Orbit Meetings take place on Wednesday afternoons three times a year across the Universities of Birmingham, Manchester and Warwick. The meetings focus on topics in group theory and representation theory. Attendees from any university are welcome at the meetings.

Next Meeting

University of Birmingham
Wednesday 12 November 2025

meeting at 13:00–16:30 followed by drinks and dinner
talks in Lecture Theatre A (G23), Watson Building (R15 on campus map)

13:00 Patricia Medina Capilla (University of Warwick)

Crown-based powers and their applications

Initially discovered by Gaschutz in the 1950s, before later being extended by Dalla Volta and Lucchini in the 1990s, the theory of crowns in finite groups has a long and rich history, with numerous applications. Central to this theory is the observation that establishing generation results for a particular class of groups, known as crown-based powers, is often sufficient to derive corresponding results for all finite groups. In this talk, we will explore how this framework can be applied to a range of generation problems, highlighting in particular how the structure of a group’s chief factors determines its generation behaviour.

14:00 Coen del Valle (Open University)

The binary actions of sporadic groups

An action of a finite group is called binary if the permutation group it induces has relational complexity 2. We will begin by discussing the concepts of relational complexity and binary actions of permutation groups, before exploring some recent progress towards classifying the binary actions of the finite simple groups, with a particular emphasis on the recently completed classification of binary actions of the sporadic groups.

15:00 Tea & Coffee

15:30 Martin Liebeck (Imperial College London)

p-exceptional permutation groups and applications to character theory

Let p be a prime. A p-exceptional permutation group is a transitive group G for which p divides the order of a point stabilizer H, but divides none of the orbit sizes of H. I will describe various classification results for p-exceptional groups, and show how they apply to questions in character theory, such as generalisations of the Gluck-Wolf theorem.

No registration is required, but if you plan to join for an early dinner (approx. 18:00) please complete this short form by Tue 04 Nov.

Future Meetings

The following meeting will take place at the University of Warwick on Wednesday 11 February 2026.

PhD Students

We strongly encourage PhD students to attend Orbit Meetings. These meetings are a great way to get know other people working in the field at nearby universities. To enable this, we will help towards travel costs for PhD students (see details here).

Funding

The Orbit Meetings are funded by an LMS Scheme 3 Grant.

Organisers

Scott Harper (Birmingham)
Jay Taylor (Manchester)
Gareth Tracey (Warwick)

General queries can be directed to Scott Harper.