Groups in Galway 2010
(In honour of Professor Ted Hurley in the year of his retirement from teaching)
2829 May, 2010
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. The webpage of last year's Groups in Galway conference is
located here.
Speakers

Marcus Bishop (NUI Galway)

Ian Chiswell (Queen Mary, London)

Anne Henke (Oxford)

Paul Hurley (IBM Research, Zurich)

Ted Hurley (NUI Galway)

Ken Johnson (Penn State Abington)

David Lewis (UCD)

Des MacHale (Cork)

Max Neunhöffer (St. Andrews)

Martin Newell (NUI Galway)

Edmund Robertson (St. Andrews)
Schedule
All talks will be in the room AM150 of the Arts Millenium Building. Move the cursor over a title for a short abstract
Fryday 28 May
09:3010:15
Ted Hurley
Some groups and elements of groups with whom we have had some acquaintance
but about whom we should know much more
This is a (personal) survey of some, older perhaps,
results and problems in group theory which should be revisited with
vigour if only because of their `applications' within and outside
Algebra. Also indeed, in Ted's opinion in any case, these are `nice' problems,
involve `nice groups' and the elements, although complicated and schizophrenic, seem to be
nice `people' when you get to know them.
10:1511:00
Marcus Bishop
A Quiver Presentation of the Descent Algebra of the Symmetric Group
We show how a presentation of the descent algebra of the
symmetric group
can be derived from a map from an algebra of binary trees
into the free Lie algebra. We then introduce a quiver whose path algebra
injects into the algebra of binary trees. Composing these two maps provides
a presentation of the descent algebra in terms of a quiver subject to relations.
11:0011:30
Coffee/tea
11:3012:15
Anne Henke
Brauer diagrams, double cosets and a new Schur algebra
Brauer algebras were introduced in 1937 in the context of
SchurWeylduality. It can be defined by a basis of pictorial (Brauer)
diagrams. Its multiplication is then given by concatenating such
diagrams. For paramter \delta =1 its basis of Brauer diagrams forms a
semigroup. It hence maybe is not surprising that Brauer algebras often
behave similar to group algebras. After introducing Brauer algebras, I
will talk about a new class of Schur algebras that is related to Brauer
algebras.
12:1513:00
Ian Chiswell
Embedding theorems for treefree groups
Sorry, no abstract available.
13:0014:30
Lunch
14:3015:15
David Lewis
Automorphisms and Involutions of Incidence Algebras
An incidence algebra can be associated to any locally finite partially ordered
set (or more generally to any quasiordered set). Since the set is locally
finite the associated incidence algebra may be regarded as a subalgebra of a
matrix algebra and for this reason incidence algebras are also sometimes
known as structural matrix algebras. We will give a quick survey of known
results on automorphisms of incidence algebras together with some new results
on involutions (antiautomorphisms of order two) of these algebras.
15:1516:00
Paul Hurley
Aspects of algebra in signal processing and sparse sampling.
Some applications of algebra in signal processing will be presented. In particular, I will touch on how polynomial rings/group algebras are a powerful tool in standard signal processing, and help to generalise and enrich its theory.
I will talk about some applications we have at IBM Research (processor information gathering, and analysis of chip designs in lithography), and outline the relatively new technique of compressive sampling (also known as compressed sensing) from a different angle.
16:0016:30
Coffee
16:3017:15
Martin Newell
Subgroups defined by commutator symmetries
Sorry, no abstract available.
17:30
Poster session and wine reception
20:00
Conference Dinner: Vina Mara, Middle Street
Saturday 29 May
09:3010:15
Des MacHale
Some problems in Group Theory I cannot solve
We collect some open problems in Group Theory which the speaker has looked at
over the years without achieving a complete solution. These problems are
mostly concerned with the following topics in finite group theory; Conjugacy
classes; Automorphism Groups; Central Factor Groups; Commutators; Isoclinism
and miscellaneous topics.
10:1511:00
Max Neunhöffer
Generalisations of Small Cancellation Theory?!
This talk describes the current status of an ongoing project with
Steven Linton, Richard Parker and Colva RoneyDougal. The ultimate
aim is to generalise the classical Small Cancellation Theory for
finitely presented groups in an algorithmic fashion using methods
from geometric group theory. The hope is that our new algorithms
will be usable for example for wordhyperbolic groups with thousands
or even millions of generators and many relations. I will describe the
main ideas for these generalisations, even though the project is still
in its infancy.
11:0011:30
Coffee/tea
11:3012:15
Ken Johnson
Applications of Group Matrices: Group presentations, Group Rings...
The DedekindFrobenius group matrix was introduced in the ?rst
papers on group representation theory. After the Noether school presented
representation theory in terms of modules it mostly disappeared from the scene.
A new look at the group matrix and its determinant, the group determinant,
has produced the realisation that it is a convenient tool in the theory of group
rings, number theory, presentations of groups, probability theory, wavelets and
several aspects of geometry. There are links to the representation theory of
wreath products and the combinatorics associated with symmetric polynomials.
I will survey some of this, and explain the connections with Ted Hurley?s recent
work.
12:1513:00
Edmund Robertson
Efficiency  a survey
Sorry, no abstract available.
Travel and Accommodation
Travel
There are regular rail
connections from Dublin to Galway, and bus
connections from all Irish cities and towns.
There are direct
flights to Galway Airport
from Belfast, Dublin, Luton, Manchester, Edinburgh, Liverpool,
Lorient, Cardiff, Leeds, Cork and Prague. The Airport is 7kms from
the NUI Galway campus. Taxis typically cost around 25 euros.
Directions to NUI Galway by road can be found here
.
NUI Galway has a number of payanddisplay
parking places for visitors. Please be aware that cars parked in other spaces on the NUI
Galway campus and not displaying a valid parking permit will be
clamped.
Accommodation: The
following are convenient for the NUI Galway campus:
The Westwood
Hotel, 091 521 442
Bologna B&B, 091523792
Abbey House B&B, 091524394
Corrib Haven B&B, 091524171
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 one of the organizers, Javier
Aramayona, Götz
Pfeiffer or Rachel
Quinlan.
Groups in Galway 2010 is generously supported by
The Millennium Research Fund, NUI
Galway
De Brun Centre for Computational
Algebra, NUI Galway
School of Mathematics, Statistics and Applied Mathematics,
NUI Galway