Research funding just announced: is an EPSRC grant, "Group actions on function approximation spaces", see the the epsrc webpage . I am now advertising a three year post doctoral research associate position. The position is available from Sept 1, 2010 and is at Grade 7 level. A description of the project is is here.
Position available:
Three year Post-doctoral Research Assistant
The project targets the a priori embedding of conservation laws into numerical code for problems with a variational formulation. There are both mathematical and scientific computation aspects to the project. The first is the mathematical understanding of how the mechanism of symmetries giving rise to conservation laws can be emulated in function approximation spaces such as those used in the finite element method. Secondly, there is the computational aspect, exploring the a priori embedding of conservation laws in typical test applications. The precise role of the post-doc will depend on his or her mathematical background and interests, but will include the development of numerical code to test the various conjectures.
Applicants must have a PhD (or equivalent) in mathematics or engineering (with a strong mathematical component) with excellent knowledge and experience in scientific computation, in particular the finite element method. Knowledge of compatible discretisation techniques, geometric integration or Lie group actions (Noether's Theorem) would be a distinct advantage.
The closing date for applications is 18 April 2010. It is anticipated that interviews will be held on May 4, 2010. Further particulars and the on-line application page is at Kent's job page
Click on Vacancies and search for Job reference number STM0128.
MA600/MA575 Key Skills + LaTeX timetable and MA599 Mini-Projects timetable
MA563 Calculus of Variations home page
I am currently on the EPSRC Strategic Advisory Team for the mathematics program.
I am a board member for the Society for the Foundations of Computational Mathematics. I co-organised the Symbolic Analysis Workshop of three (!) FoCM conferences.
This year I am part of the official delegation of the London Maths Society to the International Congress of Mathematics in Hyderabad, India. I am also on several LMS commitees this year.
In Amsterdam, Applied Geometric Algebras in Computer Science and Engineering
In Munich, ISSAC 2010 where I am on the programme committee.
In Hyderabad, ICM where I am a delegate of the LMS.
In Brisbane, the Australian maths Society conference where I am a plenary speaker.
Current Research Funding My current grant, "Symmetric variational problems", is now in its final stages. A brief description is here
Research Interests:
My research is the development of algorithms for Analysis,
in the context of symbolic computation and increasingly
numerical computation; recent papers
are on the discrete variational calculus and moving frames.
The mathematics that I use comes from commutative algebra, differential geometry, variational calculus, integrable systems and geometric integration.
I currently have three PhD students, Tania Goncalves, Richard Hoddinott, and Jun Zhao, and one MSc student, Andy Wheeler who has written his thesis now. Here is a great photo of us at the FoCM '08 banquet in Hong Kong, where Jun, Tania and Andy presented posters.
I am involved with the network grant Geometric Integration, led by Reinout Quispel and funded by the Australian Research Council. I spent 2 months study leave at the Institute of Advanced Studies at LaTrobe University working on Discrete Gradients.
The MAPLE package Indiff is now available. This is a set of functions designed to calculate reductions and compatibility conditions of systems of equations referred to a moving frame. The theory is discussed in " Algorithms for symmetric differential systems", J. Foundations of Comp. Math.,1 (2001) 335-383. The Short Manual contains installation instructions for UNIX, a guide to the procedures and three worked examples. There are two versions of the code, a readlib version and a version suitable for non-unix platforms (non readlib version). The Maple worksheets for the examples in the manual are for invariant differentation, an over determined system, and a classification problem.
Digital Atlases and Difference Forms Plenary talk at ISSAC '08, Linz.
Discrete Variational Methods Plenary talk at FoCM, Santander.
Moving Frames and Noether's Theorem.
Discrete gradients
Moving frames and invariant ODE
Moving frames and curvature flows
On a variational complex for difference systems
Towards a variational complex for finite element systems
A simple criterion for involutivity
Noether's Theorem for Smooth, Difference and Finite Element Systems , in FoCM Santander 2005. Eds: Pardo, Pinkus, Suli and Todd. CUP 2006.
A variational complex for difference equations with Peter Hydon (Surrey). Now available from Journal of Foundations of Computational Mathematics.
Towards a variational complex for the Finite Element Method with Reinout Quispel (LaTrobe). In a CRM Proceedings for the workshop on Group Theory and Numerical Analysis
Difference Forms with Peter Hydon, Journal of Foundations of Computational Mathematics.
Evolution of Curvature Invariants and Lifting Integrability, with Peter van der Kamp, Journal of Geometry and Physics
Symmetry Group Analysis of the Shallow Water and Semi-Geostrophic Equations with Nicoleta Bila and Peter Clarkson, in Quarterly Journal of Mechanics and Applied Mathematics
