Melvin Leok Professor of Mathematics Co-Director, CSME Graduate Program University of California, San Diego [ CGM | CCoM | CSME | CCSD | CRI | HDSI | TILOS ] Department of Mathematics University of California, San Diego 9500 Gilman Drive, Dept. 0112 La Jolla, CA 92093-0112, USA. Office: Email: Phone: Fax: APM 5763 mleok@ucsd.edu +1(858)534-2126 +1(858)534-5273

Announcements

• DoD Newton Award for Transformative Ideas during the COVID-19 Pandemic
  Boris Kramer (Assistant Professor of MAE, UCSD) and I have received the Newton Award for Transformative Ideas during the COVID-19 Pandemic from the Department of Defense in support of our work on Geometric Structure-Preserving Model Reduction for Large-Scale Interconnected Systems. The award, named in honor of Sir Isaac Newton’s achievements in mathematics, optics, and gravitation during the Great Plague of London in 1665, sought "transformative ideas" to resolve challenges, advance frontiers, and set new paradigms in research of immense potential benefit to the DOD and the nation at large during the COVID-19 pandemic. We received 2 of the 13 awards, which were selected from the 548 proposals that were submitted. [ UCSD Press Release ]
• Accelerated Merit Advancement to Professor, Step V
  I have received a three-year accelerated merit advancement from Professor, Step III, to Professor, Step V, which took effect July 1, 2019. Accelerations are typically awarded on the basis of unusual achievement and exceptional promise of continued growth. During the four merit reviews I have undergone since arriving at UCSD, I have received a total of three accelerations, and one half-step bonus.
• Monograph published in the Interaction of Mechanics and Mathematics series (Springer)
  Together with N. Harris McClamroch (Michigan) and Taeyoung Lee (George Washington), we have written a monograph entitled, "Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds," which has been published by Springer in the Interaction of Mechanics and Mathematics series.
  [ Publisher's Website | Description | Cover | Front Matter | Sample Chapter | Amazon ]

  Review: "This well-written and expansive book is ambitious in its scope in that it aims at sound and thorough pedagogy as far as its subject matter is concerned, and it also aims at preparing the reader for computational work: note the subtitle, viz., “A geometric approach to modeling and analysis.” In that sense it is a particularly timely book, seeing that we have computing power at our disposal like never before. There are many good examples accompanying or even guiding the text, as well as extensive problem sets for the properly serious student. This book hits its targets square and should prove very valuable to its readership, be they mathematicians, engineers, or physicists."
  Michael Berg, MAA Reviews, November 2017.

  Review: "The starting point of this impressive textbook is the important fact that there are remarkable situations where the variables that describe a dynamical system do not lie in a vector space (i.e., a simple flat algebraic structure) but rather lie in a geometrical setting allowing the differential calculus, namely a differential manifold. ... In conclusion, this book is extremely useful for each reader who wishes to develop a modern knowledge of analytical mechanics."
  Mircea Crâşmăreanu, zbMATH 1381.70005, 2018.

  Review: "This book presents a monograph on foundational geometric principles of Lagrangian and Hamiltonian dynamics and their application in studying important physical systems. ... The emphasis in this book is on global descriptions of Lagrangian and Hamiltonian dynamics, where suitable mathematical tools are available, via global analysis of dynamical properties. This treatment is novel and unique and it is the most important distinction and contribution of this text to the existing literature. Throughout the book numerous examples of Lagrangian and Hamiltonian systems are included, which are especially useful to illustrate the concepts and the way in which the developed theory can be applied in practical situations. ... The book under review succeeds in all its objectives and sets the stage for a treatment of computational issues associated with Lagrangian and Hamiltonian dynamics that evolve on a configuration manifold. It is very clearly written and it will be especially useful both for beginning researchers and for graduate students in applied mathematics, physics, or engineering.
  M. Eugenia Rosado María, AMS Mathematical Reviews, 2018.

• Plenary Talk at Foundations of Computational Mathematics 2017
  I have been invited to give a plenary talk at the Foundations of Computational Mathematics conference to be held in Barcelona, Spain in July 2017. The FoCM conference, held every three years, covers the entire spectrum of mathematical computation. Recently, I also gave plenary talks at the NUMDIFF-14, Numerical treatment of differential and differential-algebraic equations conference in Halle, Germany, and the IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control in Lyon, France.
• Kavli Fellow, National Academy of Sciences
  I have been invited in participate in the German-American Kavli Frontiers of Science symposium, which is jointly organized by the Alexander von Humboldt Foundation and the National Academy of Sciences. The symposium bring together outstanding young scientists to discuss exciting advances and opportunities in a broad range of disciplines. A committee of NAS members selects the participants from among young researchers who have already made recognized contributions to science, including recipients of major fellowships and awards. [ Poster ]
• In Memory of Jerrold E. Marsden (1942-2010)
  On September 21, 2010, my dear advisor, mentor, role model, collaborator, colleague, and friend, Jerry Marsden, lost his battle with cancer. He will be missed and remembered always. [ ICIAM Memorial Events | SIAM News Obituary ]
• Computational Geometric Mechanics at UCSD
  Melvin Leok is a professor of mathematics at the University of California, San Diego, and directs the computational geometric mechanics group, which is affiliated with the Center for Computational Mathematics, the Program in Computational Science, Mathematics, and Engineering, and the Cymer Center for Control Systems and Dynamics.
• Research Vignette on Streaming Video
  Prior to joining UCSD, I was an assistant professor at Purdue University, and the department of mathematics there commissioned a short video vignette where I describe my research in a broadly accessible fashion. This is available as a streaming video.
• NSF CAREER Award DMS-0747659
  I received a National Science Foundation Faculty Early Career Development (CAREER) Award in support of my work on Computational Geometric Mechanics: Foundations, Computation, and Applications. This is funded by the Applied Mathematics Program of the Division of Mathematical Sciences. [ Purdue University News Service Release | Inside Purdue, Pages 8-9 | Notices of the AMS, Pages 269-270 ]
• SciCADE New Talent Prize
  I was awarded the SciCADE New Talent Prize, in recognition of my work on Lie group variational integrators and their applications to optimal control, and gave a plenary lecture at the SciCADE 2007 International Conference on Scientific Computation and Differential Equations, in Saint-Malo, France. This prize recognizes the best paper submitted by a candidate under the age of 35, within 4 years of the Ph.D.

Research Opportunities

• Academic and Industrial, Science and Engineering Collaborations and Consulting Opportunities Welcomed
  I am constantly on the lookout for interesting and challenging collaborations with scientists and engineers from academia or industry. I am also available as a consultant for modeling, simulating, controlling, and quantifying uncertainty for systems that evolve on complicated nonlinear configuration spaces. Have a look at my YouTube channel for examples of applications, and if you would like to learn more about the role that geometric numerical methods might play in your application, please feel free to contact me.
  Much of my theoretical work is motivated by specific applications. To paraphrase William Morris, "Have nothing in your [mathematics] that you do not know to be useful, or believe to be beautiful."

• Graduate Positions Available in the Computational Geometric Mechanics group
  Research positions for graduate students are available in the broad area of geometric numerical methods in geometric mechanics and control. A description of my current research may be found in my research statement, bibliography, collected publications, or the abstracts below. These positions are funded by the following research grants from the National Science Foundation in applied and computational mathematics and engineering:
  • DMS-1813635, Geometric Numerical Integration of Plasma Physics and General Relativity, 2018-2021.
  • DMS-1345013, RTG: An Interdisciplinary Research Training Program in Applied Mathematics, Computational Science, and Mathematical Physics, 2014-2019.
  • DMS-1411792, Geometric Numerical Discretizations of Gauge Field Theories and Interconnected Systems, 2014-2019.
  • CMMI-1334759, Ergodic Trajectories in Discrete Mechanics, 2013-2017.
  • DMS-1065972, FRG: Error Quantification and Control for Gravitational Waveform Simulation, 2011-2015.
  • CMMI-1029445, Computational Geometric Uncertainty Propagation for Hamiltonian Systems on a Lie Group, 2010-2014.
  • DMS-1010687, CAREER: Computational Geometric Mechanics: Foundations, Computation, and Applications, 2008-2015 (transferred from DMS-0747659).
  • DMS-1001521, LTB: Generalized Variational Integrators for Large-Scale Scientific Computation, 2007-2011 (transferred from DMS-0714223).
  • DMS-0726263, Computational Geometric Mechanics and its Applications to Geometric Control Theory, 2005-2009 (transferred from DMS-0504747).
  Please contact me by email if you are interested in any of these positions. These are full-time positions, and students who are interested in internship opportunities should read my policy on internships.
• Hosting of Fedor Lynen Research Fellows of the Alexander von Humboldt Foundation
  As an alumni of the German-American Frontiers of Science symposium, I am able to host research stays for Feodor Lynen Research Fellows of the Alexander von Humboldt Foundation. This supports post-doctoral researchers (up to four years after completing a doctorate) for 6 to 24 months, and experienced researchers (up to 12 years after completing a doctorate) for 6 to 18 months, divisible into a maximum of three visits over three years.

