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

Representation Theory

University of Manchester
Wednesday 20 May 2026

Timings: meeting at 13:00–16:30, followed by dinner.
Location: talks in Frank Adams Seminar Room, First Floor, Alan Turing Building (see this interactive campus map).

13:00 Carlos Tapp Monfort (Rutgers University)

About Feit's conjecture

In 1979, Walter Feit proposed a conjecture asserting that for every finite group G and every irreducible character χ of G, there should be an element of G whose order is precisely the conductor of χ. This problem is still open. More recently, R. Boltje, A. Kleshchev, G. Navarro, and P. Tiep established a reduction theorem for the conjecture. In this talk, I will explain the associated inductive condition and present recent developments for finite groups of Lie type of small rank.

14:00 Marie Roth (University of East Anglia)

Unitriangularity of decomposition matrices: the simple adjoint finite groups of exceptional type

In 2020, Brunat–Dudas–Taylor showed that the decomposition matrix of the unipotent ℓ-blocks of a finite reductive group G in good characteristic has unitriangular shape. Their theorem holds under some conditions on the prime ℓ, in particular ℓ being good.

In this talk, we’ll discuss how to extend this result, firstly to ℓ bad (for any G simple) and then to other blocks, called isolated (for G simple of type G2 and F4). This work was part of my PhD thesis under the supervision of G. Malle and O. Dudas. 

15:00 Tea & Coffee

15:30 Michael Bate (University of York)

Simple modules, invariants and structure of affine algebraic groups over a field.

Over algebraically closed fields, there are several reasons to study reductive algebraic groups. For example, they arise naturally when you study representation theory and geometric invariant theory, and they are nicely classified by root data. Over non-algebraically closed fields, the reasons for restricting attention to reductive groups are not quite so clear cut. In this talk I will try to convince you that there is some mileage in considering a wider class of algebraic groups, the so-called "pseudo-reductive groups". These were classified by Conrad-Gabber-Prasad in the 2010s, their simple modules were described by Bate-Stewart in the 2020s, and their subgroup structure and invariant theory is beginning to be investigated. I'll describe some aspects of the representation theory and use that to motivate a couple of problems I am thinking about at the moment.

No registration is required. Dinner will be held at Bundobust Brewery, Oxford Road at 18:00. If you would like to attend dinner, then please complete this form by 06 May.

To enable a successful and welcoming environment, see the University of Manchester's Code of Conduct for this meeting.

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.