Recent advances on categorical Torelli problems

发布时间：2024-11-04 作者：浏览次数：

Speaker:	张诗卓	DateTime:	2024年11月05日（周二）上午 10:00 - 11:00
Brief Introduction to Speaker: 张诗卓，2019年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，目前在中科院数学所晨兴数学中心访问。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，最近两年主要研究Fano簇的范畴化Torelli问题。研究工作已经在Math Ann, JMPA, Journal of London Math Society, Math Z, Math research letter等杂志上发表或者接受待发表。		Place:	国交2号楼315会议室
Abstract:Let X be a Fano variety(not necessarily smooth) and denote the non-trivial semi-orthogonal component by Ku(X)Ku(X), known as the Kuznetsov component. The categorical Torelli problem asks if Ku(X)Ku(X) determines the isomorphism class of XX. I will briefly talk about the history of this topic, including the known results and popular strategies to prove these results(Hodge theoretic, moduli space theoretic and Chow theoretic). Then, I will survey the recent advances for (weighted) hypersurfaces, a cubic threefold with a geometric involution, del Pezzo threefold of Picard rank one, and a class of nodal prime Fano threefolds. Meanwhile, I will talk about infinitesimal version of categorical Torelli problem. If time permits, I will also speak about categorical Torelli problems for a class of index one prime Fano threefold as the double cover of del Pezzo threefolds. This talk is based on a series of works with Daniele Faenzi,Xun Lin, Zhiyu Liu, Soheyla Feyzbakhsh, Jorgen Renneomo, Xianyu...

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