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Instantons, monopoles, and the Skyrme model

Topological solitons have become ubiquitous in both mathematics and physics throughout the last few decades. These objectsmanifest themselves as critical points of some 'energy functional', which are(loosely speaking) stable under continuous deformations. In this talk I willgive a broad introduction to three types of topological soliton - instantons,monopoles, and skyrmions - which live in dimension 4, 3, and 3 respectively. Iwill focus mainly on their interrelationships, and in particular their role inunderstanding the Skyrme model, which is a rather appealling model of nuclearphysics (whose topological solitons are skyrmions themselves).