Chengyan Xu (Beijing International Center of Mathematics Research)
K-stability of Fano varieties
K-stability and its variants are notions invented by differential geometers, who used it to characterize the existence of Kahler-Einstein metric on a Fano variety. However, it inspires surprisingly amount of interesting algebraic geometry problems, and provides us a new way to look deeply into the geometry of Fano varieties. In the last three years, using the valuations over a variety, there has been a remarkable progress on the study of K-stability. I will survey the subject and mention (many) unknown questions.
