Mini-Workshop: Arithmetik von Gruppenringen

Abstract

The mini workshop "Arithmetic of group rings" was attended by 16 participants from Belgium, Brazil, Canada, Germany, Hungary, Israel, Italy, Romania and Spain. The expertise was a good mixture between senior and young researchers. It was a very stimulating experience and thesize of the group allowed excellent discussions amongst all participants. Very fruitful were the problem sessions, resulting in the problems listed at the end of this report.

The main highlights of the conference were:

The complete calculation of the projective Schur subgroup of the Brauer group by Aljadeff and del Rio.

Hertweck's solution of the first Zassenhaus conjecture for finite metacyclic groups.

the description of special subgroups of the unit group of integral group rings, such as the hypercentre and the finite conjugacy centre, and the relation with respect to the normalizer of the trivial units.

discussion of the present state of art via several survey talks presented and the problem sessions

The group $G$ determines its integral group ring $\mathbb{Z}G$ and its group $V(\mathbb{Z}G)$ of normalized units. Several talks addressed the interplay of the cohomological properties of these three objects. Further topics included twisted group rings, group rings over local rings, polynomial growth and identities, orders and semigroup rings, Lie structure, representation-theoretic and algorithmic methods.