Algorithmic Invariant Theory

Gregor Kemper
Technische Universitaet Muenchen
Zentrum Mathematik - M11, Boltzmannstr. 3
85748 Garching, Germany
Phone: +49 89 289 17454, Fax: +49 89 289 17457
e-mail: kemper@ma.tum.de
http://www-m11.ma.tum.de/~kemper

Table of contents

Short Abstract

Invariant theory seeks to describe the set of all polynomial functions which are constant on the orbits of a given group action, and studies their capabilities of separating orbits. One of the factors that gave new impetus to this classical subject was the emergence of new computational methods and faster computers. Nowadays, invariant theory is at the crossroads of algebraic geometry, computational commutative algebra, and representation theory. In this tutorial we study the classical questions of invariant theory and their relation to computational issues. The topics will include finite generation, Derksen's algorithm, degree bounds, and separating invariants.