His entire career has been spent at University College Dublin (UCD), where he served two terms as head of the school of mathematics.
In May 2019 at UCD, the International Conference on Linear Algebra and Matrix Theory held a celebration to honor Professor Laffey on his 75th birthday.
[4] He has also played a significant role in the establishment of the Irish Mathematical Olympiad, and had frequently served the BT Young Scientists Exhibition as a judge and reviewer.
[3] Early in his career, he developed a strong interest in matrix theory, due to the influence of Olga Taussky-Todd, with whom he often corresponded.
[5] He received the Hans Schneider Prize in 2013 in recognition of his constructive solution to the NIEP (Non-negative inverse eigenvalue problem) for non-zero spectra.