The Relational Complexity of a Finite Permutation Group

Explore the concept of relational complexity in finite permutation groups through this insightful lecture from the Hausdorff Trimester Program on Logic and Algorithms in Group Theory. Delve into a numerical invariant suggested by the model theoretic perspective, which equates the study of finite structures with finite permutation groups. Examine a key conjecture stating that almost simple primitive permutation groups with relational complexity 2 must be symmetric groups acting naturally. Discover recent progress towards proving this conjecture, combining theoretical approaches with machine computation. Gain an understanding of what relational complexity measures and learn various methods for determining or estimating it, including structural, group theoretical, and computational approaches. Investigate the speaker's related work on sporadic homogeneous structures and binary permutation groups, with references to published papers and preprints for further exploration.