Research funding just announced: is an EPSRC grant, "Group actions on function approximation spaces", see the the epsrc webpage . I will shortly be 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.
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.
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
