*ON APPLYING GROUP RINGS TO FINITE GEOMETRIES
*

Dieter Jungnickel, University of Augsburg, Germany

Whenever one studies a finite geometry with an abelian collineation group, there is a good chance that group rings can be applied. Indeed, in many situations they are the basic tool that is needed to get significant non-existence results, though they can also be useful for constructive applications. In spite of this, the method is less popular among geometers than it ought to be, in particular in Italy. So my aim is to advertise this approach, by giving a leisurely introduction and concentrating on just a few (but important) examples, focusing on finite projective planes. The lecture is part of the Socrates program, and thus the intended audience is mainly graduate students and post-docs.