Teaching

• Fall 2021, MATH 174/274, Numerical Methods for Physical Modeling [ Online Lectures ]
• Spring 2021, MATH 170C, Introduction to Numerical Analysis: Ordinary Differential Equations [ Online Lectures ]
• Spring 2021, MATH 273C, Geometric Numerical Integration [ Online Lectures ]
• Winter 2021, MATH 273B, Optimization on Manifolds [ Online Lectures ]
• Fall 2020, MATH 273A, Applied and Computational Topology [ Online Lectures ]
• Spring 2020, MATH 270C, Numerical Ordinary Differential Equations [ Online Lectures ]
• Spring 2020, MATH 273C, Geometric Numerical Integration [ Online Lectures ]
• Previous courses

Research Interests

• Computational Geometric Mechanics: Applying discrete differential geometry and discrete Lagrangian and Hamiltonian mechanics to the construction of geometric structure-preserving numerical algorithms.
• Computational Geometric Control Theory: Construction of real-time digital feedback control of mechanical systems using techniques from geometric control theory and computational geometric mechanics.
• Numerical Analysis: Derivation of accurate and efficient numerical schemes with good long-time geometric stability properties by combining geometric integration with adaptive, spectral, and multiscale techniques.

Selected Honors

• Plenary, Foundations of Computational Mathematics, Barcelona, Spain, 2017.
• Kavli Frontiers of Science Fellow, National Academy of Sciences, 2012, 2014, 2016.
• Plenary, NUMDIFF-14, Halle, Germany, 2015.
• Plenary, IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Lyon, France, 2015.
• National Science Foundation Faculty Early Career Development (CAREER) Award, DMS-0747659, 2008-2013.
• SciCADE New Talent Award, International Conference on Scientific Computation and Differential Equations, 2007.
• SIAM Student Paper Prize, Society for Industrial and Applied Mathematics, 2003.
• Leslie Fox Prize in Numerical Analysis (second prize), Institute of Mathematics and its Applications, UK, 2003.
• Josephine de Kármán Fellowship (established by Theodore von Kármán), 2003-2004.
• International Fellowship, Agency for Science, Technology, and Research, Singapore, 2002-2004.
• Poincaré Fellowship (Betty and Gordon Moore Fellowship), Caltech, 2000-2004.
• Tau Beta Pi Fellowship, Tau Beta Pi, National Engineering Honor Society, 2000-2001.
• Tan Kah Kee Foundation Postgraduate Scholarship, Singapore, 2000.

Editorial Boards

• Journal of Nonlinear Science (Springer).
• Journal of Geometric Mechanics (American Institute of Mathematical Sciences).
• Journal of Computational Dynamics (American Institute of Mathematical Sciences).

Thesis

• Foundations of Computational Geometric Mechanics, Control and Dynamical Systems, California Institute of Technology, 2004.
  A preliminary version of this thesis received the SIAM Student Paper Prize, and the Leslie Fox Prize in Numerical Analysis (second prize).
  [ Abstract | PDF ]

Publications and Preprints (search the ArXiv, AMS MathSciNet) [ BibTeX ]

