Categorical Torelli theorem for Fano varieties

Contact: Daniel Huybrechts.

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 non-trivial 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. If time allows, I will also talk about an intrinsic proof for categorical Torelli theorem for del Pezzo threefolds, based on a recent joint work with Zhiyu Liu and Soheyla Feyzbakhsh.