K-stability is introduced by Tian to characterize the existence of canonical metrics on Fano manifolds, which is clearly a geometric concept. Recently, there has been a comprehensive understanding from algebraic point of view, and it turns out that this is the suitable concept to construct the moduli space of Fano varieties. Due to many breakthroughs in the past few years, we now could construct a K-moduli space for Fano varieties with K-stability. This talk will focus on an important phenomenon of K-moduli, i.e. the wall crossing property. Roughly speaking, if we want to construct K-moduli for log Fano pairs of the form (X, cD), where X is Fano and D is proportional to the anti-canonical divisor, the moduli space will change birationally as we change the coefficient c. The full understanding of this phenonenon will undoubtedly provide important ideas and tools to study the birational geometry of different moduli spaces. This talk is based on a recent work ''On the shap of K-semistable domain and wall crossing for K-stability''.

报告人简介：周楚宇现在瑞士联邦洛桑理工学院（EPFL）从事博士后研究，他于2015年在正规外围买球十大平台取得学士学位，于2020年在北京大学取得博士学位，研究方向为高维代数几何。