# Algebra seminars, 2011-12

## In 'Past algebra seminars'

### Automorphisms of soluble groups

#### Paul Flavell, University of Birmingham

**Thursday 29 September 2011, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Polygonal complexes II

#### Ian Leary, University of Southampton

**Thursday 6 October 2011, 16:00-17:00 Watson Building, Lecture Room A**

With T Januszkiewicz, R Valle and R Vogeler I have been working on classifying polygonal complexes that admit a flag-transitive group of symmetries and have either the complete graph or the octahedral graph as vertex link. When the polygons have at least 6 sides we have a classification result. In this talk I intend to focus instead on the partial results that we have for triangles, squares and pentagons.

(The 'II' at the end of the title reflects the fact that I gave a talk on this work, focussing on polygons with at least 6 sides, at the workshop 'Geometric presentations of finite and infinite groups' at Birmingham this summer.)

### Affine W-algebras

#### Tomoyuki Arakawa, Kyoto University

**Thursday 13 October 2011, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Generalizations of representations of quivers and preprojective algebras

#### Bill Crawley-Boevey, University of Leeds

**Thursday 27 October 2011, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Topological Representations and the Model Theory of Abelian Group Rings

#### Peter Pappas, University of Oxford

**Thursday 3 November 2011, 16:00-17:00 Watson Building, Lecture Room A**

This talk will be accessible to non-specialists and details how model theory naturally leads to specific representations of abelian group rings as rings of global sections. The model-theoretic approach is motivated by algebraic results of Amitsur on the Semisimplicity Problem, on which a brief discussion will first be given.

### On simple modules for the Brauer algebra

#### Maud De Visscher, City, University of London

**Thursday 10 November 2011, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Commuting classes of matrices with entries from a finite field

#### John Britnell, University of Bristol

**Thursday 17 November 2011, 16:00-17:00 Watson Building, Lecture Room A**

This talk addresses the problem of deciding whether two classes of similar matrices contain elements which commute. I shall indicate how, over a finite field, this problem reduces (up to a field extension) to the case of nilpotent classes. The nilpotent case has been studied extensively, but chiefly over algebraically closed fields, particularly in characteristic 0. I shall describe what is known about it over various fields, and mention some open questions which have recently attracted attention.

### Fixed-point-free automorphisms of p-groups

#### Sarah Astill, University of Bristol

**Thursday 1 December 2011, 16:00-17:00 Watson Building, Lecture Room A**

Finite groups with a fixed-point-free automorphism of prime order, *r* say, are nilpotent and what's more there exist bounds on the nilpotency class dependent on the prime *r*. If we instead considered a *p*-group with a small simple group of automorphisms which contain an element of order *r* acting fixed-point-freely then can we give stronger bounds on the nilpotency class?

### Local representation theory

#### David Craven, University of Birmingham/Oxford

**Thursday 8 December 2011, 16:00-17:00 Watson Building, Room 310**

The local-global principle in representation theory of finite groups is one of the most actively researched areas of algebra. Recently, the two theories of fusion systems and perverse equivalences have started to shed light on this area. In this talk I will survey the most recent developments in this field, which touches on finite groups, derived categories, algebraic geometry, combinatorics, fusion systems and algebraic topology.

### Extremely primitive groups

#### Tim Burness, University of Southampton

**Thursday 12 January 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Modern methods and recent progress in integer factorization

#### Song Yan, University of Bedfordshire

**Thursday 19 January 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Group presentations where the generators weigh more than the relators

#### Peter Kropholler, University of Glasgow

**Thursday 26 January 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Unipotent blocks of GL_n(q) and Deligne-Lusztig varieties

#### Olivier Dudas, University of Oxford

**Thursday 2 February 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Calculating conjugacy classes of Sylow *p*-subgroups of Chevalley groups

