An Introduction to Computational Invariant Theory

Invariant theory is a relatively old branch of mathematics, which has always had a strong emphasis on computation and applications. In this talk I will start by explaining some of the basic notions of invariant theory. In particular, we will be interested in separation properties of invariants. Along the way, I will give a survey of some typical applications to areas like graph theory, equivariant dynamics, and computer vision. Then algorithmic methods for computing invariant rings of reductive groups will be discussed. I will address new algorithms covering the case of positive characteristic. As we will see, these algorithms use almost the complete toolkit from computational commutative algebra.