Representation Theory of Finite Groups and Related Topics

Areas of research interest of Nadia Mazza

The study of finitely generated modules over non semi-simple group algebras is a tantalising research subject that finds applications in several other areas of mathematics. In particular, a classification of simple modules is not possible in general; one objective is thus to determine representations that are “interesting” and “classifiable”. Endotrivial modules form such a family of modules, and the main interest in their study is related to the stable module category. Hence, cohomological algebra is also deeply rooted in this research area. In addition, links between modular representations of finite groups and topology are provided by fusion systems. This can be shown in the Martino-Priddy conjecture, which relates the cohomology of the classifying space of a finite group, over a field of prime characteristic p, with the fusion defined by that finite group on one of its Sylow p-subgroups. Recently, computer algebra has played a notable role in obtaining results in this area, through use of software such as MAGMA or GAP.