Groups in Galway 2012
1112 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.
Speakers
Confirmed speakers at the moment include

Martin Bridson (Oxford)

Rachel Camina (Cambridge)

Graham Ellis (NUI Galway)

Derek Holt (Warwick)

Jim Howie (Edinburgh)

Ian Leary (Southampton)

Conchita Martínez Pérez (Zaragoza)

Colva RoneyDougal (St Andrews)

Gerhard Röhrle (Bochum)
Schedule
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
10.0010.45
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 nontrivial 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 nonpositively curved 2complexes.
10.4511.15
Coffee/tea
11.1512.00
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 3manifolds 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.
12.151.00
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.
1.003.00
Lunch
3.003.45
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 2dimensional 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.
4.004.45
Gerhard Röhrle
Complete reducibility, geometric invariant theory and separability
We introduce Serre's notion of a Gcompletely 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 Gcomplete reducibility due to Serre
and present
some recent related work extending a fundamental result due to Jantzen on the semisimplicity of
smalldimensional
Gmodules to Gcompletely 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
9.1510.00
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 BSGSbased methods.
10.1511.00
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 prop group, that
is,
an inverse limit of finite pgroups, or, less technically, an infinite
group that can be "understood" by looking at its finite pgroup quotients.
Prop 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
prop groups, such as those of finite coclass, or those which are padic
analytic, and so provides an interesting test case for possible results
about prop 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 prop groups; technical terms will be explained.
11.0011.30
Coffee/tea
11.3012.15
Colva RoneyDougal
Generalisations of small cancellation
I'll describe some current workinprogress 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 finitelypresented
stringrewriting structures, including various types of group presentation.
12.301.15
Graham Ellis
Cohomology of some arithmetic groups
I'll describe an algorithm for calculating classifying spaces and cohomology of some
arithmetic groups.
Travel
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 payanddisplay
parking places for visitors. Cars parked in other spaces on the NUI
Galway campus and not displaying a valid parking permit will be
clamped.
Accommodation
The following hotels and guest houses are convenient for the NUI Galway campus:
 The Westwood House Hotel,
091 521 442
 The House Hotel,
091 521 442
 Bologna B&B, 091523792
 Aneesha B&B, 091524250
 Ashgrove House B&B, 091581291
 Villanova B&B, 091524849
 Coolavalla B&B, 091522415
 Rosgal B&B, 091 524723
 De Sota B&B, 091585064
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
 The Millennium Research Fund, NUI Galway
 The Office of the Registrar and Deputy President, NUI Galway
 School of Mathematics, Statistics and Applied Mathematics, NUI Galway
 The Irish Mathematical Society