Semistable Vector Bundles on Rational Homogeneous spaces

In the last decades, there has been a growing body of research on the  stability of vector bundles on projective varieties. In this talk, I will introduce the crucial concept of stability of holomorphic vector bundles over P^n. In particular, the Grauert-Mulich-Barth theorem on projective spaces will be recalled. Furthermore, I will talk about the generalized Grauert-Mulich-Barth theorem on rational homogeneous spaces. This is based on a joint work with Rong Du and Yun Gao.