Research objectives and content
The two parts of the programme utilise techniques from homotopy theory and differential geometry in the study of gauge groups; motivation comes initially from physics. Firstly, influenced by the extent to which the geometry of t'Hoof's model of quark confinement is determined by the centre of the structure group of a bundle, I am developing a model for this gauge theory involving new ideas in classifying space theory within homotopy theory: this work began in my PhD thesis. Secondly, with M.Marcolli, I defined the gauge theory describing free fermions on a two dimensional surface and computed the contribution to the frame anomaly due to the presence of singularities. This is just the first step in a programme analysing the contribution that singularities give to the different anomolies in any gauge theory using geometric methods. I have visited Aberdeen and talked about my work and plans with several members of staff. I am convinced that it is a good place to pursue my research. The team is increasingly interested in the topology and geometry mathematics related to physics and with my early training as a physicist the mathematical emphasis will be particularly beneficial for my future development as a researchworker. There are no obvious industrial connections.