Chenyang Xu: Moduli spaces of Fano varieties
Lecture 1: we will discuss the background of K-stability and algebraic geometer’s gradually evolving understanding of the concept.
Lecture 2: we will discuss the construction of K-moduli spaces.
Lecture 3: we will focus on a new finite generation theorem we proved recently (joint with Yuchen Liu and Ziquan Zhuang), which completes the solution to several main questions in K-stability, including the compactedness of the K-moduli as well as the Yau-Tian-Donaldson Conjecture for general Fano varieties.