Derek Harland (Loughborough University)
Yang-Mills instantons were discovered over thirty years ago and have had a profound impact on mathematics and theoretical physics. An instanton is a connection on a vector bundle over a four-manifold whose curvature satisfies a simple linear equation, the self-duality equation.
Generalisations of instantons to more than four dimensions were discovered in the 1980s, and interest in these has recently resurged owing to connections with supersymmetry, string theory and exceptional geometry. In this talk I will explain how these instanton equations are described naturally in the language of spinors. I will present some new examples of instantons defined on special classes of manifolds that admit Killing spinors, the simplest members of which are spheres.