Maxence Mayrand, University of Toronto
"Hyperkähler metrics near Lagrangian submanifolds and symplectic groupoids"
Feix and Kaledin independently showed that the cotangent bundle of any Kähler manifold has a hyperkähler metric on a neighbourhood of its zero section. I will explain a generalization of this result, which reduces the problem of constructing a hyperkähler metric near a complex Lagrangian submanifold in a holomorphic symplectic manifold to the existence of certain deformations of holomorphic symplectic structures. I will then use it to show that any holomorphic symplectic groupoid over a compact holomorphic Poisson surface of Kähler-type has a hyperkähler metric near its identity section. The metric is obtained by constructing a twistor space by lifting special deformations of holomorphic Poisson structures adapted from Hitchin's unobstructedness theorem. This talk is based on arXiv:2011.09282.
Zoom meeting: https://zoom.us/j/93859138328