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Aleksander Doan : Seiberg-Witten multi-monopoles on Riemann surfaces

I will discuss a generalization of the Seiberg-Witten equations on 3-manifolds and its relation to higher-dimensional gauge theory. The main new feature is the non-compactness of the moduli space of solutions. I will explain how to tackle this problem and count the solutions when the 3-manifold is the product of a surface and a circle. In this case, the problem of compactness reduces to studying degenerations of solutions to a non-linear scalar PDE resembling the Kazdan-Warner equation.

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