1. Discrete Poincaré Lemma (with M. Desbrun, and J.E. Marsden), Appl. Numer. Math. 53 (2-4), 231-248, 2005.
   [ PDF | Journal Link | BibTeX ]
2. A Lie Group Variational Integrator for the Attitude Dynamics of a Rigid Body with Applications to the 3D Pendulum (with T. Lee, and N.H. McClamroch), Proc. IEEE Conf. on Control Applications, 962-967, 2005.
   [ PDF | IEEE Xplore | BibTeX | Animation: Chaotic Motion ]
3. Controlled Lagrangians and Stabilization of the Discrete Cart-Pendulum System (with A.M. Bloch, J.E. Marsden, and D.V. Zenkov), Proc. IEEE Conf. on Decision and Control, 6579-6584, 2005.
   [ PDF | IEEE Xplore | BibTeX ]
4. Discrete Routh Reduction (with S.M. Jalnapurkar, J.E. Marsden, and M. West), J. Phys. A: Math. Gen. 39, 5521-5544 (Geometric Integration special issue, invited paper), 2006.
   [ PDF | arXiv:math.NA/0508330 | Journal Link | BibTeX ]
5. Attitude Maneuvers of a Rigid Spacecraft in a Circular Orbit (with T. Lee, and N.H. McClamroch), Proc. American Control Conf., 1742-1747, 2006.
   [ PDF | arXiv:math.OC/0509299 | IEEE Xplore | BibTeX | Animation: Fig2(a), Fig2(b), Fig2(c), Fig3(a) ]
6. Polyhedral Potential and Lie Group Variational Integrator Computations for the Full Two Body Problem (with E. Fahnestock, T. Lee, N.H. McClamroch, D.J. Scheeres), Proc. AIAA/AAS Astrodynamics Specialist Conf., AIAA-2006-6289, 2006.
   [ PDF | arXiv:math.NA/0608695 | Journal Link | BibTeX ]
7. Optimal Control of a Rigid Body using Geometrically Exact Computations on SE(3) (with T. Lee, and N.H. McClamroch), Proc. IEEE Conf. on Decision and Control, 2710-2715, 2006.
   [ PDF | arXiv:math.OC/0602588 | IEEE Xplore | BibTeX | Animation: Fig1(a), Fig2(a), Fig3(a), Fig4(a) ]
8. Deterministic Global Attitude Estimation (with T. Lee, A.K. Sanyal, and N.H. McClamroch), Proc. IEEE Conf. on Decision and Control, 3174-3179, 2006.
   [ PDF | arXiv:math.OC/0602589 | IEEE Xplore | BibTeX ]
9. Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems (with A.M. Bloch, J.E. Marsden, and D.V. Zenkov), Proc. IEEE Conf. on Decision and Control, 3333-3338, 2006.
   [ PDF | arXiv:math.OC/0602590 | IEEE Xplore | BibTeX ]
10. A Discrete Variational Integrator for Optimal Control Problems in SO(3) (with A.M. Bloch, I.I. Hussein, and A.K. Sanyal), Proc. IEEE Conf. on Decision and Control, 6636-6641, 2006.
    [ PDF | arXiv:math.OC/0509536 | IEEE Xplore | BibTeX ]
11. Global Attitude Estimation using Single Direction Measurements (with T. Lee, N.H. McClamroch, and A.K. Sanyal), Proc. American Control Conf., 3659-3664, 2007.
    [ PDF | arXiv:math.OC/0609481 | IEEE Xplore | BibTeX ]
12. Optimal Attitude Control for a Rigid Body with Symmetry (with T. Lee, and N.H. McClamroch), Proc. American Control Conf., 1073-1078, 2007.
    [ PDF | arXiv:math.OC/0609482 | IEEE Xplore | BibTeX | Animation: Fig2(a), Fig3(a), Fig4(a), Fig5(a) ]
13. Lie Group Variational Integrators for the Full Body Problem, (with T. Lee, and N.H. McClamroch), Comput. Methods Appl. Mech. Engrg. 196(29-30), 2907-2924, 2007.
    [ PDF | arXiv:math.NA/0508365 | Journal Link | BibTeX | Animation: Fig4 ]
14. Lie Group Variational Integrators for the Full Body Problem in Orbital Mechanics (with T. Lee, and N.H. McClamroch), Celestial Mechanics and Dynamical Astronomy 98(2), 121-144, 2007.
    [ PDF | Journal Link | BibTeX | Animation: Fig2 ]
15. Propagation of Uncertainty Sets for Rigid Body Attitude Flows (with N.A. Chaturvedi, T. Lee, N.H. McClamroch, and A.K. Sanyal), Proc. IEEE Conf. on Decision and Control, 2689-2694, 2007.
    [ PDF | arXiv:math.DS/0702737 | IEEE Xplore | BibTeX ]
16. A Combinatorial Optimal Control Problem for Spacecraft Formation Reconfiguration (with T. Lee, and N.H. McClamroch), Proc. IEEE Conf. on Decision and Control, 5370-5375, 2007.
    [ PDF | arXiv:math.OC/0702738 | IEEE Xplore | BibTeX | Animation: Fig2 ]
17. Global Optimal Attitude Estimation using Uncertainty Ellipsoids (with A.K. Sanyal, T. Lee, and N.H. McClamroch), Systems and Control Letters, 57(3), 236-245, 2008.
    [ PDF | arXiv:math.OC/0606083 | Journal Link | BibTeX ]
18. Time Optimal Attitude Control for a Rigid Body (with T. Lee, and N.H. McClamroch), Proc. American Control Conf., 5210-5215, 2008.
    [ PDF | arXiv:0709.2514 | IEEE Xplore | BibTeX | Animation: Fig1(a), Fig2(a) ]
19. Matching and stabilization of discrete mechanical systems (with A.M. Bloch, J.E. Marsden, and D.V. Zenkov), Proc. Appl. Math. Mech., 7, 1030603-1030604, 2007.
    [ PDF | Journal Link | BibTeX ]
20. Optimal Attitude Control of a Rigid Body using Geometrically Exact Computations on SO(3) (with T. Lee, and N.H. McClamroch), Journal of Dynamical and Control Systems, 14(4), 465-487, 2008.
    [ PDF | arXiv:math.OC/0601424 | Journal Link | BibTeX | Animation: Fig2(a), Fig3(a), Fig4(a), Fig5(a) ]
21. Global Symplectic Uncertainty Propagation on SO(3) (with T. Lee, and N.H. McClamroch), Proc. IEEE Conf. on Decision and Control, 61-66, 2008.
    [ PDF | arXiv:0803.1515 | IEEE Xplore | BibTeX ]
22. Discrete Control Systems (with T. Lee, and N.H. McClamroch), invited article for Springer Encyclopedia of Complexity and System Science, 2002-2019, 2009.
    [ PDF | arXiv:0705.3868 | Journal Link | BibTeX ]
23. Geometric Structure-Preserving Optimal Control of the Rigid Body (with A.M. Bloch, I.I. Hussein, and A.K. Sanyal), Journal of Dynamical and Control Systems, 15(3), 307-330, 2009.
    [ PDF | arXiv:0712.4400 | Journal Link | BibTeX ]
24. Lagrangian Mechanics and Variational Integrators on Two-Spheres (with T. Lee, and N.H. McClamroch), International Journal for Numerical Methods in Engineering, 79(9), 1147-1174, 2009.
    [ PDF | arXiv:0707.0022 | Journal Link | BibTeX | Animation: Fig3.1, Fig3.2, Fig3.3, Fig3.4, Fig3.5, Fig3.6, Fig3.7 ]
25. Computational Geometric Optimal Control of Rigid Bodies (with T. Lee, and N.H. McClamroch), Brockett Legacy Special Issue, Communications in Information and Systems, 8(4), 445-472, 2008.
    [ PDF | arXiv:0805.0639 | Journal Link | BibTeX ]
26. Dynamics of Connected Rigid Bodies in a Perfect Fluid (with T. Lee, and N.H. McClamroch), Proc. American Control Conf., 408-413, 2009.
    [ PDF | arXiv:0809.1488 | IEEE Xplore | BibTeX | Animation: Fig1 ]
27. Controlled Lagrangians and Stabilization of Discrete Mechanical Systems (with A.M. Bloch, J.E. Marsden, and D.V. Zenkov), Discrete and Continuous Dynamical Systems - Series S, 3(1), 19-36, 2010.
    [ PDF | arXiv:0704.3875 | Journal Link | BibTeX ]
28. Nonlinear Dynamics of the 3D Pendulum (with N.A. Chaturvedi, T. Lee, and N.H. McClamroch), Journal of Nonlinear Science, 21(1), 3-32, 2011.
    [ PDF | arXiv:0707.1196 | Journal Link | BibTeX ]
29. Variational and Geometric Structures of Discrete Dirac Mechanics (with T. Ohsawa), Foundations of Computational Mathematics, 11(5), 529-562, 2011.
    [ PDF | arXiv:0810.0740 | Journal Link | BibTeX ]
30. Dynamics of a 3D Elastic String Pendulum (with T. Lee and N.H. McClamroch), Proc. IEEE Conf. on Decision and Control, 3347-3352, 2009.
    [ PDF | arXiv:0903.0332 | IEEE Xplore | BibTeX | Animation: Fig2 ]
31. Computational Dynamics of a 3D Elastic String Pendulum Attached to a Rigid Body and an Inertially Fixed Reel Mechanism (with T. Lee, N.H. McClamroch), Nonlinear Dynamics, 64(1-2), 97-115, 2011.
    [ PDF | arXiv:0909.2083 | Journal Link | BibTeX | Animation: Fig2(a), Fig3(a), Fig4(a) ]
32. Computational Geometric Optimal Control of Connected Rigid Bodies in a Perfect Fluid (with T. Lee, N.H. McClamroch), Proc. American Control Conf., 5985-5990, 2010.
    [ PDF | arXiv:0909.3871 | BibTeX | Animation: Fig2(a), Fig3(a) ]
33. Discrete Hamilton-Jacobi Theory (with A.M. Bloch, T. Ohsawa), SIAM Journal on Control and Optimization, 49(4), 1829-1856, 2011.
    [ PDF | arXiv:0911.2258 | Journal Link | BibTeX ]
34. Discrete Hamiltonian Variational Integrators (with J. Zhang), IMA Journal of Numerical Analysis, 31(4), 1497-1532, 2011.
    [ PDF | arXiv:1001.1408 | Journal Link | BibTeX ]
35. Geometric Tracking Control of a Quadrotor UAV on SE(3) (with T. Lee, N.H. McClamroch), Proc. IEEE Conf. on Decision and Control, 5420-5425, 2010.
    [ PDF | arXiv:1003.2005 | IEEE Xplore | BibTeX ]
36. Discrete Hamilton-Jacobi Theory and Discrete Optimal Control (with T. Ohsawa, A.M. Bloch), Proc. IEEE Conf. on Decision and Control, 5438-5443, 2010.
    [ PDF | IEEE Xplore | BibTeX ]
37. Stokes-Dirac Structures through Reduction of Infinite-Dimensional Dirac Structures (with J. Vankerschaver, H. Yoshimura, J.E. Marsden), Proc. IEEE Conf. on Decision and Control, 6265-6270, 2010.
    [ PDF | arXiv:1010.2547 | IEEE Xplore | BibTeX ]
38. Discrete Dirac Structures and Implicit Discrete Lagrangian and Hamiltonian Systems (with T. Ohsawa), XVIII International Fall Workshop on Geometry and Physics, 91-102, AIP Conference Proceedings 1260, 2010.
    [ PDF | Journal Link | BibTeX ]
39. Geometric Numerical Integration of Complex Dynamics of Tethered Spacecraft (with T. Lee, N. H. McClamroch), Proc. American Control Conf., 1885-1891, 2011.
    [ PDF | arXiv:1010.1724 | BibTeX ]
40. Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3) (with T. Lee, N. H. McClamroch), Asian Journal of Control, 15(3), 1-18, 2013,
    [ PDF | Journal Link | BibTeX ]
41. Prolongation-Collocation Variational Integrators (with T. Shingel), IMA Journal of Numerical Analysis, 32(3), 1194-1216, 2012.
    [ PDF | arXiv:1101.1995 | Journal Link | BibTeX ]
42. On the Geometry of Multi-Dirac Structures and Gerstenhaber Algebras (with J. Vankerschaver, H. Yoshimura), Journal of Geometry and Physics, 61(8), 1415-1425, 2011. 2011.
    [ PDF | arXiv:1102.2835 | Journal Link | BibTeX ]
