The previous lecture in this series is here. The next lecture in this series is here.
In this lecture I will introduce the concepts of Hermitian-Einstein connections and metrics and of stability of vector bundles. The first one is purely differential-geometric while the second has its origins in algebraic geometry. The Kobayashi-Hitchin correspondence says that they are essentially the same. I will present its proof using the continuity method.
This video is part of the London Mathematical Society‘s Online Graduate Lecture Series. These are supported by the LMS, and organized by the Brussels-London Geometry Research Network.