School of Mathematics, Statistics and Physics

Seminar Item

Pure Maths (Algebra and Geometry) - Nick Gill (South Wales)

Using model theory to "classify" finite permutation groups

Date/Time: Monday 30 November, 1.30pm - Algebra and Geometry Seminar

Venue: Zoom

Abstract: Building on work of Lachlan, the model theorist Greg Cherlin showed that, in principle, it is possible to classify permutation groups using homogeneous actions on finite relational structures. This classification has a number of rather attractive properties, most notably by its elimination of sporadic behaviour: all permutation group actions occur naturally in infinite families in a certain precise way.

I will give a description of how this classification works, and then consider the problem of working out exactly where any given permutation group should fit in such a classification. To do this one needs to work out the RELATIONAL COMPLEXITY of a finite permutation group, a statistic that is easy to describe but rather tricky to calculate.

The work I will describe in this talk has all been conducted in collaboration with Pablo Spiga as well as, at various times, Bianca Loda, Francesca Dalla Volta, Scott Hudson, Francis Hunt and Martin Liebeck.