The Computational Geometric Mechanics group at the University
of California, San Diego
Research Objectives
The computational geometric mechanics group is focused on developing a self-consistent discretization of geometry and mechanics to enable the systematic construction of geometric structure-preserving numerical schemes based on the approach of geometric mechanics, with a view towards obtaining more robust and accurate numerical implementations of feedback and optimal control laws arising from geometric control theory.
The activities
of the group are partially funded by research grants from the National Science Foundation in applied and
computational mathematics and engineering:
Prof. Ping Xu, Penn State
University, Feb 7-10, 2011.
Prof. Darryl Holm, Imperial College, Dec 17-21, 2012.
Prof. Sergio Blanes,
Universidad Politecnica de Valencia, Spain, Jan-Feb 2013 and Jul-Oct
2013.
Prof. Gerard Awanou, University of Illinois, Chicago, Nov 4-6, 2013.
Dr. David Martin de Diego (ICMAT), Prof. Juan Carlos Marrero
(University of La Laguna), Feb 2014.
Prof. Yajuan Sun, Chinese Academy of Sciences, Aug 2014-Feb 2015.
Affiliated and Alumni Members
Dr. Helen Parks,
Ph.D. in Mathematics,
University of California, San Diego, 2015, and NSF Graduate Research
Fellow. [ Thesis ]
Dr. James Hall, Ph.D.
in Mathematics (CSME), University of California, San
Diego, 2013. [ Thesis ]
Dr. Hall stayed at UCSD for the 2013/2014 academic year as a
postdoctoral scholar and took up a permanent
position as a research scientist at Intel in Portland, OR, starting July
2014.
Dr. Tomoki
Ohsawa, Ph.D. in Applied and Interdisciplinary Mathematics,
University of Michigan, 2010. Postdoctoral scholar/teaching
visitor, University of California, San Diego, 2010-2012.
Currently a
tenure-track assistant professor of mathematics at the University of
Texas, Dallas. His first position after UCSD was a tenure-track assistant
professorship at the University of Michigan, Dearborn.
Dr.
Joris Vankerschaver, Ph.D. in Mathematics, Ghent University, 2007.
Postdoctoral scholar/teaching visitor, University of California, San
Diego, 2010-2012.
After UCSD, Dr. Vankerschaver spent one year as a
postdoctoral scholar with Prof. Darryl Holm
at Imperial College. He is currently a Scientific Software Developer at
Enthought in Cambridge, UK.
Dr. Tatiana Shingel,
Ph.D. in Mathematics, Cambridge University, 2009.
Postdoctoral scholar/teaching visitor, University of California, San
Diego, 2009-2012.
After UCSD, Dr. Shingel was a postdoc at Jacobs University, Bremen,
Germany, and is currently a data scientist at ViaSat.
Dr.
Diana Sosa Martín, Ph.D. in Mathematics, University of
La Laguna, Spain, 2008. Visiting assistant professor, Purdue
University, 2008-2009.
Currently an assistant professor of mathematics,
University of La Laguna, Spain.
Dr. Taeyoung
Lee,
Ph.D. in Aerospace Engineering, University of Michigan, 2008. (co-advised
with
Prof. N. Harris McClamroch)
Currently a tenured associate professor of mechanical and aerospace
engineering,
George Washington University. [ Thesis ]
Jingjing Zhang, was a visiting graduate student from the Institute of
Computational Mathematics, Chinese Academy of Sciences. Her one year visit to our group
was funded by a fellowship from the
Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
She defended her thesis in May 2010, and is currently an assistant
professor in Henan Polytechnic University, Jiaozuo, China. (co-advised
with Prof. Jialin Hong)
Giulia Ortolan, a
Ph.D. student in Information Engineering at the University of Padova,
Italy, visited our group for a period of four months on a
scholarship from the University of Padova.
Cuicui Liao was a Ph.D. student in Mathematics at the Harbin
Institute of Technology who visited our group on a
postgraduate scholarship from the Chinese Scholarship Council, from
September 2010 to December 2011. She graduated with her Ph.D. in July
2013, and is currently an assistant professor of mathematics in Jiangnan
University, China.
Zahra Ebrahimzadeh, a Ph.D. candidate in Solid Mechanics in the
Department of Mechanical Engineering at Isfahan University of Technology,
visited our research group from March 2012 to October 2012.
Masako Kishida,
M.S. in Applied and Interdisciplinary Mathematics
(Michigan), received her Ph.D. in Mechanical Engineering at UIUC
in 2010, and has been a Lecturer in Electrical and Computer
Engineering at the University of Canterbury, New Zealand, since
2013.
Leilani Gilpin,
undergraduate research assistant, received a double major in mathematics
and computer science from UCSD, currently a NSF graduate fellow at
Stanford University.
Nathan Orlow, NSF REU student.
Charles Roldan, NSF REU student.
Wooi-Chen Ng, summer undergraduate research assistant.
Research Opportunities
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.
Academic
and Industrial, Science and Engineering Collaborations
Welcomed
We are constantly on the lookout for interesting and challenging
collaborations with scientists and engineers from academia or industry.
If you have an interesting application for which geometric
numerical methods might be relevant, please feel free to contact us.
Much of our 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."