Lesley Sibner will continue her investigations of analytic problems in gauge field theory. This will involve the study of the Yang-Mills-Higgs model. Physically the Higgs model describes the interaction of elementary particles and the field equations explain the phenomena of superconductivity in vortices and the behavior of magnetic monopoles. Sibner's research is mainly directed towards studying the possible singular sets in solutions of these field equations. It is known that low energy usually implies regularity in the solution of the field equations. In fact the singular examples of Uhlenbeck have large energy. Part of the current project will be aimed at showing that these are the only examples with point singularities. In the context of more complex singular sets recent developments lead naturally to the notions of capacity and Hausdorff dimension. Investigations in this direction will follow on from Sibner's conditions for removing singular sets.
