Shizhuo Zhang:Categorical Torelli problem for Fano varieties

Abstract: It is well known that for a smooth Fano variety, bounded derived category of coherent sheaves determine their isomorphism classes. It is natural to ask whether it is possible to reconstruct them with less information, say a semi-orthogonal component, known as categorical Torelli problem. I will talk about recent progress on this problem, in particular for Fano threefolds and fourfolds.It is based on the work myself and the joint work with Zhiyu Liu, Augustinas Jacovskis and Soheyla Feyzbakhsh.