URTAGSPractical
The session will take place on Thursday June 11 2026 at the University of Strasbourg, Salle de conférence (ground floor)
The address is:
IRMA - Université de StrasbourgSalle de conférence (ground floor)
10, rue du Général Zimmer
67000 Strasbourg, France
Schedule
| 10:30–12:00 | Ruxuan Zhang: A Survey on Derived Torelli Theorems for K3 Surfaces and Hyperkähler Manifolds |
| 12:00–13:30 | lunch |
| 13:30–14:30 | Reinder Meinsma: Categorical Torelli Theorems for Fano double covers |
| 14:30–15:00 | coffee break |
| 15:00–16:00 | Pietro Beri: TBA |
Speakers, titles and abstracts
Ruxuan Zhang: A Survey on Derived Torelli Theorems for K3 Surfaces and Hyperkähler Manifolds
The bounded derived category D^b(X) encodes deep information of an algebraic variety. For K3 surfaces, the celebrated derived Torelli theorem by Mukai and Orlov states that two K3 surfaces are derived equivalent if and only if there exists a Hodge isometry between their Mukai lattices. In recent years, this elegant theory has been extensively generalized to higher-dimensional compact hyperkähler manifolds. This talk aims to provide a survey of the developments in this field. We will begin by reviewing the classical derived Torelli theorem for K3 surfaces and introduce essential tools such as the Mukai lattice. We will then give an overview of some of the recent results of the generalization to hyperkähler manifolds.
Reinder Meinsma: Categorical Torelli Theorems for Fano double covers
Fano varieties can be completely recovered up to isomorphism from their bounded derived categories of coherent sheaves, as was proved by Bondal and Orlov. In many cases, the derived category of a Fano variety has a natural decomposition into smaller pieces, and the most interesting piece is called the Kuznetsov component. The categorical Torelli problem is the question of whether a Fano variety can be recovered from its Kuznetsov component. In this talk, I will prove categorical Torelli theorems for several families of Fano varieties which appear as double covers. The proof proceeds through a careful study of the branch divisors, which happen to be K3 surfaces, and consists of a healthy mixture of explicit geometry and derived categories. This is joint work with Augustinas Jacovskis.