The Nahm Equations and Magnetic Monopoles

Magnetic monopoles are theoretical elementary particles of a single magnetic parity. Mathematically they are modelled as solutions to the Bogomolny equations, a dimensional reduction of the anti-self-duality equations to three dimensions. Constructingsolutions to these equations is not straight-forward, but using an analogue of the ADHM construction, Nahm wrote down a system of equations whose solutions can be used to construct monopoles — the Nahm equations. In this talk I will introduce what magneticmonopoles and the Nahm equations are, and will describe the correspondence between solutions as proved by Nakajima.