K-stability is a notion in algebraic geometry which originated from complex differential geometry. By the recent advances in Donaldson-Tian-Yau problem, it is now clear that K-stability is one of the fundamental notions in algebraic geometry. However, its current formulation involves many technicalities which make it hard for beginners to grasp. The goal of this winter school is to introduce the concept of K-stability to young mathematicians in algebraic and complex geometry, through the main lecture series and additional research talks. It also aims at using K-stability as a motivation to introduce several important technical notions in modern algebraic geometry. 

◆ Main Lecture Series by Chenyang Xu (Beijing University)

◇ Title  Lectures on K-stability theory [Lecture Note Download]

             - Day 1:  K-stability and birational geometry

             - Day 2: Valuative criterion

             - Day 3: Local and global 

◇ Abstract  I will start with the definition of K-stability of Fano varieties. Then I will enter the main topic of this lecture series: how to use higher dimensional geometry to tell whether a Fano variety is K-semistable? Arguably, this is one of the most important questions in complex geometry and algebraic geometry. Even many natural examples are challenging. In recent years, people have developed a circle of ideals to investigate it, using deep minimal model program theory and other machineries. In my lectures, I will discuss Odaka’s criterion that a K-semistable Fano variety can only have Kawamata log terminal singularity, Li-Xu’s theorem on special degeneration, Fujita’s valuative criterion and a corresponding local notion of K-(semi)stability.

◆ Invited seminar speakers

     Tomoyuki Hisamoto (Nagoya University)

          : Stability of a Fano manifold in terms of the Ding energy functional 

     Chen Jiang (IPMU, Tokyo)

          : Volumes and alpha-invariants of K-semistable Q-Fano varieties

     Feng Wang (Zhejiang University, Hangzhou)

          : Differential geometric meaning of K-stability

     Joonyeong Won (IBS-CGP, Pohang)

          : Some invariants to determine K-stability for Fano varieties        

◆ Organized by Jun-Muk Hwang

◆ Supported by National Researcher Program (NRF)

◆ Contact: Ms. DaEun Kim (dekim@kias.re.kr)