Fusion systems and localities

• Applicant: Professorin Ellen Henke, Ph.D.
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 511577973

The abstract algebraic concept of a group is central in contemporary mathematics, since it enables us to handle objects of a diverse mathematical origin in a uniform way. Examples of groups arise from symmetries of other mathematical or geometrical objects. On the other hand, a given group leads again to new algebraic, topological and geometric structures. In particular, to every group one associates a topological space, called the classifying space. For finite groups, properties related to a fixed prime p play an important role in more than one context, in particular both in purely algebraic approaches and in the study of classifying spaces of finite groups. The relatively new theory of saturated fusion systems and associated localities leads to a deeper understanding of the connections between the different approaches related to a prime. There are however still many open questions. For the prime 2, it is an important long-term goal to classify the "simple building blocks'' of saturated fusion systems. This project will make a significant contribution to such a classification by implementing a new conceptual approach using localities. Our results will also feed into a simplified proof of the classification of finite simple groups, which is an important theorem listing all the "simple building blocks'' of finite groups.

• DFG Programme: Research Grants