43. General Techniques for Constructing Variational Integrators (with T. Shingel), Frontiers of Mathematics in China (Special issue on computational mathematics, invited paper), 7(2), 273-303, 2012.
    [ PDF | arXiv:1102.2685 | Journal Link | BibTeX ]
44. Stable Manifolds of Saddle Points for Pendulum Dynamics on S² and SO(3) (with T. Lee, N.H. McClamroch), Proc. IEEE Conf. on Decision and Control, 3915-3921, 2011.
    [ PDF | arXiv:1103.2822 | BibTeX ]
45. Variational Integrators, invited article for Springer Encyclopedia of Applied and Computational Mathematics, 1519-1525, 2015.
    [ PDF | BibTeX ]
46. The Hamilton-Pontryagin Principle and Multi-Dirac Structures for Classical Field Theories (with J. Vankerschaver, H. Yoshimura), Journal of Mathematical Physics, 53(7), 072903 (25 pages), 2012.
    [ PDF | arXiv:1207.2814 | Journal Link | BibTeX ]
47. Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3) (with T. Lee, N.H. McClamroch), Proc. American Control Conf., 4649-4654, 2012.
    [ PDF | arXiv:1109.4457 | BibTeX ]
48. Hamilton--Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints (with T. Ohsawa, D. Sosa), Journal of Mathematical Physics, 53(7), 072905 (29 pages), 2012.
    [ PDF | arXiv:1109.6056 | Journal Link | BibTeX ]
49. Generating Functionals and Lagrangian PDEs (with C. Liao, J. Vankerschaver), Journal of Mathematical Physics, 54(8), 082901 (22 pages), 2013.
    [ PDF | arXiv:1111.0280 | Journal Link | BibTeX ]
50. Dynamics and Control of a Chain Pendulum on a Cart (with T. Lee and N. H. McClamroch), Proc. IEEE Conf. on Decision and Control, 2502-2508, 2012.
    [ PDF | arXiv:1211.4604 | BibTeX ]
51. Hamel's Formalism and Variational Integrators on a Sphere (with A.M. Bloch, and D.V. Zenkov), Proc. IEEE Conf. on Decision and Control, 7504-7510, 2012.
    [ PDF | arXiv:1211.4607 | BibTeX ]
52. High-Fidelity Numerical Simulation of Complex Dynamics of Tethered Spacecraft (with T. Lee, and N.H. McClamroch), Acta Astronautica, 99, 215-230, 2014.
    [ PDF | arXiv | Journal Link | BibTeX ]
53. Dirac Structures and Hamilton-Jacobi Theory for Lagrangian Mechanics on Lie Algebroids (with D. Sosa), Journal of Geometric Mechanics, 4(4), 421-442, 2012.
    [ PDF | arXiv:1211.4561 | BibTeX ]
54. A novel formulation of point vortex dynamics on the sphere: geometrical and numerical aspects (with J. Vankerschaver), Journal of Nonlinear Science, 24(1), 1-37, 2014.
    [ PDF | arXiv:1211.4560 | Journal Link | BibTeX ]
55. Spectral Variational Integrators (with J. Hall), Numerische Mathematik, 130 (4), 681-740, 2015.
    [ PDF | arXiv:1211.4534 | Journal Link | BibTeX ]
56. Symplectic Semiclassical Wave Packet Dynamics (with T. Ohsawa), Journal of Physica A, 46(40), 405201 (28 pages), 2013.
    [ PDF | arXiv:1302.1139 | Journal Link | BibTeX ]
57. Coordinate-free Formulation for Dynamics and Control of a Chain Pendulum on a Cart (with T. Lee, and N.H. McClamroch), under revision, 2013.
    [ PDF | BibTeX ]
58. Lie Group Spectral Variational Integrators (with J. Hall), Foundations of Computational Mathematics, 17(1), 199-257, 2017.
    [ PDF | arXiv:1402.3327 | Journal Link | BibTeX ]
59. Geometric Representations of Whitney Forms and their Generalization to Minkowski Spacetime (with J. Salamon, and J. Moody), under revision, 2014.
    [ PDF | arXiv:1402.7109 | BibTeX ]
60. Space-Time Finite-Element Exterior Calculus and Variational Discretizations of Gauge Field Theories (with J. Salamon, and J. Moody), Proc. Mathematical Theory of Networks and Systems, 743-747, 2014.
    [ PDF | BibTeX ]
61. A Novel Variational Formulation for Thermoelastic Problems (with Z. Ebrahimzadeh, and M. Mahzoon), Communications in Nonlinear Science and Numerical Simulation, 22 (1-3), 263-268, 2015.
    [ PDF | Journal Link | BibTeX ]
62. Global Formulations of Lagrangian and Hamiltonian Mechanics on Two-Spheres (with T. Lee, and N.H. McClamroch), Proc. IEEE Conf. Decision and Control, 6010-6015, 2015.
    [ PDF | arXiv:1503.02620 | IEEE Xplore | BibTeX ]
63. Global Formulations of Lagrangian and Hamiltonian Dynamics on Embedded Manifolds (with T. Lee, and N.H. McClamroch), Proc. IMA Conf. on Mathematics of Robotics, 2015.
    [ PDF | BibTeX ]
64. Geometric formulations of Furuta pendulum control problems (with T. Lee, and N.H. McClamroch), Mathematics in Engineering, Science and Aerospace, 7(1), 69-81, 2016.
    [ PDF | Journal Link | BibTeX ]
65. Spectral-Collocation Variational Integrators (with Y. Li, and B. Wu), Journal of Computational Physics, 332, 83-98, 2017.
    [ PDF | Journal Link | BibTeX ]
66. Spectral variational integrators for semi-discrete Hamiltonian wave equations (with Y. Li, and B. Wu), Journal of Computational and Applied Mathematics, 325, 56-73, 2017.
    [ PDF | Journal Link | BibTeX ]
67. Lagrangian and Hamiltonian Taylor Variational Integrators (with J.M. Schmitt, and T. Shingel), BIT Numerical Mathematics, 58(2), 457-488, 2018.
    [ PDF | arXiv:1703.06599 | Journal Link | BibTeX ]
68. Variational integrators for interconnected Lagrange-Dirac systems (with H. Parks), Journal of Nonlinear Science, 27(5), 1399-1434, 2017.
    [ PDF | arXiv:1603.01554 | Journal Link | BibTeX ]
69. Interpolation on Symmetric Spaces via the Generalized Polar Decomposition (with E.S. Gawlik), Foundations of Computational Mathematics, 18(3), 757-788, 2018.
    [ PDF | arXiv:1605.06666 | Journal Link | BibTeX ]
70. Iterative Computation of the Frechet Derivative of the Polar Decomposition (with E.S. Gawlik), SIAM Journal on Matrix Analysis and Applications, 38(4), 1354-1379, 2017.
    [ PDF | arXiv:1608.04491 | Journal Link | BibTeX ]
71. Embedding-Based Interpolation on the Special Orthogonal Group (with E.S. Gawlik), SIAM Journal on Scientific Computing, 40(2), A721-A746, 2018.
    [ PDF | arXiv:1608.05738 | Journal Link | BibTeX ]
72. Properties of Hamiltonian Variational Integrators (with J.M. Schmitt), IMA Journal of Numerical Analysis, 38, 377-398, 2018.
    [ PDF | Journal Link | BibTeX ]
73. Geometric Exponential Integrators (with X. Shen), Journal of Computational Physics, 382, 27-42, 2019.
    [ PDF | arXiv:1703.00929 | Journal Link | BibTeX ]
74. Constructing Equivalence-Preserving Dirac Variational Integrators with Forces (with H. Parks), IMA Journal of Numerical Analysis, 39(4), 1706-1726, 2019.
    [ PDF | arXiv:1703.03045 | Journal Link | BibTeX ]
75. Lie Group Variational Integrators for Rigid Body Dynamics using Quaternions (with X. Shen), Journal of Computational Physics, submitted, 2019.
    [ PDF | arXiv:1705.04404 | BibTeX ]
76. High-Order Retractions on Matrix Manifolds using Projected Polynomials (with E.S. Gawlik), SIAM Journal on Matrix Analysis and Applications, 39(2), 801-828, 2018.
    [ PDF | arXiv:1705.05554 | Journal Link | BibTeX ]
77. Connecting Information Geometry and Geometric Mechanics (with J. Zhang), Entropy (Special Issue on Information Geometry II), 19(10), 518 (31 pages), 2017.
    [ PDF | Journal Link | BibTeX ]
78. Construction and comparison of multidimensional spectral variational integrators and spectral collocation methods (with Y. Li, and B. Wu), Applied Numerical Mathematics, 132, 35-50, 2018.
    [ PDF | Journal Link | BibTeX ]
79. An Empirical Chaos Expansion Method for Uncertainty Quantification (with G. Wilkins), International Journal of Numerical Methods in Engineering, submitted, 2019.
    [ PDF | BibTeX ]
80. Variational Discretizations of Gauge Field Theories using Group-equivariant Interpolation, Foundations of Computational Mathematics, 19(5), 965-989, 2019.
    [ PDF | Journal Link | BibTeX ]
81. Geometric Symmetry Reduction of the Unobservable Subspace for Kalman Filtering (with X. Shen), International Journal of Robotics Research, submitted, 2019.
    [ PDF | arXiv:1901.03474 | BibTeX ]
82. Adaptive Hamiltonian Variational Integrators and Symplectic Accelerated Optimization (with V. Duruisseaux, J. Schmitt), SIAM Journal on Scientific Computing, 43(4), A2949-A2980 (32 pages), 2021.
    [ PDF | arXiv:1709.01975 | Journal Link | BibTeX ]
83. A Variational Formulation of Accelerated Optimization on Riemannian Manifolds (with V. Duruisseaux), SIAM Journal on Mathematics of Data Science, submitted, 2021.
    [ PDF | arXiv:2101.06552 | BibTeX ]
84. Multisymplectic Hamiltonian Variational Integrators (with B. Tran), International Journal of Computer Mathematics (Special Issue on Geometric Numerical Integration, Twenty-Five Years Later), submitted, 2021.
    [ PDF | arXiv:2101.07536 | BibTeX ]
85. Variational Structures in Cochain Projection Based Variational Discretizations of Lagrangian PDEs (with B. Tran), Foundations of Computational Mathematics, submitted, 2021.
    [ PDF | arXiv:2103.09338 | BibTeX ]
86. Accelerated Optimization on Riemannian Manifolds via Discrete Constrained Variational Integrators (with V. Duruisseaux), Journal of Nonlinear Science, submitted, 2021.
    [ PDF | arXiv:2104.07176 | BibTeX ]
87. Variational Symplectic Accelerated Optimization on Lie Groups (with T. Lee and M. Tao), Proc. IEEE Conf. Decision and Control, accepted, 2021.
    [ PDF | arXiv:2103.14166 | BibTeX ]
88. Generalized Galerkin Variational Integrators, preprint, 2004.
    [ PDF | arXiv:math.NA/0508360 | BibTeX ]
89. A Discrete Theory of Connections on Principal Bundles (with J.E. Marsden, and A.D. Weinstein), preprint, 2004.
    [ PDF | arXiv:math.DG/0508338 | BibTeX ]
90. Discrete Exterior Calculus (with M. Desbrun, A.N. Hirani, and J.E. Marsden), preprint, 2003.
    [ PDF | arXiv:math.DG/0508341 | BibTeX ]
91. Estimating the Attractor Dimension of the Equatorial Weather System, Acta Phys. Pol. A 85, S27-S35, 1994.
    [ PDF | Journal Link | BibTeX ]

