IVHS via Kuznetsov components and categorical Torelli theorems for weighted hypersurfaces

We prove the Kuznetsov components of a series of hypersurface in projective space reconstruct the hypersurfaces. Our method allow us to work for hypersurfaces in weighted projective space, and obtain the reconstruction theorem of veronese double cone, which is a long-time open case. I will show how to construct the infinitesimal variation of Hodge structure from certain Kuznetsov components. Using classical generic Torelli theorem, this implies the Kuznetsov components reconstruct the algebraic variety generically. Joint with J. Rennemo and S.Z. Zhang.