ICTS

In this talk I will discuss the Taubes-Pidstrygach generalisation of the Seiberg-Witten equations. In this generalisation, the spinor representation is replaced with an appropriate hyperKahler manifold. I will discuss its relation with many well-known gauge theories. In the Riemannian case, the solutions to the generalised equations admit an interpretation in terms of (de-generate) almost-Hermitian metric on the base manifold. When the underlying manifold is Kahler,  I will discuss a Hitchin-Kobayashi -type correspondence for the  for the generalised equations. The novelty in this case lies in the fact that the correspondence narrows down to studying the well-known Kazdan-Warner equations. If time permits, I will talk about an interpretation of the equations on a Kahler surface as equations the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. I will try to keep the talk elementary in nature, making it accessible to a wider audience.