Institute for Advanced Study

IAS Distinguished Fellow Profile

Dr Elizabeth Mansfield

IAS Fellow 2002

Dr Elizabeth Mansfield is a Reader in Mathematics at the Institute of Mathematics and Statistics, University of Kent, Canterbury, England.

She is involved in various research programs, including the external research program of CATHODE II, the ESPRIT working group on symbolic computation for ordinary differential equations.

Dr Mansfield has authored numerous articles on the application of algebraic methods to analysis, in particular to over determined systems, symmetry, symbolic integration, and variational complexes.  Applications have been to shallow water systems, nonlinear heat diffusion, higher dimensional nonlinear Schroedinger and sine Gordon systems, and to meterological models.  The implementation of algorithms developed, in Maple, has also been a theme in her research

During the time Dr Mansfield was at the Institute for Advanced Study she collaborated with Dr Reinout Quispel, who is a Reader in the Department of Mathematics at La Trobe University.  The two main topics of research were:

• Discrete symplectic structures. These mimic the Hamiltonian structure of mechanical systems, but for discrete (finite difference) equations.
• Variational complexes for the finite element method of numerical integration.

Dr Mansfield also worked on her own project, reduction relations in algebras of differential invariants, as well as writing up an extensive set of notes which were sent to collaborators E. Hubert and INRIA (France) and A. Szanto (North Carolina).

 Dr Mansfield expressed her gratitude for the excellent facilities at Institute for Advanced Study, (IAS) and the hospitality shown to her at the IAS.