Moduli Spaces and Related Topics | Bridgeland Stability Conditions Applied to the Fargues–Fontaine Curve

Time:Wednesday, 14:00-15:00 June 12, 2024

Venue:C654, Shuangqing Complex Building A 清华大学双清综合楼A座 C654

Organizer:Xiang He, Chenglong Yu, Dingxin Zhang, Jie Zhou

Speaker:张诗卓 (Simons Laufer Mathematical Sciences Institute/复旦大学上海数学中心)


Let $X$ be a not necessarily smooth Fano variety and denote by \Ku(X) the non-trivial semi-orthogonal component. The Categorical Torelli problem asks if \Ku(X) determines the isomorphism class of $X$. In my talk, I will briefly talk about the history of this topic including the known results and popular strategies to prove these results. 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 talk 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 work joint with Xun Lin, Daniele Faenzi, Zhiyu Liu, Soheyla Feyzbakhsh, Jorgen Renneomo, Xianyu Hu, Sabastian-Casalaina Martin, and Zheng Zhang.

DATEJune 11, 2024
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