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Contributions to Training

Allan Wittkopf: I am co-supervising Allan for his Ph.D (with M. Monagan of SFU). [Allan's Homepage] . Allan helped develop some of the key ideas and implementations for the Standard Form Package. He has also implemented the RIF package, which is available from his web address, and also in Maple V, Release 6 (due in early 2000). He is a specialist in large scale symbolic computation. He obtained an MSc from SFU in 1994 (his supervisors were T. Tang and R. Russell).

Colin Rust: I co-supervised Colin as a PhD student with W. Fulton (Thesis: Rankings of Derivatives for Elimination Algorithms and Formal Solvability of Analytic Partial Differential Equations, University of Chicago, 1998). He investigated and solved a problem I had posed to him of classifying all complete orderings of partial derivatives left invariant under differentiation. The classical Riquier Rankings are a special case of his classification. Also using Gröbner basis methods, he developed a rigorous theory of elimination algorithms and related formal existence and uniqueness theorems for systems of analytic PDE. [Retrieve PostScript] [Retrieve DVI] .

Ilias Kotsireas: is the first Postdoctoral fellow to arrive at the newly formed Ontario Research Centre for Computer Algebra. I am co-supervising Ilias in my rôle as a principal scientist ORCCA. He has worked on the N-body problem, using Gröbner Basis Computations in terms of invariants of symmetry groups. [Ilias' Homepage] .

Patrick Doran-Wu: I was Patrick's Ph.D co-supervisor (with Bluman) at UBC (Thesis: Extension of Lie's Algorithm: A Potential Symmetries Classification of PDE's, (UBC, 1996)). [Retrieve Thesis] . Patrick made extensive use of the Standard Form Package in his Ph.D investigation of a generalization of Lie symmetry called Potential symmetry. The use of the Standard Form Package enabled him to perform experiments which led to new results about potential symmetries (e.g. see ``The Use of Factors to Discover Potential Systems of Linearizations'', Bluman G.W. and Doran-Wu P.R., Acta Applicandae Mathematicae Vol 41, pp1-23, 1995).

Ian Lisle: graduated with a Ph.D in applied mathematics from UBC in 1992 (Thesis: Equivalence Transformations for Classes of Differential Equations, UBC, 1992). [Retrieve Thesis] [Lisle's Homepage] . He formulated moving frame versions of my standard form and initial data algorithms, and applied them in the theory of local equivalence for differential equations given in his thesis. He showed that performing calculations in moving frames invariant under an equivalence group of a family of PDEs can lead to considerable simplifications in group classifying such families. He is a specialist in the geometry and structure of infinite Lie pseudogroups of differential equations.

Ping Lin: Obtained his Ph.D from UBC supervised by Uri Ascher (Thesis: Regularization Methods for Differential Equations and Their Numerical Solution, UBC, 1995). He has been using techniques from Differential-Algebraic Equations to facilitate the numerical solution of the Navier-Stokes equations. [Retrieve Thesis] [Ping's Homepage] .

Alan Boulton: I was Alan's co-supervisor (with Bluman) at UBC for his Master's thesis (New symmetries from old: exploiting Lie algebra structure to find symmetries of differential equations, 1993, UBC, Vancouver). [Retrieve PostScript Thesis] . He showed that the a priori knowledge of some subalgebra of Lie symmetries of a physical system governed by differential equations can be used to considerably simplify the problem of explicitly finding the full group of symmetries of such systems. The Standard Form and Initial Data Algorithms were important parts of his method.

Next: Administrative and Committee Work Up: Curriculum Vitae for Greg Previous: Selected Seminars
Greg Reid 2006-08-31