**Speaker:** Patrick Browne (Shannon)

**Title:** *Erdős–Ko–Rado Type Problems in Root Systems*

**Abstract:**

Given a Lie algebra, two roots are strongly orthogonal if neither their sum nor difference is a root. In this talk, we investigate sets of mutually strongly orthogonal roots. In particular, those such that any two such sets have the property that the difference between their sums can itself be expressed as the sum of a strongly orthogonal set of roots. We discuss this property and its relationship to Erdős–Ko–Rado type problems and finally discuss applications in terms of the existence of finite projective planes of certain orders. This is joint work with Qëndrim R. Gashi, University of Prishtina.