Seiberg-Witten multi-monopoles on Riemann surfaces

Geometry/topology Seminar

Aleksander Doan (Stony Brook)

Monday, March 27, 2017 -
3:15pm to 4:15pm
Location: 
119 Physics

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.