Infinitesimal categorical Torelli: an application to Kuznetsov' Fano 3-folds conjecture

In this talk, we introduce the infinitesimal categorical Torelli for Fano 3-folds. We obtain a commutative diagram connecting the infinitesimal spaces
of the geometric spaces and the categories. These are joint works with Jacovskis Augustinas, Zhiyu Liu, and Shizhuo Zhang. In a joint work with
Shizhuo Zhang, we give a simple new disproof of Kuznetsov's Fano 3-folds conjecture for degree 2 and index two Fano 3-fold based on infinitesimal
categorical Torelli theorems.