Groups in Galway 2010

(In honour of Professor Ted Hurley in the year of his retirement from teaching)

28-29 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.



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

09:30-10:15 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.

10:15-11:00 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.

11:00-11:30 Coffee/tea

11:30-12:15 Anne Henke Brauer diagrams, double cosets and a new Schur algebra Brauer algebras were introduced in 1937 in the context of Schur-Weyl-duality. 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 semi-group. 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.

12:15-13:00 Ian Chiswell Embedding theorems for tree-free groups Sorry, no abstract available.

13:00-14:30 Lunch

14:30-15:15 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 quasi-ordered 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 (anti-automorphisms of order two) of these algebras.

15:15-16:00 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.

16:00-16:30 Coffee

16:30-17:15 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

09:30-10:15 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.

10:15-11:00 Max Neunhöffer Generalisations of Small Cancellation Theory?! This talk describes the current status of an ongoing project with Steven Linton, Richard Parker and Colva Roney-Dougal. 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 word-hyperbolic 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.

11:00-11:30 Coffee/tea

11:30-12:15 Ken Johnson Applications of Group Matrices: Group presentations, Group Rings... The Dedekind-Frobenius 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.

12:15-13:00 Edmund Robertson Efficiency - a survey Sorry, no abstract available.

Travel and Accommodation

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

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