Gabriel-Roiter measure (H. Krause) 
----------------------

Given a finite dimensional algebra A, the Gabriel-Roiter measure 
provides a method to study the combinatorial properties of the set of 
isomorphism classes of indecomposable A-modules. For instance, Roiter used 
this measure to prove the first Brauer-Thrall conjecture. More recently, 
Ringel extended this theory, proving for example a refinement of the first 
Brauer-Thrall conjecture. In my lecture, I will give an elementary 
introduction into this beautiful theory. A reference is Ringel's survey 
"Foundation of the Representation Theory of Artin Algebras, Using the 
Gabriel-Roiter Measure", which is available from his homepage 
http://www.math.uni-bielefeld.de/~ringel/.