Upcoming and Recent Invited Presentations

• Center for Computational Mathematics, Flatiron Institute, New York, NY, November 2019.
• Applied Mathematics Seminar, University of California, Riverside, CA, October 2019.
• Applied Mathematics Seminar, University of Warwick, Coventry, UK, October 2019.
• Structure Preservation and General Relativity, Newton Institute, Cambridge, UK, September 30-October 4, 2019.
• Keynote, Meeting of the Society for Natural Philosophy, Chicago, IL, September 13-15, 2019.
• Geometric Numerical Integration of Differential Equations, Beijing, China, September 9-13, 2019.
• Program Seminar, Newton Institute, Cambridge, UK, July 2019.
• Geometric Mechanics Seminar, Imperial College, London, UK, July 2019.
• Control Seminar, University of Cambridge, Cambridge, UK, July 2019.
• Control Seminar, University of Oxford, Oxford, UK, July 2019.
• Geometric Mechanics and Robotics, SIAM Dynamical Systems, Snowbird, UT, May 2019.
• Computational and Applied Mathematics Colloqium, University of Chicago, IL, April 2019.
• Geometric Approaches to Mechanics and Control, AMS Sectional Meeting, Honolulu, HI, March 2019.
• Numerical Methods for Partial Differential Equations, AMS Sectional Meeting, Honolulu, HI, March 2019.
• Computational Challenges in Gravitational Wave Astronomy, IPAM, Los Angles, CA, January 28-February 1, 2019.
• Mathematics Colloquium, Nanyang Technological University, Singapore, December 2018.
• Applied and Computational Mathematics Seminar, National University of Singapore, Singapore, December 2018.
• Geometric Mechanics, AMS Fall Central Sectional Meeting, Ann Arbor, MI, October 2018.
• Hamiltonian Systems, from Topology to Applications through Analysis I, MSRI, Berkeley, CA, October 8-12, 2018.
• Lunch with Hamilton Seminar, MSRI, Berkeley, CA, September 2018.
• RobertFest (in honor of Robert Littlejohn), Berkeley, CA, August 17-19, 2018.
• Institute of Computational Mathematics Seminar, Chinese Academy of Sciences, Beijing, China, July 2018.
• Geometric Mechanics and Control, Beijing, China, July 24-26, 2018.
• Numerical Analysis of Complex PDE Models, Ewin Schrodinger Institute, Vienna, Austria, June 11-15, 2018.
• Nonlinear Data: Theory and Algorithms, Oberwolfach, Germany, April 22-28, 2018.
• Workshop on General Relativity and Finite Element Exterior Calculus, UCSD, La Jolla, CA, January 2018.
• MS2Discovery Seminar, Wilfrid Laurier University, Waterloo, Canada, September 2017.
• Plenary talk, Foundations of Computational Mathematics, Barcelona, Spain, July 10-19, 2017.
• Dynamical Systems and Geometric Mechanics, An International Conference in Honor of Juergen Scheurle, Munich, Germany, June 12-14, 2017.
• Variational Principles in Mechanics, SIAM Dynamical Systems, Snowbird, UT, May 2017.
• Applied Mathematics Seminar, University of California, Irvine, CA, May 2017.
• Special Seminar, North Carolina State University, Raleigh, NC, January 2017.
• Mathematics Colloquium, TU Munich, Munich, Germany, Dec 2016.
• Geometric Algorithms and Methods for Plasma Physics Workshop, Max-Planck Institute for Plasma Physics, Munich, Germany, Sep 2016.
• Mathematics of Shapes and Applications, Institute for Mathematical Sciences, NUS, Singapore, Jul 2016.
• Geometric Methods in Mechanics and Control with Applications, Canadian Mathematical Society Summer Meeting, Edmonton, Canada, Jun 2016.
• Applied Mathematics Seminar, University of Wisconsin, Madison, Oct 2015.
• Discretization in Geometry and Dynamics, Lake Ammersee, Germany, Oct 2015.
• Mathematics Colloquium, University of Arizona, Tucson, AZ, Sep 2015.
• Plenary speaker, NUMDIFF-14, Numerical treatment of differential and differential-algebraic equations, Halle, Germany, Sep 2015.
• Plenary speaker, IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Lyon, France, Jul 2015.
• Joint STAMP-GMC Meeting, Miraflores de la Sierra, Madrid, Spain, Jun 2015.
• Integrability in Mechanics and Geometry: Theory and Computations, ICERM, Providence, RI, Jun 2015.
• Advanced Numerical Methods in the Mathematical Sciences, Texas A&M University, College Station, TX, May 2015.
• Mathematics Seminar, Rutgers University, Camden, NJ, Apr 2015.
• Geometries Defined by Differential Forms, Joint Mathematics Meetings, San Antonio, TX, Jan 2015.
• Semi-Plenary speaker, Geometric integration and computational mechanics workshop, FoCM, Montevideo, Uruguay. Dec 2014.
• Center for Control, Dynamical Systems, and Computations Seminar, UC Santa Barbara, CA, Nov 2014.
• Mathematics Colloquium, Louisiana State University, Baton Rouge, LA, May 2014.
• Computational Science Colloquium, San Diego State University, San Diego, CA, Jan 2014.
• Conference on Numerical Analysis and Scientific Computing, MPI Leipzig, Germany, Jan 2014.
• Discrete Curvatures, CIRM, Luminy, France, Nov 2013.
• Modern Applications of Homology and Cohomology, IMA, Minneapolis, MN, Oct 2013.
• Geometry and Topology in Control, Allerton Conference, Monticello, IL, Oct 2013.
• Variational Techniques in Structure-Preserving Methods for PDEs, SciCADE, Valladolid, Spain, Sep 2013.
• Mathematics Colloquium, Johann Bernoulli Institute, University of Groningen, Netherlands, Sep 2013.
• Topics in Numerical Analysis for Differential Equations, ICMAT, Madrid, Spain, Jul 2013.
• Smooth and Discrete Geometrical Approaches to Control, SIAM Controls, San Diego, CA, Jul 2013.
• Variational Principles, SIAM Dynamical Systems, Snowbird, UT, May 2013.
• Geometric Approximation, Approximation Theory 14, San Antonio, TX, Apr 2013.
• Special seminar, Rutgers University, Piscataway, NJ, Feb 2013.
• IRSES Meeting on DIfferential Geometry and Mechanics, Ghent, Belgium, Jan 2013.
• Geometric methods in mechanical and dynamical systems special session, AMS Fall Western Section Meeting, Tucson, AZ, Oct 2012.
• Structured Matrix Computations in Non-Euclidean Geometries: Algorithms and Applications, CIRM, Luminy, France, Oct 2012.
• Geometry, Symmetry, Dynamics, and Control: The Legacy of Jerry Marsden, Fields Institute, Toronto, Jul 2012.
• Center for Applied Mathematics Colloquium, Cornell University, Ithaca, NY, Feb 2012.
• Mathematics Colloquium (Oliver Club), Cornell University, Ithaca, NY, Feb 2012.
• Mathematics Colloquium, Penn State University, State College, PA, Sep, 2011.
• Applied Dynamics and Geometric Mechanics Workshop, Oberwolfach, Germany, Aug 2011.
• Rough Paths and Combinatorics in Control Theory, UCSD, San Diego, CA, Jul 2011.
• Marsden Memorial minisymposium, ICIAM, Vancouver, Canada, Jul 2011.
• Computational Methods in Dynamics, ICTP, Jul 2011.
• KAM Theory and Geometric Integration Workshop, BIRS, Canada, Jun 2011.
• Symmetry in Variational Problems minisymposium, SIAM Applications of Dynamical Systems, Snowbird, UT, May 2011.
• Seventh Annual Structured Integration Workshop, Caltech, Pasadena, CA, May 2011.
• Mathematics Colloquium, University of Illinois, Chicago, Apr 2011.
• Geometric Numerical Integration Workshop, Oberwolfach, Germany, Mar 2011.
• Geometric Control on Nonlinear Manifolds special session, IEEE CDC, Atlanta, GA, Dec 2010.
• PIMS Seminar, University of British Columbia, Vancouver, Canada, Aug 2010.
• New Geometric and Numeric Tools for the Analysis of Differential Equations Workshop, BIRS, Canada, Aug 2010.
• Nonlinear Dynamics and Control minisymposium, CAIMS Annual Meeting, St. John's, Newfoundland, Canada, Jul 2010.
• Computational Methods for Dynamical Systems Analysis minisymposium, USNCTAM 2010, State College, PA. Jun 2010.
• Applied Mathematics Seminar, CSU Northridge, Northridge, CA, Apr 2010.
• Sixth Annual Structured Integrators Workshop, University of California, San Diego, CA. Apr 2010.
• Center for Computational Mathematics Seminar, University of California, San Diego, CA. Apr 2010.
• Cymer Center for Control Systems and Dynamics Seminar, University of California, San Diego, CA. Apr 2010.
• Colloquium, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, Oct 2009.
• Computational and Applied Mathematics Colloquium, Penn State University, State College, PA, Oct 2009.
• XVIII Fall Workshop on Geometry and Physics, Benasque, Spain, Sep 2009.
• Mechanics and Control Seminar, Beijing Institute of Technology, May 2009.
• Applied Mathematics Seminar, Stanford University, May 2009.
• Applied Mathematics and Statistics Seminar, Johns Hopkins University, Baltimore, MD, Feb 2009.
• Physical Mathematics Seminar, Massachusetts Institute of Technology, Cambridge, MA, Feb 2009.
• Mathematics Special Colloquium, University of Minnesota, MN, Dec 2008.
• Applied Mathematics Seminar, Texas A&M University, College Station, TX, Dec 2008.
• Mathematics Special Colloquium, University of California, San Diego, CA, Nov 2008.
• CDS Seminar, Caltech, Pasadena, CA, Nov 2008.
• Center for Applied Mathematics Colloquium, University of Notre Dame, Notre Dame, IN, Nov 2008.
• Applied and Interdisciplinary Mathematics Seminar, University of Michigan, Ann Arbor, MI, Nov 2008.
• Geometric Mechanics, Control, and Integrability minisymposium, AMS Southeastern Sectional Meeting, Huntsville, AL, Oct 2008.
• Dynamics Seminar, Department of Mathematics, Cornell University, NY, Oct 2008.
• Advances in Time-Integration minisymposium, World Congress on Computational Mechanics, Venice, Italy, Jul 2008.
• Geometric Integration and Computational Mechanics Workshop, Foundations of Computational Mathematics, Hong Kong, China, Jun 2008.
• Scientic Computing Seminar, Department of Mathematics, Tsinghua University, Beijing, China, Jun 2008.
• Institute of Computational Mathematics Seminar, Chinese Academy of Sciences, Beijing, China, Jun 2008.
• Fourth Annual Structured Integrators Workshop, Stanford, CA, Apr 2008.
• Geometric Numerical Integration Special Session, Joint Meeting of the AMS-NZMS, Welington, New Zealand, Dec 2007.
• Discrete Differential Geometry, Berlin, Germany, Jul 2007.
• Geometric and Symplectic Integration minisymposium, SciCADE, Saint-Malo, France, Jul 2007.
• Effective Computational Methods for Highly Oscillatory Problems, Newton Institute, University of Cambridge, UK, Jul 2007.
• Minicourse, First International Summer School on Geometry, Mechanics, and Control, Cantabria, Spain, Jun 2007.
• Geometric Methods in Dynamical Systems minisymposium, SIAM DS07, Snowbird, UT, May 2007.
• Applied Mathematics Seminar, Imperial College, London, UK, May 2007.
• Highly Oscillatory Problems Seminar, Newton Institute, University of Cambridge, UK, May 2007.
• Center for Applied Mathematics Colloquium, University of Notre Dame, Notre Dame, IN, Apr 2007.
• Mathematics Colloquium, University of Iowa, Iowa City, IA, Mar 2007.
• CDS/CIMMS Lunchtime Seminar, Caltech, Pasadena, CA, Dec 2006.
• Applied Mathematics Colloquium, University of Maryland, Baltimore County, Nov 2006.
• Mathematical Sciences Colloquium, Rensselaer Polytechnic Institute, Troy, NY, Oct 2006.
• Applications of the Geometric Phase in Classical Mechanics minisymposium, SIAM Annual Meeting, Boston, MA, Jul 2006.
• Geometry and Dynamical Systems with Applications Seminar, Arizona State University, Tempe, AZ, Apr 2006.
• Dynamics Seminar, University of Colorado, Boulder, CO, Feb 2006.
• Mathematics Colloquium, Colorado School of Mines, CO, Feb 2006.
• Applied and Interdisciplinary Mathematics Seminar, University of Michigan, Ann Arbor, MI, Feb 2006.
• Mathematics Colloquium, University of South Carolina, Columbia, SC, Feb 2006.
• Mathematics Colloquium, Texas A&M University, College Station, TX, Feb 2006.
• Mathematics Colloquium, Colorado State University, Fort Collins, CO, Feb 2006.
• Mathematics Special Colloquium, Purdue University, West Lafayette, IN, Feb 2006.
• Joint Numerical Analysis and Differential Equations Seminar, North Carolina State University, NC, Jan 2006.
• Contemporary Dynamical Systems special session, AMS National Meeting, San Antonio, TX, Jan 2006.
• Applied Mathematics Seminar, Mathematics, University of Waterloo, Canada, Dec 2005.
• Control Seminar, College of Engineering, University of Michigan, Ann Arbor, MI, Oct 2005.
• Differential Geometry and Analysis Seminar, University of Toledo, Toledo, OH. Sep 2005.
• Computer and Computational Sciences, CCS-2, LANL, Los Alamos, NM. Aug 2005.
• Geometric Dynamics and its Applications minisymposium, SIAM DS05, Snowbird, UT, May 2005.
• Special Seminar, Mathematics, University of California, Berkeley, CA, Apr 2005.
• Mathematical Physics Seminar, University of Minnesota, Twin Cities, MN, Mar 2005.
• Joint Numerical Analysis and Differential Equations Seminar, North Carolina State University, NC, Jan 2005.
• Mathematics Colloquium, University of California, San Diego, CA, Dec 2004.
• Flight Dynamics and Control Seminar, University of Michigan, Ann Arbor, MI, Oct 2004.
• Geometry Seminar (two sessions), University of Michigan, Ann Arbor, MI, Oct 2004.
• Applied Mathematics Seminar, University of California, San Diego, CA, Aug 2004.
• Temasek Laboratories, National University of Singapore, Jul 2004.
• Mathematics Seminar (four sessions), National University of Singapore, Jul 2004.
• Geometric Dynamics and Applications minisymposium, AIMS Conference on Dynamical Systems and Differential Equations, Pomona, CA, June 2004.
• Applied Mathematics and Numerical Analysis Seminar, University of Minnesota, Twin Cities, MN, Jan 2004.

