A workshop focusing on linear algebra and quadratic forms took place at the University of Galway on February 26th and 27th, 2024. The event featured presentations by speakers: Dr. Dan Hawtin (University of Rijeka), Dr. Stefano Lia (University College Dublin), Dr R. Quinlan (University of Galway), as well as Dr P. Ó Catháin (DCU) and Dr P. Browne(TUS).

The audience comprised undergraduate and postgraduate students from the University of Galway and ATU Galway, alongside their respective lecturing staff, as well as lecturing staff from the Technological University Shannon (TUS). Notably, five universities were represented throughout the workshop.

The first day delved into fundamental concepts of linear algebra, including eigenvectors, invariant subspaces, generalized eigenvalues and vectors, the Jordan canonical form, and the Cayley-Hamilton theorem explored in different variations.

The second day shifted focus to quadratic forms over the rational field, followed by a discussion on projective planes and culminating in an exploration of the Bruck-Ryser theorem.

This workshop facilitated a valuable exchange of knowledge and ideas among participants from various academic institutions, fostering a deeper understanding of these advanced mathematical concepts.

The third workshop was held at the All Hallows campus of DCU in Dublin. This workshop attracted students and researchers from the greater Dublin area including UCD and Trinity. We were honoured to have Dr Ciarán Mac an Bhaird (Fiontar & Scoil na Gaeilge) open the workshop and Prof. John Appleby of the School of mathematical sciences at DCU, provide the closing talk on dynamical systems and linear algebra. In addition to this we were grateful for financial support for hosting from both Fiontar & Scoil na Gaeilge - DCU and the school of mathematical sciences, DCU.

Topics covered were introduction to eigenvectors, invariant subspaces, generalized eigenvalues and vectors, Jordan canonical form and finally the Cayley–Hamilton theorem in three flavors. The second day of the workshop mainly focused on Quadratic forms over the rationals and finished with a discussion of the Bruck-Ryser theorem.