20251024 Jaime Pedregal Pastor

In this fourth lecture on the Seiberg–Witten invariants we will finally introduce the Seiberg–Witten equations and set up
the basic framework we will need to study the moduli space of its solutions. We will start by studying basic properties of spinor
bundles and Dirac operators. Then we will introduce the equations and their gauge symmetries, and explain how they can be
extended to Sobolev spaces so that weak solutions are allowed. If time permits, we will briefly sketch how the Seiberg–Witten
equations can be regarded as the smallest topologically allowed minima of the Seiberg–Witten action functional.