Enrico Fatighenti (Warwick)
A new approach to Torelli's Theorem for K3 surfaces (following Verbitsky, O'Grady and Huybrechts)

Torelli's theorem is a classical subject in algebraic geometry: it gives the answer to the question of whether the integral Hodge structure of a manifold is enough to determine the isomorphism class of the manifold itself. In this talk we prove the classical Torelli theorem for K3 surfaces, first proved in the 1970s, following the ideas that Misha Verbitsky used to give a proof of a birational version of Torelli's Theorem for some hyperk\"ahler manifolds. It turns out that this proof, when restricted to K3 case, provides an elegant proof for the global Torelli theorem. We mainly follow the ideas of O'Grady and Huybrechts in adapting the proof of the K3 case.