Professional Service

• Organizing committee member, German-American Kavli Frontiers of Science Symposium, Potsdam, Germany, Mar 2016.
• Local organizing committee member, US National Congress in Computational Mechanics, San Diego, CA, Jul 2015.
• Organizing committee member, German-American Kavli Frontiers of Science Symposium, Irvine, CA, Apr 2014.
• Local organizing committee member, Pacific Coast Gravity Meeting, La Jolla, CA, Mar 2014.
• Selection committee member, John Butcher Prize in Numerical Analysis, SciCADE, Valladolid, Spain, Sep 2013.
• Co-organizer, Smooth and Discrete Geometrical Approaches to Control, SIAM Controls, San Diego, CA, Jul 2013.
• Co-organizer, computational methods for geometric PDEs minisymposium, ICIAM, Vancouver, Canada, Jul, 2011.
• Organizing committee member, geometric methods for optimal control semester, Madrid, Spain, Jul-Dec 2010.
• Co-organizer, Sixth Annual Structured Integrators Workshop, University of California, San Diego, CA, Apr 2010.
• Co-organizer, 26th Pacific Coast Gravity Meeting, Mar 2010.
• Organizer, computational mechanics minisymposium, SciCADE 2009, Beijing, China, May 2009.
• Co-organizer, geometric mechanics and its applications minisymposium (MS 121), SIAM DS09, May 2009.
• Co-organizer, Fifth Annual Structured Integrators Workshop, Caltech, Pasadena, CA, May 2009.
• Co-organizer, nonlinear dynamics and control of mechanical systems invited session, IEEE Conference on Decision and Control, Dec 2006.
• Co-organizer, contemporary dynamical systems special session, AMS National Meeting, Jan 2006.
• Co-organizer, geometric dynamics and its applications minisymposium (MS 59, 70), SIAM DS05, May 2005.
• Co-organizer, CIMMS Workshop on Discrete Geometry for Mechanics, Caltech, Pasadena, CA, Oct 2003.
• Co-organizer, discrete geometry and geometric integration minisymposium (MS 38, 62), SIAM DS03, May 2003.
• Co-organizer, CIMMS Workshop on Networks, Optimization and Duality, Caltech, Pasadena, CA, Jul 2002.
• Co-organizer, geometric integration minisymposium (MS 51, 69), SIAM DS01, May 2001.
• Referee, Advances in Difference Equations, Aerospace Science and Technology, Applied Numerical Mathematics, Celestial Mechanics and Dynamical Astronomy, Communications in Contemporary Mathematics, Communications in Numerical Methods in Engineering, Computational Science & Discovery, Discrete and Continuous Dynamical Systems, ESAIM: Control, Optimisation and Calculus of Variations, Foundations of Computational Mathematics, IEEE Transactions on Automatic Control, IET Control Theory & Applications, IMA Journal of Numerical Analysis, Journal of Computational Physics, Journal of Mathematical Physics, Journal of Nonlinear Science, Journal of Physics A, Journal of Symplectic Geometry, Mathematical and Computer Modelling, Nonlinearity, Numerical Algorithms, Numerische Mathematik, Physica D, Physics Letters A, Proceedings of the Royal Society A, SIAM Applied Dynamical Systems, SIAM Multiscale Modeling and Simulation, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), Soft Computing and Automation Journal, Transport in Porous Media.
• Reviewer, IEEE Conference on Decision and Control 2005, 2006, 2007, 2008, IEEE Multi-conference on Systems and Control 2007, American Control Conference 2008, Mathematical Reviews, Springer Books, Swiss National Science Foundation.
• Panel member, Mathematical Sciences, National Science Foundation, October 2014.
• Panel member, Mathematical Sciences, National Science Foundation, Oct 2013.
• Panel member, Mathematical Sciences, National Science Foundation, Nov 2011.
• Panel member, Mathematical Sciences Graduate Research Fellowship, National Science Foundation, Feb 2010.
• Panel member, Applied Mathematics, National Science Foundation, Mar 2009.
• Panel member, Computational Mathematics, National Science Foundation, Mar 2008.

