Title: Stability of syzygy bundles on varieties of Picard number one

Abstract: The syzygy bundles is the kernel of the evaluation a globally generated ample line bundle. In this talk, I will first discuss the stability of syzygy bundles on varieties of Picard number one. Then, as an application, I will show the stability of syzygy bundles on hyperkähler varieties. This is a joint work with Chen Jiang.