and homogeneous variational integrators and their applications to geometric optimal control theory

## Melvin Leok

*Abstract*

*Speaker's Bio*

Melvin Leok is a tenured professor of mathematics at the University of California, San Diego, where his research is supported in part by grants from the National Science Foundation in applied and computational mathematics, including a Faculty Early Career Development (CAREER) award. He serves on the editorial boards of the Journal of Nonlinear Science, the SIAM Journal on Control and Optimization, the LMS Journal of Computation and Mathematics, the Journal of Geometric Mechanics, and the Journal of Computational Dynamics.

Prior to joining UCSD, he was a tenure-track assistant professor of mathematics at Purdue University, a visiting assistant professor of control and dynamical systems at the California Institute of Technology, and a T.H. Hildebrandt research assistant professor of mathematics at the University of Michigan, Ann Arbor. At Purdue, he was a nominee for the Packard Fellowship for Science and Engineering, and at Michigan, he received a Horace H. Rackham Faculty Fellowship and Grant, and a Margaret and Herman Sokol Spring/Summer Research Grant.

He received his B.S. with honors and M.S. in Mathematics in 2000, and his Ph.D. in Control and Dynamical Systems with a minor in Applied and Computational Mathematics under the direction of Jerrold Marsden in 2004, all from the California Institute of Technology.

His primary research interests are in computational geometric mechanics, computational geometric control theory, discrete geometry, and structure-preserving numerical schemes, and particularly how these subjects relate to systems with symmetry and multiscale systems.

He was the recipient of the SciCADE New Talent Prize in 2007 for his work on Lie Group and Homogeneous Variational Integrators, and the SIAM Student Paper Prize, and the Leslie Fox Prize (second prize) in Numerical Analysis, both in 2003, for his work on Foundations of Computational Geometric Mechanics. While a doctoral student at Caltech, he held a Poincaré Fellowship (2000-2004), a Josephine de Kármán Fellowship (2003-2004), an International Fellowship from the Agency for Science, Technology, and Research (2002-2004), a Tau Beta Pi Fellowship (2000-2001), and a Tan Kah Kee Foundation Postgraduate Scholarship (2000).

As a Caltech undergraduate, he received the Loke Cheng-Kim Foundation Scholarship (1996-2000), the Carnation Scholarship (1998-2000), the Herbert J. Ryser Scholarship (1999), the E.T. Bell Undergraduate Mathematics Research Prize (1999), and the Jack E. Froehlich Memorial Award (1999).