Harry Braden

Symmetry, Curves and Monopoles

The modern approach to integrability proceeds via a Riemann surface, the spectral curve. In many applications this curve is specified by transcendental constraints in terms of periods. In some cases, including the construction of magnetic monopoles, physical symmetries are inherited by the spectral curve and there may be consequent simplifications of the transcendental constraints. We shall look at this interplay of ideas.