We survey some recent results concerning the so called Categorical Torelli problem. This is
to say how one can reconstruct a smooth projective variety up to isomorphism, by using the …

We prove a general criterion that guarantees that an admissible subcategory KK of the
derived category of an abelian category is equivalent to the bounded derived category of the …

We give an alternative proof of the theorem by Kuznetsov and Lunts stating that any
separated scheme of finite type over a field of characteristic zero admits a categorical …

We give a structure theorem for Calabi-Yau triangulated category with a hereditary cluster
tilting object. We prove that an algebraic d-Calabi-Yau triangulated category with a d-cluster …

We study the problem of when triangulated categories admit unique infinity-categorical
enhancements. Our results use Lurie's theory of prestable infinity-categories to give …

We work over a perfect field. Recent work of the third-named author established a Derived
Auslander Correspondence that relates finite-dimensional self-injective algebras that are …

Inspired by the intrinsic formality of graded algebras, we prove a necessary and sufficient
condition for strongly uniqueness of DG-enhancements. This approach offers a …

We prove a derived version of the Gabriel–Popescu theorem in the framework of dg-
categories and t-structures. This exhibits any pretriangulated dg-category with a suitable t …

We show that, over an arbitrary commutative ring, the localizations of the categories of dg
categories, of unital and of strictly unital $ A_\infty $ categories with respect to the …

We prove the equivalence of the deformation theory for a higher dimensional Calabi--Yau
manifold and that for its dg category of perfect complexes by giving a natural isomorphism of …