This talk will be gived by Professor Frank Kutzschebauch in the 2016/2017 CAS research group Several Complex Variables and Complex Dynamics.

Abstract

Given a reductive group $G=K^\C$ ($K$ maximal compact subgroup) acting algebraically/holomorphically on $\C^n$.

Is there an algebraic / holomorphic change of variables which conjugates the action of $G$ into a linear action?

We review the history mainly of the holomorphic part of the problem. Then we discuss the counterexamples to the problem found by Derksen and the speaker and explain recent positive results of Larusson, Schwarz and the speaker.