# Dr Joe Gildea

Joe graduated from University College Dublin with a BA degree in Mathematics and Statistics. He received his Higher Diploma in Applied Science in 2002, MSc in Mathematics in 2003 and PhD in Mathematics in 2008 from National University of Ireland Galway. He joined the Department in April 2013.

## Qualifications

B.A. HDip. MSc. PhD.

## Overview

Before joining the University of Chester, Joe spent 6 years lecturing Mathematics to Mechanical, Mechatronic and Electronic Engineers (both online and full-time students) at the Institute of Technology Sligo, Ireland. During his time there, he served on several committees, co-ordinated 1^{st} Year Mechanical Engineers and was the contact point for the peer-mentoring program. In 2011he was nominated for a National Excellence in Teaching Award.

Before joining Institute of Technology Sligo, Joe spent 7 years at National University of Ireland Galway. Whilst studying there, he provided tutorials for the Mathematics Department and extra support for the mature students and Disability offices. He also worked for the Access office delivering Mathematics modules to mature students and school leavers. Previously, he spent 3 years teaching Mathematics to aircraft engineers and apprentice electricians/mechanics at FAS Finglas.

- Shortcuts
- Teaching
- Research
- Published Work

## Teaching

Joe was nominated for the Most Inspiring Lecturer at the “Above and Beyond” awards in 2015. He was also nominated for the Most Inspiring Lecturer and shortlisted for the Most Innovative Lecturer at the “Above and Beyond” awards in 2014.

During his time at Institute of Technology, he taught Algebra, Calculus, Linear Algebra, Sequences & Series, Differential Equations, Laplace Transforms, z-Transforms and Fourier Transforms. During his time with the Access office, he taught basic Mathematics to mature students and school leavers in order to prepare them for Mathematics at University level. He tutored on many courses for the Mathematics department; Mathematics for 1^{st} and 2^{nd} Year Commerce, Arts, Engineering and Science students and Statistics and Group Theory for 3rd Year Mathematics students.

## Research

Joe is researching in Group Algebras and their Applications, in particular:

- Units, Zassenhaus Conjecture, Lie Nilpotency Indices, Symmetric and Unitary Units.
- Applications of Group Algebras in Coding Theory and Communication.

## Published work

- Torsion units for some projected special linear groups, accepted for publication in the International Journal of Group Theory.
- Torsion Units for for a Ree group, Tits group and a Steinberg triality group, accepted for publication in Rendiconti del Circolo Matematico di Palermo.
- (with K. O'Brien) Torsion units for some untwisted exceptional groups of lie type, accepted for publication in Acta Scientiarum Mathematicarum.
- Torsion Units for Some Almost Simple Groups, accepted for publication in Czechoslovak Mathematical Journal.
- (with A. Tylyschak) Torsion units in the integral group ring PSL(3,4), Journal of Algebra and it's applications, 15(1), 9 pages, 2016.
- (with Z. Balogh and L. Creedon) Involutions and Unitary Subgroups in Group Algebras, Acta Scientiarum Mathematicarum, 79(3-4), 391-400, 2013
- Zassenhaus conjecture for integral group ring of simple linear groups, Journal of Algebra and its Applications, 10 (6), 10 pages, 2013.
- Units of Group Algebras of non-abelian groups of order 16 and exponent 4 over F
_{2}^{k}, Results in Mathematics, 61 (3-4), 245-254, 2012. - Units of the group algebra F
_{2}^{k}(C_{2}×D_{8}), Journal of Algebra and its Applications, 10(4), 643-647, 2011, doi: 10.1142/S0219498811004720. - The Structure of the Unit Group of the Group Algebra F
_{2}^{k}A_{4}, Czechoslovak Mathematical Journal, 61(2), 531-539, 2011. - (with F. Monaghan) Units of some group algebras of groups of order 12 over any finite field of characteristic 3, Algebra Discrete Math., 11(1), 46-58, 2011
- Units of the group algebra F
_{3}^{k}(C_{3}^{2 }⋊ C_{2}), Acta Scientiarum Mathematicarum, 77(1-2), 63-72, 2011. - (with L. Creedon) The structure of the Unit Group of the Group Algebra F
_{ 2}^{k}D_{8, }Canadian Mathematical Bulletin, 54(2), 237-243, 2011, doi:10.4153/CMB-2010-098-5. - Units of the group algebra F
_{5}^{k}(C_{5 }⋊ C_{4}) , International Electronic Journal of Algebra, 9, 220-227, 2011. - The structure of the Unitary Units of the Group Algebra F
_{2}^{k}D_{8}, International Electronic Journal of Algebra, 9, 171-176, 2011. - The Stucture of U (F
_{5}^{k}D_{10}), Serdica Mathematical Journal, 36(3), 247-254, 2010. - The Structure of the Unit Group of the Group Algebra of Pauli's group over any field of characteristic 2, International Journal of Algebra and Computation, 20(5), 721-729, 2010.
- The Structure of the Unit Group of the Group Algebra F
_{3}^{k}(C_{3 }x D_{6}), Communications in Algebra, 38(9), 3311-3317, 2010. - The Stucture of U (F
_{5}^{k}D_{20}), International Electronic Journal of Algebra, 8, 153-160, 2010. - The Center of the Maximal p-subgroup of U(F
_{p}^{k }D_{2p}^{m}) , Glasgow Mathematical Journal, 51(3), 651-657, (2009). - Unitary Units of The Group Algebra F
_{2}^{k }Q_{8 , }International Journal of Algebra and Computation, 19(2), 283-286, (2009). (with L. Creedon). - The Order of U(F
_{2}^{k }D_{10}) when 5|(2^{k}-1) , International Journal of Pure and Applied Mathematics, 49(4), 525-530, (2008). - The Special Circulant Matrix and Units in Group Rings, Acta Mathematica Academiae Paedagogiace Nyíregyháziensis, 24(2), 5221-225, (2008).
- On the Order of U(F
_{p}^{k }D_{2p}^{m}), International Journal of Pure and Applied Mathematics, 46(2), 267-272, (2008). - (with L. Creedon) The structure of the group algebra F
_{3}^{k }D_{6}, International Journal of Pure and Applied Mathematics, 45(2), 315-320, (2008).