Abstract

Motivated from the categorical Torelli theorems, we introduce two types of infinitesimal categorical problems, connecting infinitesimal Torelli problems with a commutative diagram. Our constructions are general, and the main examples in this talk are nontrivial components of derived categories of Fano 3-folds. The infinitesimal categorical Torelli theorems for Fano 3-folds are summarized. I will talk about the unknown cases, and explain how the infinitesimal categorical Torelli theorems apply to Kuznetsov Fano 3-folds conjecture, and the categorical Torelli problems for hypersurfaces. This is based on joint works with J. Augustinas, Zhiyu Liu, and Shizhuo Zhang.

Speaker

I am a student at Yau Mathematical Sciences Center, Tsinghua University, Beijing. My supervisor is Professor William Donovan. My research is in algebraic geometry. I am interested in geometry of derived categories, especially the indecomposability problems. I am also interested in Hochschild (co)homology theory, para-canonical systems, Hodge theory, rational points of algebraic varieties, and number theory.

个人主页：

https://linlinsai.github.io/