Personal tools

You are here: Home / BLOC / Seventy-third BLOC meeting

# Seventy-third BLOC meeting

BLOC

Bristol Leicester Oxford Colloquium

The seventy-third meeting will be held on Friday 27th May 2016 in the Department of Mathematics, City University, London. The room is BG02.

Programme:

12.15 Lunch: Banana Tree, 418 St. Johns Street

13.30 Martina Lanini (Edinburgh) Filtered modules on moment graphs and periodic patterns
(Abstract below)

14.30 Drew Duffield (Leicester) Auslander-Reiten Components of Brauer Graph Algebras
(Abstract below)

Tea

16.15 Jay Taylor (Padova) Self Normalising Sylow 2-Subgroups
(Abstract below)

Abstracts:

Martina Lanini: In this talk, I will present a joint project with Peter Fiebig, aimed at developing new tools to attack problems in the representation theory of complex affine Kac-Moody algebras and algebraic groups in positive characteristic. I will introduce a new combinatorial category, realised using moment graph techniques, which exhibits a certain periodicity behaviour. The periodic patterns appearing in our category are the same expected to govern certain multiplicity formulae for representations of the above mentioned objects.

Drew Duffield: One approach to the representation theory of algebras is to study the module category of an algebra. This can be achieved, at least in part, by describing the indecomposable modules of an algebra and the irreducible morphisms between them. The Auslander-Reiten quiver of an algebra is a means of presenting this information. Of particular interest is a class of algebras known as Brauer graph algebras. These are symmetric special biserial algebras that have a presentation in the form of a (decorated) ribbon graph called a Brauer graph. An interesting feature of Brauer graph algebras is that one can often read off aspects of the representation theory by performing a series of combinatorial games on the Brauer graph, which removes the need for potentially difficult and lengthy calculations. The purpose of this talk is show that one can read off information regarding the Auslander-Reiten theory of a Brauer graph algebra from its underlying Brauer graph. We begin by providing an algorithm for constructing the stable Auslander-Reiten component containing a given indecomposable module of a Brauer graph algebra using only information from its Brauer graph. We then show that the structure of the Auslander-Reiten quiver is closely related to the distinct Green walks around the Brauer graph and detail the relationship between the precise shape of the stable Auslander-Reiten components for domestic Brauer graph algebras and their underlying graph. Furthermore, we show that the specific component containing a given simple or indecomposable projective module for any Brauer graph algebra is determined by the edge in the Brauer graph associated to the module.

Jay Taylor: It is well known that the character table of a finite group does not determine the group up to isomorphism. This fact naturally leads one to consider how much structural information about a finite group can be determined from its character table. If G is a finite group and $\ell$ is an odd prime then Navarro, Tiep, and Turull, were able to show that G has a self-normalising Sylow $\ell$-subgroup if and only if G has no non-trivial irreducible character whose degree is coprime to $\ell$ and whose values are contained in a cyclotomic field $\mathbb{Q}(\zeta)$ with $\zeta$ a primitive nth-root of unity with n coprime to $\ell$. In particular, the existence of a self-normalising $\ell$-Sylow can be read from the character table. In this talk we will discuss work on extending this result to the case where $\ell$=2. This is based on joint work with Mandi Schaeffer-Fry.

Please let Chris Bowman know by May 20th if you are coming to the meeting, especially if you are coming for lunch and/or wish to stay for a meal in the evening.

There will be time for informal discussions during the day.

The meeting is supported by an LMS Scheme 3 grant. This is used to help offset travel costs for those from institutions participating in the scheme, with priority given to speakers and postgraduates. Please note that, if travelling by train, then you should purchase an advance ticket where possible, since the grant will not cover standard open return tickets to London during peak hours.

Travel information is HERE.

Contact details

Department of Mathematics
University of Leicester
Leicester LE1 7RH
United Kingdom

Tel.: +44 (0)116 229 7407

Campus Based Courses