Chuyu Zhou, Lecture 2: Non-linear Wall Crossing Theory

In this lecture, we will talk about two properties of K-semistable domains in non-proportional setting. One is the finiteness criterion, which states that the number of domains is finite for a family of couples. The other is about the shape of each domain, which states that they are semi-algebraic sets. These two properties together lead to a satisfactory wall crossing theory for K-stability in non-proportional case. Time permits, I will present a comparison between GIT-stability and K-stability in non-proportional setting.