K-stability is an algebraic notion that characterizes when a smooth Fano variety admits a Kahler-Einstein metric. An important motivation for understanding this notion is the K-moduli conjecture, which asserts that K-polystable Fano varieties are parametrized by a projective good moduli space. I will survey recent activity on this problem and then discuss joint work with Chenyang Xu verifying the separatedness of the moduli space.
Speaker(s): Harold Blum (University of Utah)