Professor Greg Reid

PhD University of Waikato, 1984, New Zealand.

Current position:   Full Professor, Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada, member since 1999.

Held Natural Sciences and Engineering Research Council (NSERC) grants from the government of Canada, continuously since 1991.

A principal scientist of the Ontario Research Center for Computer Algebra (ORCCA) a joint initiative  of the Universities of Waterloo and Western Ontario, since 1999, co-investigator on grants for this center.

1990 - 1999:  Faculty in Mathematics, University of British Columbia Okanagan (tenured).
1989 - 90:  Western Washington University (non-tenured).
1986 - 88:  Postdoctoral Fellow,  University of British Columbia.
1985 - 86:  University of Southern California (non-tenured).

Research Interests:

Early career interests included separation of variables in Riemannian spaces for Schrodinger type PDE, followed by research on non-local symmetries of partial differential equations.  The difficulty of the computations involving the related overdetermined systems of PDE motivated Reid's interest in developing  automatic symbolic methods for analyzing and simplifying such systems.

One of the best known results is the extensive reduced involutive form (rifsimp) algorithm implemented in Maple, for simplifying systems to rif form.  This package is frequently called whenever Maple's dsolve or pdsolve routines are used.  It has been used frequently in research on determining symmetries of differential equations.  This package its theory and implementation was developed in collaboration with Allan Wittkopf and Colin Rust.  An interest was also developed in algorithmically determining the Cartan structure of Lie pseudo groups of symmetries with Ian Lisle, and the use of invariant differential operators to facilitate such computations.

Reid's recent research has been to use numerical techniques to determine geometric features of the solutions of approximate nonlinear PDE (including overdetermined PDE).  Applications include approximate symmetry and geometry of PDE.  This has as a by-product yielded stable methods for numerical algebraic geometry, using ideas from jet geometry.  

Most recently Reid's research has explored approximate real algebraic geometry, which is much more difficult than the easier complex case.  In particular methods from optimization, such as semi-definite programming have been used in conjunction with methods jet geometric techniques.  Collaborators include Henry Wolkowicz and Fei Wang.