Andrea Spiro (Università di Camerino)
An instanton on a quaternionic Kähler manifold is a connection on a principle bundle, whose curvature is pointwise adapted to the quaternionic structure of the tangent space.
These instantons are special solutions to the Yang-Mills equations and are natural generalisations of the anti-self-dual solutions to the Yang-Mills equations on S4, fully classified by Atiyah-Drinfeld-Hitchin-Manin in the '80s.
We are going to present a novel approach which provides a complete (local) description of each instanton on a quaternionic Kaehler manifold in terms of a single complex function, the prepotential.
This approach yields radical simplifications and immediate generalisations of important results like Uhlenbeck's Compactness Theorem for Yang-Mills fields.
