Gabriele C. Nebe is a professor of mathematics at the Abteilung Reine Mathematik of the Universität Ulm in Germany. One aspect of her work is the construction and investigation of dense lattices and good codes, which can be applied to correct errors in information transmission systems. With Eric Rains and Neil Sloane, she is writing a book on codes and their connection to the invariant theory of groups.
As a Radcliffe fellow, Nebe plans to investigate integral representations of finite groups. Many interesting conjectures in representation theory can be formulated in the language of (p-adic) group rings. She wants to continue her study of these rings and develop new methods with which to analyze and describe them.
In Nebe’s thesis, for which she received two prizes from the University of Aachen, she classified maximal finite matrix groups. Since these groups are automorphism groups of highly symmetric lattices, this classification led to the discovery of many interesting lattices. In the academic year 1995–1996, Nebe continued her study of lattices as a DFG Fellow at the University of Bordeaux, France. Back in Aachen, she became interested in the more abstract topic of group rings. In her habilitation thesis, she developed a powerful method that allows her to describe an infinite series of rather complicated integral group rings. For this work and her construction of extremal lattices, she received the Merckle-Forschungspreis in 2002.