K-stability of log Fano hyperplane arrangements

Recently, the theory of K-stability for Fano manifolds (more generally, log Fano pairs) is rapidly developing. In this talk, I will explain “a valuative criterion” for K-stability of log Fano pairs introduced by myself and C. Li which seems easier than the original definition. Moreover, I will show one of its application, that is, I will give the answer which log Fano hyperplane arrangements are K-stable or not.