Padraig Ó Catháin

Dr.

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Since January 2022, I am a lecturer in the School of Enterprise and Irish at Dublin City University. The Irish language is the primary mode of communication within the school, which offers degree programmes in subjects including Business, Education and the Arts.

I graduated from the University of Galway in 2012 with a PhD in mathematics, in algebraic combinatorics studying group actions on Hadamard matrices and related topics. I spent the following ten years abroad: I worked as a postdoc at the University of Queensland and Monash University from 2012 to 2015. Under the supervision of Prof Darryn Bryant and Dr Daniel Horsley, I investigated applications of design theory to compressed sensing (a new approach to signal processing). For the year 2015-16, I was at Aalto University working with Prof Petteri Kaski in the Department of Computer Science and Prof Camilla Hollanti in the Department of Mathematics. We worked on the complexity of certain nearest neighbour problems and applications of combinatorics to private communication. In the period 2016-21, I was an assistant professor at Worcester Polytechnic Institute, where I taught a range of courses in discrete mathematics and algebra from early undergraduate through to advanced postgraduate level. I was awarded the 2015 Kirkman Medal of the Institute of Combinatorics and its Applications at the CanaDAM conference held in Toronto in June 2017.

Peer Reviewed Journal

Year Publication
2024 Browne, P.J.; Gashi, Q.R.; Catháin, P. (2024) 'A Bollobás-Type Problem: From Root Systems to Erdős–Ko–Rado'. Annals of Combinatorics, . [Link] [DOI]
2023 Oliver Gnilke; Guillermo Nunez Ponasso; Padraig Ó Catháin; Oktay Olmez (2023) 'Invariants of quadratic forms and applications in design theory'. Linear Algebra and Its Applications, . https://doi.org/10.1016/j.laa.2023.11.002
2022 Daniel Horsley; Padraig Ó Catháin (2022) 'Good sequencings of partial Steiner systems'. DESIGNS CODES AND CRYPTOGRAPHY, 90 :2375-2383.
2022 Santiago Barrera Acevedo; Heiko Dietrich; Padraig Ó Catháin (2022) 'Cocyclic two-circulant core Hadamard matrices'. Journal of Algebraic Combinatorics, 55 :201-215. [Link] https://doi.org/10.1007/s10801-021-01033-x
2021 Browne, P.; Egan, R.; Hegarty, F.; Catháin, P. (2021) 'A survey of the hadamard maximal determinant problem'. Electronic Journal of Combinatorics, 28 . [Link] [DOI]
2020 (2020) 'Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time'. Algorithmica, . [DOI]
2019 (2019) 'Morphisms of Butson classes'. Linear Algebra and Its Applications, . [Link] [DOI]
2019 (2019) 'Dimensions of semi-simple matrix algebras'. Pi Mu Epsilon Journal, .
2019 (2019) 'Improved user-private information retrieval via finite geometry'. Designs, Codes, and Cryptography, . [Link] [DOI]
2019 (2019) 'Constructing cocyclic Hadamard matrices of order 4p'. Journal of Combinatorial Designs, . [Link] https://doi.org/10.1002/jcd.21664
2019 (2019) 'Homomorphisms of matrix algebras and constructions of Butson-Hadamard matrices'. Disc. Math, .
2019 Acevedo, Santiago Barrera; Cathain, Padraig O.; Dietrich, Heiko (2019) 'Constructing cocyclic Hadamard matrices of order 4p'. Journal of Combinatorial Designs, 27 (11):627-642. [DOI]
2019 Scopus - Elsevier (2019) 'Spectra of Hadamard matrices'. Australasian Journal of Combinatorics, . [Link]
2018 (2018) 'Remark on a result of Constantine'. Annals of Combinatorics, .
2018 (2018) 'Sparsification of Matrices and Compressed Sensing'. Bulletin of the Irish Mathematical Society, .
2018 (2018) 'Construction of the outer automorphism of $S_6$ via a complex Hadamard matrix'. Mathematics in Computer Science, . [Link] [DOI]
2017 (2017) 'Compressed Sensing With Combinatorial Designs: Theory and Simulations'. IEEE Transactions on Information Theory, . [DOI]
2015 (2015) 'An asymptotic existence result on compressed sensing matrices'. Linear Algebra and Its Applications, . [Link] http://dx.doi.org/10.1016/j.laa.2015.02.010
2013 (2013) 'Nesting symmetric designs'. Irish Math. Soc. Bull, .
2013 (2013) 'Inequivalence of Difference sets: On a remark of Baumert'. EJC, .
2012 (2012) 'Difference sets and doubly transitive actions on Hadamard matrices'. J. Combin. Theory Ser. A, .
2011 (2011) 'The cocyclic Hadamard matrices of order less than 40'. Designs, Codes, and Cryptography, . [Link] [DOI]
2010 (2010) 'On twin prime power Hadamard matrices'. Cryptography and Communications, . [Link] [DOI]

Conference Publication

Year Publication
2017 (2017) 10th International Workshop on Coding and Cryptography Improved User-Private Information Retrieval with Finite Geometry
2016 (2016) A faster subquadratic algorithm for finding outlier correlations [DOI]
2016 Matti Karppa; Petteri Kaski; Jukka Kohonen; Padraig Ó Catháin (2016) Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time [DOI]
2015 (2015) Algebraic design theory and Hadamard matrices Trades in complex Hadamard matrices
2015 (2015) Algebraic design theory and Hadamard matrices Classifying cocyclic Butson Hadamard matrices

Book

Year Publication
2011 (2011) Automorphisms of pairwise combinatorial designs.
2008 (2008) Group Actions on Hadamard matrices.
Certain data included herein are derived from the © Web of Science (2024) of Clarivate. All rights reserved.

Honors and Awards

Date Title Awarding Body
01/07/2023 Kirkman medal Institute of Combinatorics and its Applications

Research Interests

Mathematics, specifically algebra, combinatorics and their applications