# 2021-22

### In Term 1 seminars are held on Tuesdays at 15:00 on Zoom. In Term 2 seminars will be held on Mondays at 17:00 in B3.02 and via MSTeams.

#### Term 1:

16th November: Lucia Morotti (Hannover University).

Title: Decomposition of spin representations of symmetric groups in characteristic 2

Abstract: Any representation of a double cover of a symmetric group $tilde Sn$ can also be viewed as a representation of Sn when reduced to characteristic 2. However not much is known about the corresponding decomposition matrices. For example, while decomposition numbers of Specht modules indexed by 2-parts partitions are known, the decomposition numbers of spin irreducible modules indexed by 2-parts partitions are still mostly unknown, with in most cases only multiplicities of maximal composition factors (under a certain ordering of the modular irreducible representations) being known.

In this talk I will characterise irreducible representations that appear when reducing 2-parts spin representations to characteristic 2 and describe part of the corresponding rows of the decomposition matrices.

30th November: Dávid Szabó (Rényi Institute, Budapest).

Title: Class 2 nilpotent and twisted Heisenberg groups

Abstract: Every finitely generated nilpotent group G of class at most 2 can be
obtained from 2-generated such groups using central and subdirect
products. As a corollary, G embeds to a generalisation of the 3 x 3
Heisenberg matrix group with entries coming from suitable abelian groups
depending on G. In this talk, we present the key ideas of these statements and briefly
mention how they emerged from investigating the so-called Jordan
property of various transformation groups.

7th December: Barbara Baumeister (Bielefeld University).

14th December: Ralf Koehl (Giessen University).

#### Term 2:

17th January: Dave Benson (Aberdeen)

24th January: Vincent Knibbeler (Loughborough)

31st January: Leonid Positselski (Czech Academy of Sciences)

7th February: Nick Gill (Open University)