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# Benjamin Bakker (University of Georgia – Athens), Mini-school on Abelian and Symplectic Varieties

## April 18, 2017 @ 4:40 pm - 5:30 pm

**Title **A global Torelli theorem for singular symplectic varieties

**Abstract: **The local and global deformation theories of holomorphic symplectic manifolds enjoy many beautiful properties. By work of Namikawa, some of the local results generalize to singular symplectic varieties, but the moduli theory is badly behaved. In joint work with C. Lehn we show that for locally trivial deformations the entire picture is exactly analogous to the smooth case. In particular, we prove a global Torelli theorem and deduce some applications to birational contractions of moduli spaces of vector bundles on K3 surfaces. In place of twistor lines, the crucial global input is Verbitsky’s work on ergodic complex structures using Ratner’s theorems.