Education

• Ph.D., Control and Dynamical Systems (minor in Applied and Computational Mathematics), California Institute of Technology, 2004.
• M.S., Mathematics, California Institute of Technology, 2000.
• B.S. with honor, Mathematics, California Institute of Technology, 2000.

Upcoming Conferences (Confirmed)

• Computational Challenges in Gravitational Wave Astronomy, IPAM, Los Angles, CA, January 28-February 1, 2019.
• Geometric Numerical Integration of Differential Equations, Beijing, China, September 8-13, 2019.
• Keynote, Meeting of the Society for Natural Philosophy, Chicago, IL, September 13-15, 2019.
• Structure Preservation and General Relativity, Newton Institute, Cambridge, UK, September 30-October 4, 2019.

Interesting Upcoming Conferences

Recent Conferences Attended

• IMA Tutorial/Workshop: New Paradigms in Computation, Minneapolis, MN, March 28-30, 2005.
• IPAM Grand Challenge Problems in Computational Astrophysics, N-Body Problems in Astrophysics, Los Angeles, CA, April 18-22, 2005.
• IPAM Grand Challenge Problems in Computational Astrophysics, Relativistic Astrophysics, Los Angeles, CA, May 2-6, 2005.
• SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May 22-26, 2005.
• Summer School on Control in Quantum Systems, California Institute of Technology, Pasadena, CA, Aug 8-14, 2005.
• IMA New Directions Short Course: Quantum Computation, Minneapolis, MN, Aug 15-26, 2005.
• Workshop in Celebration of Bjorn Engquist 60th Birthday: International Forum on Multiscale Methods and Partial Differential Equations, Los Angeles, CA, August 26-27, 2005.
• Frontiers of Applied Analysis, Pittsburgh, PA, September 8-10, 2005.
• IPAM Bridging Time and Length Scales in Materials Science and Bio-Physics, Multiscale Analysis and Computation, Los Angeles, CA, November 14-16, 2005.
• Multiscale Modeling and Computation - Basic Theory and the Geosciences, Pasadena, CA, November 17-18, 2005.
• AMS National Meeting, San Antonio, TX, January 12-15, 2006.
• Geometric Numerical Integration Workshop, Oberwolfach, Germany, March 19-25, 2006.
• Advanced Computational Electromagnetics Workshop, Boston, MA, May 4-6, 2006.
• SIAM Annual Meeting, Boston, Massachusetts, July 10-14, 2006.
• International Congress of Mathematicians, Madrid, Spain, August 22-30, 2006.
• IMA Tutorial: Algebraic Geometric Methods in Engineering, Minneapolis, Minnesota, September 15-16, 2006.
• MSRI Workshop on Application of topology in science and engineering, Berkeley, California, September 18-22, 2006.
• IEEE Conference on Decision and Control, San Diego, California, December 13-15, 2006.
• Geometry of Mechanism Science, Notre Dame, Indiana, March 1-3, 2007.
• Highly Oscillatory Problems: Computation, Theory and Application, Newton Institute, Cambridge, United Kingdom, May 7-20, 2007.
• SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, May 28-June 1, 2007.
• First International Summer School on Geometry, Mechanics and Control, Castro Urdiales, Spain, June 25-29, 2007.
• Effective Computational Methods for Highly Oscillatory Problems, Newton Institute, Cambridge, United Kingdom, July 2-6, 2007.
• SciCADE, Saint-Malo, France, July 9-13, 2007.
• Discrete Differential Geometry, Berlin, Germany, July 16-20, 2007.
• BIRS Geometric Mechanics, Banff, Canada, August 12-17, 2007.
• Joint AMS-NZMS Meeting, Wellington, New Zealand, December 12-15, 2007.
• Gene Golub Symposium, Urbana, IL, February 29 - March 1, 2008.
• Fourth Annual Structured Integrators Workshop, Stanford, CA, April 24-25, 2008.
• Foundations of Computational Mathematics, Hong Kong, China, June 16-26, 2008.
• World Congress on Computational Mechanics, Venice, Italy, June 30 - July 4, 2008.
• AMS Southeastern Sectional Meeting, Huntsville, AL, October 24-26, 2008.
• Groupoidfest 2008, Riverside, CA, November 22-23, 2008.
• Fifth Annual Structured Integrators Workshop, Pasadena, CA, May 7-8, 2009.
• SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May 17-21, 2009.
• SciCADE 2009, Beijing, China, May 25-29, 2009.
• XVIII International Fall Workshop on Geometry and Physics, Benasque, Spain, September 6-11, 2009.
• IEEE Conference on Decision and Control, Shanghai, China, Dec 16-18, 2009.
• Pacific Coast Gravity Meeting, La Jolla, CA, March 26-27, 2010.
• Sixth Annual Structured Integrators Workshop, La Jolla, CA, April 26-27, 2010.
• HarrisFest 2010, Ann Arbor, MI, May 22, 2010.
• 16th US National Congress of Theoretical and Applied Mechanics, State College, PA, June 27-July 2, 2010.
• Geometry, Mechanics, and Dynamics: A Workshop celebrating the 60th Birthday of Tudor Ratiu, CIRM, France, July 12-16, 2010.
• CAIMS Annual Meeting, St. John's, Newfoundland and Labrador, Canada, July 17-20, 2010.
• BIRS Workshop: New Geometric and Numeric Tools for the Analysis of Differential Equations, Banff, Canada, August 13-15, 2010.
• Symmetry, Separation, Super-integrability and Special Functions, University of Minnesota, September 17-19, 2010.
• Geometric and Topological Methods in Control and Robotics, Madrid, Spain, October 4-6, 2010.
• NSF CMMI Research and Innovation Conference, Atlanta, GA, January 4-7, 2011.
• Geometric Numerical Integration Workshop, Oberwolfach, Germany, March 20-26, 2011.
• SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May 22-26, 2011.
• BIRS Workshop: KAM theory and Geometric Integration, Banff, Canada, June 5-10, 2011.
• Computational Methods in Dynamics, ICTP, Trieste, Italy, July 4-8, 2011.
• International Congress on Industrial and Applied Mathematics, Vancouver, BC, Canada, July 18-22, 2011.
• Applied Dynamics and Geometric Mechanics Workshop, Oberwolfach, Germany, August 14-20, 2011.
• German-American Frontiers of Science Symposium, Potsdam, Germany, May 10-13, 2012.
• Symmetries of Differential Equations: Frames, Invariants and Applications, Minneapolis, MN, May 17-19, 2012.
• Geometry, Symmetry, Dynamics, and Control: The Legacy of Jerry Marsden, Fields Institute, Toronto, July 23-27, 2012.
• Structured Matrix Computations in Non-Euclidean Geometries: Algorithms and Applications, CIRM, Luminy, France, October 8-12, 2012.
• AMS Western Section Meeting, Tucson, AZ, October 27-28, 2012.
• IEEE Conference on Decision and Control, Maui, Hawaii, December 10-13, 2012.
• IRSES Meeting on Differential Geometry and Mechanics, Ghent, Belgium, January 14-16, 2013.
• 14th International Conference on Approximation Theory, San Antonio, Texas, April 7-10, 2013.
• SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, May 19-23, 2013.
• International Linear Algebra Society 2013 Meeting, Providence, RI, June 3-7, 2013.
• Workshop on Reduced-Order Modeling in General Relativity, Caltech, Pasadena, CA, June 6-7, 2013.
• Topics in Numerical Analysis for Differential Equations, ICMAT, Madrid, Spain, July 8-12, 2013.
• Weinstein Symposium, Institute Henri Poincare, Paris, France, July 18-20, 2013.
• SciCADE 2013, Volladolid, Spain, September 16-20, 2013.
• Allerton Conference on Communication, Control and Computing, Monticello, IL, October 2-4, 2013.
• Modern Applications of Homology and Cohomology, IMA, Minneapolis, MN, October 28-November 1, 2013.
• Discrete Curvature, CIRM, Luminy, France, November 18-22, 2013.
• Conference on Numerical Analysis and Scientific Computing, MPI Leipzig, January 7-9, 2014.
• German-American Frontiers of Science Symposium, Irvine, CA, April 4-6, 2014.
• Foundations of Computational Mathematics, Montevideo, Uruguay, December 11-20, 2014.
• Advanced Numerical Methods in the Mathematical Sciences, Institute for Scientific Computation, Texas A&M University, College Station, TX, May 4-8, 2015.
• SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May 17-21, 2015.
• Integrability in Mechanics and Geometry: Theory and Computations, ICERM, Providence, RI, June 1-5, 2015.
• Joint STAMP-GMC Meeting, Miraflores de la Sierra, Madrid, Spain, June 29-July 3, 2015.
• IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Lyon, France, July 4-7, 2015.
• European Solid Mechanics Conference, Madrid, Spain, July 6-10, 2015.
• US National Congress on Computational Mechanics, San Diego, CA, July 26-30, 2015.
• NUMDIFF-14 Numerical Solution of Differential and Differential-Algebraic Equations, Halle, Germany, September 7-11, 2015.
• Discretization in Geometry and Dynamics, Herrsching am Ammersee, Germany, October 5-9, 2015.
• German-American Frontiers of Science Symposium, Potsdam, Germany, Mar 10-13, 2016.
• Geometric Numerical Integration, Oberwolfach, Germany, March 20-26, 2016.
• SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, May 21-25, 2017.
• Dynamical Systems and Geometric Mechanics, An International Conference in Honor of Juergen Scheurle, Munich, Germany, June 12-14, 2017.
• New Trends in Applied Geometric Mechanics - Celebrating Darryl Holm's 70th Birthday, ICMAT, Madrid, Spain, July 3-7, 2017.
• Foundations of Computational Mathematics, Barcelona, Spain, July 10-19, 2017.
• Nonlinear Data: Theory and Algorithms, Oberwolfach, Germany, April 22-28, 2018.
• Interplay of tensor structured formats with advanced PDE discretizations, Erwin Schrodinger Institute, Vienna, Austria, June 11-15, 2018.
• RobertFest (in honor of Robert Littlejohn), Berkeley, CA, August 17-19, 2018.
• Hamiltonian Systems, from Topology to Applications through Analysis I, MSRI, Berkeley, CA, October 8-12, 2018.

