Shifted Hyperkahler Structures

The notion of a shifted symplectic structure has recently been developed as the analogue of a (holomorphic) symplectic structure in derived algebraic geometry. I will the corresponding notion for hyperkahler manifolds in derived algebraic geometry, and explain how this can provide new constructions of hyperkahler manifolds or derived hyperkahler desingularizations. This talk is based on joint work with Ludmil Kazarkov and Pranav Pandit.