School of Physics - Theses

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On hyperbolic monopoles

Chan, Joseph Yew Choe ( 2017)

Magnetic monopoles are solutions to first order non-linear partial differential equations called the Bogolmonyi equations. Magnetic monopoles in three dimensional hyperbolic space can be treated as instantons invariant under rotations. The earlier portion of this thesis is a readable introduction to magnetic monopoles and instantons. In the latter portion, discrete Nahm equations are introduced for gauge groups beyond SU(2) which leads to results on rational maps, spectral curves and an extension of a result of Braam and Austin.