<p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">This talk will be about the multi-monopole equations, which are a "higher rank" generalisation of the Seiberg-Witten equations. I will begin by reviewing some basics of ordinary SW theory on 3 and 4-manifolds, before describing the non-compactness phenomenon that occurs in the multi-monopole case. This behaviour ruins our chance of defining a simple topological invariant from these equations. Despite this, there are still interesting applications to the existence of Z2 harmonic spinors and G2 geometry. I'll then explain how to understand multi-monopoles on product 3-manifolds from a dimensional reduction of the equations. If time permits, I will talk about some of my own results, which construct multi-monopoles on mapping tori via an adiabatic limit. </span></p>
