I am now a Fellow of the IMA, that is, Institute of Mathematics and its Applications.

In January 2015, I was elected to a Vice Presidency of the IMA, with responsibility for Learned Societies. This means I chair the IMA Research Committee and attend Executive Board and Council meetings, amongst other activities. I care deeply about access of girls to advanced mathematics teaching in schools, about socially aware mathematics, about funding mathematics research across the whole country, and about dealing with implicit bias.

The book is now available from CUP (above link), also Amazon

An errata page will appear soon :(

My two former graduate students, Tania Goncalves and Jun Zhao pursue their careers, congratulations to them both! Here is a great photo of us at the FoCM '08 banquet in Hong Kong, where Jun, Tania and Andy Wheeler presented posters.

This coming year, 2015-16 I am teaching on MA593/MA561 Lie groups and algebras, and MA588, Mathematical Techniques and Differential Equations. I alternate teaching Lie groups and algebras with teaching Mathematics and Music, which involves Chladni patterns on drums, digital signal processing ie recording music, and the geometry of music and music composition.

I was Vice Chair of ACM's SIGSAM, Special Interest Group in Symbolic and Algebraic Manipulation, for two years.

I served on the EPSRC Strategic Advisory Team for the mathematics program, for five years (at least!!).

I served as a board member for the Society for the Foundations of Computational Mathematics for maybe ten years!! I co-organised the Symbolic Analysis Workshop of three (!) FoCM conferences.

I was part of the official delegation of the London Maths Society to the International Congress of Mathematics in Hyderabad, India.

My research is the development of algorithms for Analysis, in the context of symbolic computation and increasingly numerical computation; recent papers are on various forms of 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.

** Earlier Research Funding **

My previous EPSRC grant, "Symmetric variational
problems", which funded Tania and Jun, is now just finshed. A brief description is
here

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 generic platforms
(non readlib
version, ie, maple just reads the file in whole, and you don't use the **with** command).
I currently have this working for Maple 9. The Maple
worksheets for the examples in the manual are for
invariant
differentation, an
over determined system, and a
classification problem.

Noether's Second Theorem for smooth and discrete systems.

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, and/or invariant ODE and/or curvature flows.

Discrete gradients

Moment maps for discrete symplectic mappings. Available from the Isaac Newton Institute website, Discrete Integrable Systems and Special Functions workshop.

On a variational complex for difference systems

Towards a variational complex for finite element systems

A simple criterion for involutivity

Extensions of Noether's Second Theorem: from continuous to discrete systems with Peter Hydon. In the Proceedings of the Royal Society.

On Moving Frames and Noether's Theorem with Tania Goncalves. In Studies in Applied Mathematics.

Discrete variational calculus for B-spline Approximated Curves with Jun Zhao.

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

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

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