题    目: Categorical aspects of Torelli problem and infinitesimal Torelli problem

报告人：张诗卓  研究员

单   位：韩国基础科学研究所（IBS）

时   间：8月25日  15:00

地   点：数学院一楼报告厅

摘   要: Torelli problem is one of the most classical problems in algebraic geometry. It asks if the Hodge structure on the cohomology of an algebraic variety determines itself uniquely. In the case of Fano variety X, it asks the period map, which sends X to its intermediate Jacobian J(X) is injective. On the other hand, we say the infinitesimal Torelli theorem holds for X if the differential of the period map is injective. Torelli problems and its infinitesimal version were intensively studied subjects. I will introduce the modern perspective for both problems, namely categorical Torelli problems and infinitesimal categorical Torelli problems. Then I will talk about recent results for Fano hypersurfaces, Gushel-Mukai varieties. If time allows, I will talk about a geometric interpretation of the kernel of differential of period map for Gushel-Mukai threefolds via Bridgeland moduli spaces from an interesting category, called the Kuznetsov component.

简   介：现韩国基础科学研究所（IBS）几何物理中心高等研究员, 2019年博士毕业于印第安纳大学，后于爱丁堡大学，德国波恩马普所，法国图卢兹数学所，德国Hausdorff 数学研究所，美国加州大学伯克利分校MSRI数学研究所做博后及访问学者。张诗卓博士的研究方向是代数簇的凝聚层导出范畴，Bridgeland 稳定性条件以及在Fano簇上模空间以及hyperkahler簇的应用, Fano簇的范畴化Torelli问题，研究工作已经在Math. Ann., Compositio Math., JMPA, J. LMS, Math. Z., Math Research Letter等杂志上发表。