Elliptic PDE theory on manifolds and the dimension of the Seiberg-Witten moduli space

This talk is part of the following reading seminar: Seiberg-Witten theory (Fall 2025).

Abstract

In this talk, we will introduce differential operators on manifolds and give some basic results about elliptic operators (and elliptic complexes). The goal is to prove that every $L^{2,2}$-solution of the Seiberg-Witten equations is gauge-equivalent to a smooth one and to compute the expected dimension of the Seiberg-Witten moduli space.