Computational Invariant Theory and Applications

Gregor Kemper

When a problem displays some symmetry, invariant theory is usually a helpful tool for the solution of the problem. This applies to problems like algebraic equations, equivariant dynamics, image processing and some problems in materials science. On the other hand, the computation of invariants requires a heavy use of methods from computational commutative algebra.

In this talk I will give a survey of the tools and difficulties involved in the computation of invariant rings. We will also look at some applications, and at structural questions concerning the invariant ring. Apart from being interesting in themselves, the structural properties have a strong influence on the feasibility of computations.