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 E7
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 x1,...,xk ∈ G, there exists y ∈ G such that xi and 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(Gn), where G is a finite simple group and Gn a direct product of n copies of G: we will discuss whether the good generation properties of G affect the generating graph Γ(Gn) with particular attention to some questions on the diameter of Γ(Gn).
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