Chenyang Xu, K-stability of Fano Varieties

K-stability of Fano varieties was initiated as a central topic in complex geometry, for its relation with the Kähler-Einstein metric. It turns out that the machinery of higher dimensional geometry, developed around the minimal model program, provides a fundamental tool to study it, and therefore makes it an active algebraic subject. This meeting of two well-studied fields has made a number of major conjectures solved. In this talk, I will survey the recent development.