Kahler-Einstein metric, K-stability and moduli spaces

The question of whether a smooth complex variety with a positive first Chern class, called a Fano variety, has a Kahler-Einstein metric has been a major topic in complex geometry since the 1980s. In the last decade, algebraic geometry, or more specifically higher dimensional geometry has played a surprising role in advancing our understanding of this problem. 

The interplay between complex geometry and algebraic geometry has also provided deep insights into higher dimensional geometry, peaked by the algebraic construction of a projective moduli space that parametrizes Fano varieties. More precisely, the moduli space parametrizes Fano variety satisfying the stability condition which is used to characterize the existence of a Kahler-Einstein metric - known as K-stability. In the lecture, I will explain the major ideas behind the recent progress of the subject.

You can learn more about Professor Xu here.