Other Interesting Conferences

• BIRS Numerical Relativity, Banff, Canada, April 16 - 21, 2005.
• SciCADE 2005, Nagoya, Japan, May 23-27, 2005.
• Dundee Numerical Analysis Conference, Dundee, Scotland, June 28 - July 1, 2005.
• Geometric Integration and Computational Mechanics Minisymposium, Foundations of Computational Mathematics, Santander, Spain, June 30 - July 9, 2005.
• Numerical Relativity, Global Problems in Mathematical Relativity, Newton Institute, Cambridge, UK, August 15-21, 2005.
• IEEE Conference on Control Applications, Toronto, Canada, August 28-31, 2005.
• Compatible Discretizations for Partial Differential Equations, Oslo, Norway, September 26-28, 2005.
• IEEE Conference on Decision and Control, Seville, Spain, December 12-15, 2005.
• Workshop on Structured Integration, Palo Alto, California, March 10-11,2006.
• American Control Conference, Minneapolis, Minnesota, June 14-16, 2006.
• IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Nagoya, Japan, July 19-21, 2006.
• International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan, July 24-28, 2006.
• AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Keystone, Colorado, August 21-24, 2006.
• IPAM Workshop on Mathematical Challenges and Opportunities in Sensor Networking, Los Angeles, California, January 8-12, 2007.
• Analysis on Graphs and its Applications, Newton Institute, Cambridge, United Kingdom, January 8 - June 29, 2007.
• International Congress on Industrial and Applied Mathematics, Zurich, Switzerland, July 16-20, 2007.
• IMA Summer Program: Classical and Quantum Approaches in Molecular Modeling, Minneapolis, Minnesota, July 23-August 3, 2007.
• Trimester on Combinatorics and Control, Madrid and Benasque, Spain, April-June, 2010.
• Discrete Differential Geometry and Applications, University of Tennessee, Knoxville, TN, May 17-21, 2010.
• Highly Oscillatory Problems: From Theory to Applications, Newton Institute, Cambridge, United Kingdom, September 12-17, 2010.
• Foundations of Computational Mathematics, Budapest, Hungary, July 4-14, 2011.
• Stochastic Systems, Simulation and Control, ICMAT, Madrid, Spain, November 5-9, 2012.
• Manifolds and Geometric Integration Colloquium (MAGIC) 2013, Geilo, Norway, February 26-March 1, 2013.
• Conference in Honor of Alan Weinstein, EPFL, Lausanne, Switzerland, July 22-26, 2013.
• SciCADE, International Conference on Scientific Computation and Differential Equations, Potsdam, Germany, September 14-18, 2015.
• Connections in Geometric Numerical Integration and Structure-Preserving Discretization, BIRS, Banff, Canada, Jun 11-16, 2017.
• Leslie Fox Prize Meeting, University of Strathclyde, Glasgow, Scotland, June 26, 2017.
• SciCADE, International Conference on Scientific Computation and Differential Equations, Bath, United Kingdom, September 11-15, 2017.

Erdös Number

1. Erdös, P.; Graham, R. L.; Montgomery, P.; Rothschild, B. L.; Spencer, J.; Straus, E. G.; Euclidean Ramsey theorems. I., J. Combinatorial Theory Ser. A, 14 (1973), 341-363.
2. Golubitsky, M. A.; Rothschild, B. L.; Primitive subalgebras of exceptional Lie algebras. Bull. Amer. Math. Soc. 77 1971 983-986.
3. Golubitsky, M. A.; Marsden, J. E.; The Morse lemma in infinite dimensions via singularity theory. SIAM J. Math. Anal. 14 (1983), no. 6, 1037-1044.
4. Desbrun, M.; Leok, M.; Marsden, J. E.; Discrete Poincaré Lemma, Appl. Numer. Math. 53(2-4), 231-248, 2005.

• Interestingly, three of my collaborators have Erdös number 3. They are, Anthony M. Bloch, Jerrold E. Marsden, and Alan D. Weinstein.
• Useful sites in this regard are the Erdös Number Project and the AMS MathSciNet Collaboration Distance Page.

Collaborators

• Anthony Bloch, Mathematics, University of Michigan, Ann Arbor.
• Mathieu Desbrun, Computer Science, California Institute of Technology.
• Anil Hirani, Computer Science, University of Illinois, Urbana-Champaign.
• Islam Hussein, Mechanical Engineering, Worcester Polytechnic Institute.
• Sameer Jalnapurkar, Mathematics, Indian Institute of Science, Bangalore.
• Jerrold Marsden, Control and Dynamical Systems, California Institute of Technology.
• N. Harris McClamroch, Aerospace Engineering, University of Michigan, Ann Arbor.
• Amit Sanyal, Mechanical Engineering, University of Hawaii at Manoa.
• Alan Weinstein, Mathematics, University of California, Berkeley.
• Matthew West, Aeronautics and Astronautics, Stanford University.
• Dmitry Zenkov, Mathematics, North Carolina State University.

Students

• Taeyoung Lee, Ph.D. in Aerospace Engineering (Distinguished Achievement Award, Ivor K. Mclvor Award, Rackham Predoctoral Fellow, and Rackham International Student Fellow), University of Michigan, Ann Arbor. (co-advised with N. Harris McClamroch)
• Masako Kishida, M.S. in Applied and Interdisciplinary Mathematics, University of Michigan, Ann Arbor.

Biographical Sketch

Melvin Leok is a professor of mathematics at the University of California, San Diego. His research focuses on computational geometric mechanics, computational geometric control theory, discrete geometry, and structure-preserving numerical schemes, and particularly how these subjects relate to systems with symmetry. He received his Ph.D. in 2004 from the California Institute of Technology in Control and Dynamical Systems under the direction of Jerrold Marsden. He is a three-time NAS Kavli Frontiers of Science Fellow, and has received the NSF Faculty Early Career Development (CAREER) award, the SciCADE New Talent Prize, the SIAM Student Paper Prize, and the Leslie Fox Prize (second prize) in Numerical Analysis. He has given plenary talks at Foundations of Computational Mathematics, NUMDIFF, and the IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control. He serves on the editorial boards of the Journal of Nonlinear Science, the Journal of Geometric Mechanics, and the Journal of Computational Dynamics, and has served on the editorial boards of the SIAM Journal on Control and Optimization, and the LMS Journal of Computation and Mathematics.

SciCADE New Talent Award	SIAM Student Paper Prize	Leslie Fox Prize

Recommended Books