Brendan Guilfoyle

I am a mathematician and my main area of research is geometry. Over the past decade I have spent most of my efforts investigating the geometry of spaces of geodesics and their applications.

This work has culminated in the proof, in collaboration with Wilhelm Klingenberg, of an 80 year-old conjecture in classical surface theory called the Caratheodory Conjecture. More details of this can be found here.

More recently I have been developing neutral metrics as topological tools on 4-manifolds. My recent preprint The causal topology of neutral 4-manifolds with null boundary with Nikos Georgiou, is described in the video below:

I am a founding member of the Network for Irish Educational Standards, and have tried to highlight the decline of academic standards at second and third levels in the Republic of Ireland. While there continues to be denial and obfuscation on this crucial issue, there are some indications that people are finally waking up to this threat to the integrity of the Irish educational system.

The Network has recently started an educational standards blog, which raises and comments upon topical educational issues.