Symmetric calorons and the rotation map

Josh Cork, University of Leeds. Part of the geometry seminar series.

There has long been interest in finding symmetric solutions to variational problems, and integrable systems. We shall look at calorons - periodic anti-self-dual connections - and their symmetries. In particular, unlike other similar objects, calorons reveal a somewhat special discrete symmetry called the rotation map, which acts like a gauge transformation but is not periodic itself. We shall state results regarding the fixed points under cyclic symmetry groups incorporating the rotation map, give an overview of the different techniques involved in constructing such solutions.

Josh Cork, University of Leeds