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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.
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.
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 ]
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 ]
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.
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.
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 ]
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 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:
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.
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| SciCADE New Talent Award | SIAM Student Paper Prize | Leslie Fox Prize |
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