Combinatorics in finite classical groups

• Applicant: Professorin Dr. Margit Rösler, since 10/2023
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 459964179

Extremal combinatorics of subsets of a finite set is intimately related to classical coding and design theory. There are well known analogies between the combinatorics of subsets of a finite set and the combinatorics of permutations of a finite set on one hand and the combinatorics of subspaces of a finite vector space on the other hand. Within this project we consider these analogies simultaneously and study the combinatorics of automorphims of finite vector spaces, in particular that of finite classical groups. We investigate extremal combinatorial problems within this setting, which can be considered as q-analogs of classical extremal combinatorial problems arising in the symmetric group. In particular we study intersecting sets, packings, and different notions of transitivity for subsets. Such concepts can be interpreted as codes and designs in the conjugacy class association scheme of the underlying group, which brings in powerful algebraic methods, including representation theory of finite classical groups.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Professor Dr. Kai-Uwe Schmidt, until 10/2023 (†)