CTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> Mathematics Department, NUI, Galway

Padraig Ó Catháin
Publications

Papers in Refereed Journals

Inequivalence of Difference sets: On a remark of Baumert, submitted. (2012)
Difference sets and doubly transitive group actions on Hadamard matrices, Journal of Combinatorial Theory, Series A, 119, 6, pp. 1235-1249 (2012). Includes a description of a new family of skew-Hadamard difference sets.
The cocyclic Hadamard matrices of order less than 40, with Marc Roeder, Designs, Codes and Cryptography, 58, 1, pp. 73-88. (2011)
On Twin Prime Power Hadamard matrices, with Richard Stafford, Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences, 2, 2, pp. 261-269. (2010)
Difference sets and doubly transitive actions on Hadamard matrices II, this paper contains the analysis of the affine doubly transitive groups, completing the classification of difference sets arising from doubly transitive group actions on Hadamard matrices.
Classification of Hadamard matrices of order 4p, (joint with Jason Hill), this paper will contain a classification of the cocyclic Hadamard matrices of order 4p for prime p <25.

Theses

October 2008: Masters Thesis
December 2011:PhD Thesis (final version).

Seminar Presentations

May 2012: Difference sets and Hadamard matrices, Departmental seminar, NUI Galway. (Focus on classification of difference sets.)
March 2012: Difference sets and Hadamard matrices, Departmental seminar, NUI Maynooth. (Focus on projective planes and symmetric designs.)
February 2012: Hadamard matrices and difference sets, Algebra seminar, UCD. (Focus on permutation groups.)
November 2011: Doubly transitive group actions on designs and Hadamard matrices, Algebra Seminar, Bristol.

Conference Presentations

Note that copies of slides, where available, are presented purely for historical interest. My views may well have changed in the meantime!

June 2012: Symmetric designs, difference sets and Hadamard matrices, Croatian Mathematical Congress.
December 2011: Classification of cocyclic Hadamard matrices, 35th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing.
November 2011: Doubly transitive groups and Hadamard matrices, International Workshop on Hadamard matrices and their applications, Melbourne.
November 2011: Automorphisms of Hadamard matrices and skew difference sets. Algebraic Combinatorics: in memory of Bob Liebler, Fort Collins, Colorado.
April 2011: Doubly transitive group actions on Hadamard matrices and skew difference sets. De Brun workshop on Groups, Combinatorics and Computing.
June 2010: An application of doubly transitive groups in design theory. Postgraduate Group Theory Conference, St. Andrews.
May 2010: Design Theory. De Brun Centre review. (Not presented for personal reasons.)
July 2009: The cocyclic Hadamard matrices of order less than 40. International Conference on Design Theory and Applications, N.U.I., Galway.
June 2009: Design theory for coding theorists, Workshop on Groebner Bases, Geometric Codes and Order Domains, Trento.
April 2008: Coyclic Hadamard matrices, Postgraduate Group Theory conference, Oxford.

Seminars in Galway

February 2012: Strongly Regular Graphs III, Linear Algebra seminar.
January 2012: Strongly Regular Graphs I, Linear Algebra seminar.
October 2011: On Grammians of (0,1) matrices, Linear Algebra seminar.
October 2011: Defence Talk.
March 2011: The Lie-Kolchin Theorem, Algebraic groups seminar.
January 2011: Finding the regular subgroups of a permutation group, Postgraduate student seminar.
November 2010: The definition of an algebraic group, Algebraic groups seminar.
October 2010: An introduction to Ramsey theory, Postgraduate student seminar.
February 2010: An introduction to cyclotomy, Postgraduate student seminar.
February 2009: The cup product in cohomology, Algebraic topology reading group.
September 2008: Cocyclic matrices, Postgraduate student seminar.

Poster Presentations

As for the talks, the information presented in these posters is likely to be out of date.

2008 Poster
Presented at: Groups in Galway 2008, De Brún Conference 2008 (Galway), Joint EMS/LMS meeting 2008 (Edinburgh).
2009 Poster
Presented at: British Mathematics Colloquium 2009 (Galway), Groups in Galway 2009.
2010 Poster
Presented at: NUIG College of Science Research Day, NUIG School of Mathematics Research Day, SFI Research Day.
2011 Poster
Presented at: School of Mathematics Research Day, Groups in Galway 2011. Awarded prize for best poster at the former.

Reviews

Review of Flood and Wilson:The Great Mathematicians for the Bulletin of the London Mathematical Society.

Online Data

Cocyclic Hadamard matrices

A portion of the data that I have generated is available online, here. If you find any of the information on these pages useful, please send me a short email about it.

Padraig Ó Catháin Publications