School of Mathematical Sciences

Topological Obstructions in Gauge Theory menu

Topological Obstructions in Gauge Theory

Jarrod Williams
Wed, 06/05/2015 - 13:00

In his seminal paper of 1931, Dirac posited the existence of the magnetic monopole in an attempt to explain the quantisation of electric charge. Since then, the monopole has played a central role in questions related to inflationary cosmology, particle confinement and electromagnetic duality, to name just a few. On the other hand, the subject of topological solitons has been one of great interest in various branches of pure mathematics, from integrable systems to algebraic geometry. In this talk I will describe the topological characterisations of the monopole, touching on the mathematics of fibre bundles and the related Chern invariants, and address the question of which gauge theories allow for their existence. If time permits, I will discuss various generalisations of the magnetic monopole, such as instantons, and some exact solutions of the governing field equations.