Risc Colloquium

Computational efforts in invariant theory have been mainly focused on polynomial invariants of linear actions. Yet rational invariants have interesting geometric properties and they can be computed for a wider class of relevant actions. The talk will first review a construction that applies to any rational action of an algebraic group and computes generating sets of rational invariants endowed with rewrite rules. It is based on Gröbner bases. I will then focus on diagonal actions of tori and finite groups and show how the computations rely solely on linear algebra over the integers. The constructions induce complete symmetry reduction schemes of polynomial and dynamical systems and applies to great effect for parameter reduction in models from mathematical biology.

This talk is partly based on joint works with Irina Kogan (North Carolina State University) or George Labahn (University of Waterloo)