Colloquium

In this talk, we will discuss our construction of compact Hausdorff Moishezon moduli spaces parametrizing smoothable K-stable Fano varieties. The solution relies on the recent solution of the Yau-Tian-Donaldson conjecture by Chen-Donaldson-Sun and Tian. In particular, we prove the uniqueness of the degeneration of Fano Kahler-Einstein manifolds and more algebraic properties that are needed to construct an algebraic moduli space. (This is a joint work with Chi Li and Chenyang Xu).