题目：Stability conditions and homological approach to geometry of Fano varieties.

报告人：张诗卓

报告1， 时间：4月17日（周四）上午11:00-12:00 知新楼 1032

Kuznetsov components of Fano varieties, stability conditions

报告2， 时间：4月21日（周一）上午11:00-12:00 知新楼 1032

Bridgeland moduli spaces on Kuznetsov components and classical moduli spaces.

报告3， 时间：4月22日（周二）上午11:00-12:00 知新楼 1044

Application to (birational) geometry of Fano varieties and hyperKahler varieties.

摘要: Start with general definition of stability conditions on a triangulated categories, I will introduce (weak) stability conditions on curves, surfaces and corresponding (semi)stable objects on them. Then I will talk about derived category of several class of Fano threefolds and fourfolds, introducing the non-trivial semi-orthogonal component, called Kuznetsov components. Then I will briefly describe the construction of stability conditions on Kuznetsov components of these Fano varieties and give Bridgeland moduli interpretation of several classical moduli space of sheaves of small dimension. After that I will talk about modern perspective on (infinitesimal) Torelli problems for Fano varieties in terms of Kuznetsov components and how the Bridgeland moduli spaces and other homological method play roles in these problems.

报告人简介：张诗卓，现任韩国基础科学研究所几何物理中心高级研究员，将于2025年入职中山大学（广州）担任副教授。 主要从事代数几何, 尤其导出范畴、Bridgeland Stability。 相关重要研究成果发表 “Compos. Math.”、“J. Math. Pures Appl.”、“Math. Ann.”、“Ann. Inst. Fourier”等国际重要学术期刊上。

邀请人：

郝峰 数学学院教授