Jørgen Vold Rennemo (UiO) - Categorical Torelli theorems for weighted hypersurfaces

The derived category of a Fano variety will often have a semiorthogonal decomposition consisting of a sequence of exceptional line bundles and a remaining subcategory, which we will call the Kuznetsov category. The categorical Torelli problem asks whether knowing this category up to exact equivalence is enough to determine the variety up to isomorphism. We will explain how a technique based on a computation of the Hochschild-Serre algebra of the category shows that the answer is yes in many cases, including many weighted hypersurface and a Veronese double cone. This is joint work with Xun Lin and Shizhuo Zhang.