Large Structures Seminar: Evelyne Hubert

The original motivation for this research in collaboration with George Labahn (U. of Waterloo, Canada) is to provide an algorithmic scheme for the reduction of parameters in physical, chemical or biological models by elaborating on the interpretation of this problem as ‘nondimensionalisation’.

Scalings form a class of group actions on affine spaces that have both theoretical and practical importance. A scaling is accurately described by an integer matrix. Tools from linear algebra over the integers are exploited to compute a minimal generating set of rational invariants, trivial rewriting and rational sections for such a group action. The primary tools used are Hermite normal forms and their unimodular multipliers.

The same information is sufficient to offer a complete symmetry reduction scheme for either polynomial systems or dynamical systems. A special case of the symmetry reduction algorithm applies to reduce the number of parameters in mathematical models.

Our approach is reminiscent of the premisces of the Buckinmgham-Pi theorem. Note though that we do not resort to fractional powers and that we can rewrite the original equations in terms of the new variables by a simple substitution.