FRG workshop, 2011

M. Verbitsky

Title: Subtwistor metric on the moduli of hyperkähler manifolds and its applications


I will explain the proof of global Torelli theorem for hyperkähler manifolds. There are three key results in the proof; two of them are point-set topology, and the third one involves an interesting (non-Riemannian and not even Finsler) metric on the moduli space, called a subtwistor metric, and the Montgomery-Gleason solution of Hilbert's Fifth problem. I will explain the proof and propose other uses for this metric.