Groups in Galway 2012

11-12 May, 2012

Groups in Galway has been running on an annual basis since 1978. The scope of the conference covers all areas of group theory, applications, and related fields. All who are interested are invited to attend. There is no conference fee. The webpage of last year's Groups in Galway conference is located here.


Confirmed speakers at the moment include


Below is a tentative schedule which may still change but only minimally. All talks will be in AC201 in the Concourse.

Move the cursor over a title for a short abstract.

Friday 11 May

10.00-10.45 Martin Bridson Show me a finite quotient! Using the Higman Embedding Theorem and old ideas of Adian and Rabin, one can prove in a straightforward way that many decision problems for finitely presented groups are unsolvable. But certain natural problems do not lend themselves to this template, and as a result the question of whether they are algorithmically decidable or not has remained unresolved until recently. Such problems include the question of whether a group has a non-trivial linear representation, or a linear representation with infinite image, or whether the group is large (i.e.has a subgroup of finite index that maps onto a free group).

In this talk I'll describe recent work with Henry Wilton in which we prove that all of these problems are undecidable, even among the fundamental groups of compact non-positively curved 2-complexes.

10.45-11.15 Coffee/tea

11.15-12.00 Jim Howie Killing numbers for free products The killing number or weight of a group is defined to be the least number of elements that can generate the group as a normal subgroup of itself. An old conjecture of Lennox and Wiegold is that the killing number of a free product of groups is bounded below by half the number of free factors. Special cases of this conjecture are related to problems in the topology of 3-manifolds to do with Dehn surgery on knots.

I will survey some of the known results about these problems and discuss some possible approaches to solving them in more generality.

12.15-1.00 Conchita Martínez Pérez Equivariant Euler classes and posets of finite subgroups for certain solvable groups Euler classes were first defined by Lück and are closely related to several Euler characteristics which have been considered in the literature. In this talk, we consider solvable groups of cohomological type FP. We use some special properties of their posets of finite subgroups a and some character theory of finite groups to derive a formula for their equivariant Euler class.

1.00-3.00 Lunch

3.00-3.45 Ian Leary Platonic polygonal complexes Examples of platonic polygonal complexes include the five regular solids, the tesselations of the Euclidean and hyperbolic planes by regular polygons, and the 2-dimensional faces of the tesselation of each Euclidean space by equal cubes. There are a lot more, and classifying them all seems to be far too difficult. I shall discuss recent joint work with T. Januszkiewicz, R. Valle and R. Vogeler in which we classify some families of these complexes.

4.00-4.45 Gerhard Röhrle Complete reducibility, geometric invariant theory and separability We introduce Serre's notion of a G-completely reducible subgroup of a reductive linear algebraic group G and give a geometric interpretation which allows to utilize powerful methods from geometric invariant theory in order to study this concept. We discuss some basic representation theoretic criteria for G-complete reducibility due to Serre and present some recent related work extending a fundamental result due to Jantzen on the semisimplicity of small-dimensional G-modules to G-completely reducible subgroups.

4.50 Poster Competition and Wine Reception in C219 in Áras de Brún

7.30 Conference Dinner: Vina Mara, Middle Street

Saturday 12 May

9.15-10.00 Derek Holt Computation in finite matrix groups We start by reviewing the well established "Base and Strong Generator" (BSGS) and the more recent "Composition Tree" approaches to computing in finite matrix groups. The Composition Tree algorithm identifies the composition factors of the group and solves the constructive membership testing problem. We go on to describe how this information can be used as a basis for further structural computations in the groups, such as finding Sylow subgroups, and computing normalisers, centralisers, and conjugacy classes. A longer term goal is to compute character tables of finite matrix groups that are too large for BSGS-based methods.

10.15-11.00 Rachel Camina The Nottingham group - an introduction and a survey of recent results The Nottingham group was introduced to the group theory community by Dave Johnson in the 1990s. It is a fascinating example of a pro-p group, that is, an inverse limit of finite p-groups, or, less technically, an infinite group that can be "understood" by looking at its finite p-group quotients. Pro-p groups arise naturally as Galois groups and are thus also of interest to number theorists. The Nottingham group does not fit into a known class of pro-p groups, such as those of finite coclass, or those which are p-adic analytic, and so provides an interesting test case for possible results about pro-p groups. Since the 1990s many authors have studied and proved results about the Nottingham group and now seems a good time to step back and see what we know. This talk will be an introduction to the Nottingham group and the world of pro-p groups; technical terms will be explained.

11.00-11.30 Coffee/tea

11.30-12.15 Colva Roney-Dougal Generalisations of small cancellation I'll describe some current work-in-progress with Burdges, Linton, Neunhoeffer and Parker. We are using geometric ideas from small cancellation theory to develop a new class of practical algorithms. We solve the word problem in a wide variety of finitely-presented string-rewriting structures, including various types of group presentation.

12.30-1.15 Graham Ellis Cohomology of some arithmetic groups I'll describe an algorithm for calculating classifying spaces and cohomology of some arithmetic groups.


There are regular rail connections from Dublin to Galway, and bus connections from all Irish cities and towns.
From Dublin airport there are also direct busses to Galway operated by Citylink and GoBus.
Galway Airport seems out of operation, but please check again. There are flights to Shannon from Birmingham, Bristol, Edinburgh, Heathrow and Manchester by Aer Lingus.

Directions to NUI Galway by road can be found here .
NUI Galway has a number of pay-and-display parking places for visitors. Cars parked in other spaces on the NUI Galway campus and not displaying a valid parking permit will be clamped.


The following hotels and guest houses are convenient for the NUI Galway campus: Please contact Ireland West for further information about accommodation near NUI Galway.

For further information, please keep an eye on this website which will be updated regularly, or contact the organisers Javier Aramayona and Claas Röver.

Groups in Galway 2012 is generously supported by