#### Peter Mosch, Ruhr-Universität Bochum

**Thursday 9 February 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### A quaternionic approach to E_{7}

#### Rob Wilson, Queen Mary, University of London

**Thursday 16 February 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### On the archaeology of unipotent radicals

#### David Stewart, University of Oxford

**Thursday 23 February 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Is Babai afraid of spiders?

#### Nick Gill, Open University

**Thursday 1 March 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Computation in finite matrix groups

#### Derek Holt, University of Warwick

**Thursday 15 March 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Local/global conjectures in representation theory

#### Charles Eaton, University of Manchester

**Thursday 22 March 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### The spread of a finite group

#### Simon Guest, University of Southampton

**Thursday 10 May 2012, 14:00-15:00 Watson Building, Lecture Room A**

Let *G* be a finite group. We say that *G* has spread at least *k* if for any *k* distinct nontrivial elements *x*_{1},...,*x _{k}* ∈

*G*, there exists

*y*∈

*G*such that

*x*and

_{i}*y*generate

*G*for every

*i*=1,...,

*k*. If

*G*does not have spread at least 1 then

*G*is said to have spread 0. Using elementary methods we can prove that if

*G*has a non-trivial normal subgroup

*N*such that

*G*/

*N*is non-cyclic then

*G*must have spread 0. It has been conjectured by Guralnick and Kantor that the converse is true. They can prove that the converse holds in many cases. We will discuss some recent joint work with Tim Burness involving the remaining cases.

### The generating graph of direct powers of simple groups

#### Eleonora Crestani, University of Southampton

**Thursday 10 May 2012, 15:00-16:00 Watson Building, Lecture Room A**

For a finite group *G*, the generating graph Γ(*G*) is a graph whose vertices are the non-identity elements of *G* and two distinct vertices are connected by an edge if and only if they generate *G*. Many results on the generation of finite simple groups *G* can be equivalently stated as theorems on the generating graph of *G*: this assures to Γ(*G*) several good properties. In this talk, we will consider Γ(*G ^{n}*), where

*G*is a finite simple group and

*G*a direct product of

^{n}*n*copies of

*G*: we will discuss whether the good generation properties of

*G*affect the generating graph Γ(

*G*) with particular attention to some questions on the diameter of Γ(

^{n}*G*).

^{n}### Products of finite nilpotent groups

#### John Cossey (Canberra)

**Thursday 10 May 2012, 16:00-17:00 Watson Building, Lecture Room A**

Suppose *A* and *B* are subgroups of a group *G*. We say that *G* is the product of *A* and *B* if *G*=*AB*={*ab* : *a* ∈ *A*, *b* ∈ *B*}. A natural question to ask is whether properties of *G* can be deduced from properties of *A* and *B*. There is an extensive literature on this question. Many properties have been considered- see for example the book of Amberg, Franciosi and de Giovanni and that of Ballester-Bolinches, Esteban-Romero and Asaad.

Many results concentrate on the case of *A* and *B* nilpotent. Most results are aimed at restricting the structure of non-nilpotent products *G*; for example, under appropriate restrictions, *G* will be supersoluble. However very little is known about the structure when *G* is itself nilpotent.

If *G* is nilpotent, there are many invariants we could consider: derived length, class, coclass, breadth and rank as examples. Very little is known about any of these. I will describe what is known.

### Using model theory to understand modules

#### Mike Prest, University of Manchester

**Thursday 17 May 2012, 16:00-17:00 Watson Building, Lecture Room C**

Abstract not available

### TBA

#### Robert Marsh, University of Leeds

**Tuesday 29 May 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

### Geometric characterizations of symplectic groups, modules and Lie algebras

#### Hans Cuypers, Technische Universiteit Eindhoven

**Thursday 31 May 2012, 16:00-17:00 Physics West 103**

Abstract not available

### Kazhdan–Lusztig Cells and Categorification

#### Dmitriy Rumynin, University of Warwick

**Thursday 7 June 2012, 16:00-17:00 Watson Building, Lecture Room A**

Abstract not available

We address the challenges facing society and the economy, from shedding light on the refugee crisis, to character education in schools, through to developing leaders in the NHS.