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

Simple Groups

University of Birmingham
Wednesday 11 November 2026

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

13:00 Marina Anagnostopoulou-Merkouri (University of Bristol)

Regular orbits of simple groups

Let G be a transitive permutation group on a set Ω with point stabiliser H. A base for G is a subset of Ω whose pointwise stabiliser in G is trivial. The minimal size of a base is called the base size of G, denoted by b(G), and this classical invariant has been widely studied for many years, finding many applications.

We will see that b(G) coincides with the smallest positive integer k such that G has a regular orbit on the Cartesian product (G/H)^k. As a natural generalisation, we can consider the minimal number r such that G has a regular orbit on (G/H_1) x ... x (G/H_r) for any core-free subgroups H_1,..., H_r of G. We call this invariant the regularity number of G.

In this talk, we will explain how a combination of probabilistic, combinatorial, computational and geometric methods can be used to study the regularity number of finite almost simple and simple algebraic groups, as well as several other related problems. In particular, we will discuss a generalisation of Cameron’s famous base size conjecture and some recent progress on similar problems for simple algebraic groups.

I will report on joint work with Tim Burness.

14:00 Martin van Beek (University of Manchester)

Realizing representations in finite groups and fusion systems

We know a great deal about the modular representation theory of finite groups and the p-local structure of finite simple groups. Across these groups, the same actions and representations seem to recur in their p-local subgroups. This raises two questions:

• Which actions and representations can occur in the p-local subgroups of finite simple groups?

• When can we recognize a finite simple group from a  p-local subgroup exhibiting one of these actions?

In this talk, we will answer these questions for certain classes of groups and representations, using the language of fusion systems.

15:00 Tea & Coffee

15:30 Inna Capdeboscq (University of Warwick)

[title TBA]

[abstract TBA]

No registration is required, but registration for dinner has closed.

The School of Mathematics at the University of Birmingham is committed to providing a welcoming, inclusive and safe community for all. Please see their Inclusivity Charter for staff, students and visitors.

Future meetings

The following meeting will held at the University of Warwick on Wednesday 10 February 2027. 

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 supported by a London Mathematical Society Scheme 3 Grant and by the Isaac Newton Institute and the Heilbronn Institute (Additional Funding Programme for Mathematical Sciences, delivered by EPSRC EP/V521917/1).

Organisers

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

General queries can be directed to Scott Harper.