1 Dec 2005; Mat-Nat Faculty (UITO), room U6=C321. Thursday 10:15-12:00

Markus Schmidmeier (Florida Atlantic University, USA; Visiting Professor NTNU, Norway)  

"Nilpotent Linear Operators".

Linear operators occur in abundance, within mathematics and outside. We focus on operators which act nilpotently on a finite-dimensional vector space.

The Invariant Subspace Problem asks for the classification of all triples (V,U,T), where V is a finite dimensional vector space, T:V->V a linear operator acting nilpotently, say with nilpotency index n, and U a subspace of V which is invariant under the action of T.

Obviously, the classification problem depends on n, and it will turn out that the decisive case is n=6.  For n<6, there are only finitely many isomorphism types of indecomposable triples, while for n>6 we deal with what is called a problem of ``wild'' type. For n=6 we will exhibit a description of all indecomposable triples obtained in joint work with Claus M. Ringel (Bielefeld).