Recent advances on categorical Torelli problems
报告专家：张诗卓（韩国基础科学研究所（IBS））
报告时间：2024年9月25日（星期三）晚上16：00-17:00
报告地点：西南数学中心516报告厅
报告摘要：Let X be a Fano variety(not necessarily smooth) and denote the non-trivial semi-orthogonal component by \Ku(X), known as the Kuznetsov component. The categorical Torelli problem asks if \Ku(X) determines the isomorphism class of X. 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 some new approaches to solving these problems. 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 Hu, Sabastian-Casalaina Martin, and Zheng Zhang.
专家简介：张诗卓博士现在韩国基础科学研究所（IBS）几何物理中心任高级研究员。于2019年获印第安纳大学数学博士学位，2019年10月到2022年9月在爱丁堡大学数学学院从事博士后研究。2022年10月到2024年1月分别在德国波恩马克斯-普朗克数学研究所，法国图卢兹数学研究所以及德国豪斯多夫数学研究所做博后以及访问学者。2024年春季学期在加州大学伯克利分校美国数学研究所MSRI/SLM在非交换代数几何计划中做博士后，在数学知名刊物Math Ann, J. Math. Pures Appl. J.London.Math Soc, Math Z, Math Res Lette, Ann.Inst.Fourier等发表10余篇论文。目前的研究方向是代数几何，主要包括代数簇凝聚层导出范畴，Bridgeland稳定性条件以及模空间，低维Fano簇的导出范畴以及对应hyperKahler几何中的应用。
邀请人：张斌
