Zhi Jiang, On Syzygies of Abelian Varieties

Syzygies of ample line bundles on abelian varieties have attracted lots of attentions in recent years. People tried to study these geometric objects by different methods, including Okounkov bodies, X-methods from MMP, and generic vanishing theory. We will report some progress on this subject based on the work of Jiang-Pareschi, Caucci, and Ito based on cohomological rank functions.