2nd meeting: Representations of Groups

University of Birmingham, Wednesday January 14th, 2015

If you wish to attend, please contact b.fairbairn [at] bbk.ac.uk

2:00-3:00 David Stewart (Cambridge) Cohomology for finite and algebraic groups

The representation theory for finite groups of Lie type in defining characteristic is rather complicated, but owing to the link with algebraic groups, there are quite a few tools. I want to give an overview of some of the theory and show how some of these can be used to bound the cohomology of finite groups with coefficients in simple modules, motivated by an old conjecture of Guralnick.

3:00-4:00 Melanie de Boeck (Kent) Foulkes modules for the symmetric group

The action of the symmetric group \mathfrak{S}_{mn} on set partitions of sets of size mn into n sets of size m gives rise to a permutation module called the Foulkes module.  Structurally, very little is known about Foulkes modules, even over \mathbb{C}.  In this talk, we will introduce Foulkes modules and their twisted analogues before presenting some results which shed light on the irreducible constituents of the ordinary characters of twisted Foulkes modules.

4:00-4:30 Coffee

4:30-5:30 Gunter Malle (Kaiserslautern) Local-global conjectures in the representation theory of finite groups

More than 60 years ago Richard Brauer developed the theory of representations of finite groups over arbitrary fields. It showed a strong connection between the representation theory of a finite group and that of its p-local subgroups, for p a prime. Many more such connections have been observed in the meantime, but most of these are still conjectural.

Recently, a new reduction approach has offered the hope to solve all of these fundamental conjectures by using the classification of finite simple groups.  In our talk we will try and explain the nature of these problems and will report on recent progress which might eventually lead to a solution of these long standing fundamental questions.

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