Groups, Computing, Designs

 De Brún Centre for Computational Algebra

National University of Ireland, galway 

welcome

Welcome to the webpage of our research group in computational group theory, algebraic design theory, and applications. This group was established at NUI Galway in 2008, and receives financial support from Science Foundation Ireland as well as other sources.

Scope

The group conducts research in two main domains.

Computational Group Theory (CGT)
Our purpose is to establish a new area of CGT: computing with matrix groups over infinite fields. We are developing special techniques for the efficient handling of linear groups over infinite fields by computer, and are using those techniques to answer a number of vital computational questions. A primary objective is the development of software that enables practical computing in this class of groups.

Algebraic Design Theory
A separate area of our research combines computational algebra and combinatorial design  theory, and deals with problems arising in a new meta-theory covering all known types of pairwise combinatorial designs. These problems include deriving computational approaches to solving the 'norm equation' over group rings; determining the structure of an ideal in a certain infinite associative ring given a presentation of that ring; and calculating the automorphism group of a design and its regular subgroups. The ideal question is closely related to the problem of proving the famous Hadamard Conjecture.

Collaboration

Centre for the Mathematics of Symmetry and Computation  (CMSC) at the University of Western Australia (director: Professor Cheryl Praeger); CGT and Design Theory.

people

NUI Galway group
•    Alla Detinko (CGT) more details..
•    Ronan Egan (Design Theory)
•    Dane Flannery (CGT and Design Theory) more details..   
•    Barry Hurley (CGT) 
•    Pádraig O'Catháin (Design Theory) more details..

External Collaborators
 •    Warwick de Launey, Center for Communications Research, USA (Design Theory). In Memoriam
•    Bettina Eick, TU Braunschweig, Germany (CGT) more details..
•    Kathy Horadam, RMIT University, Australia (Design Theory) more details..
•    Eamonn O’Brien, University of Auckland, New Zealand (CGT) more details..
 •    Tobias Rossmann, Universität Bielefeld, Germany (CGT) more details..

funding

We have been supported by Science Foundation Ireland’s Research Frontier Programme (three grants), and also by the SFI Mathematics Initiative 2007. We acknowledge the support of Deutsche Akademische Austauschdienst (DAAD), Australian Research Council, the Irish Research Council of Science, Engineering and Technology, Enterprise Ireland, the Marsden Fund of New Zealand, and RMIT University. NUI Galway support has been received in the form of PhD and Masters fellowships (including one Hardiman Research Scholarship), and grants from the Millennium Research Fund and the Office of the Registrar & Deputy President.


To contact us: Dane Flannery: dane.flannery@nuigalway.ie; ph. +353 91493587
                       Alla Detinko:    alla.detinko@nuigalway.ie