Maxence Mayrand will speak on

Singular hyperkähler quotients

Abstract: When a compact Lie group acts freely and in a Hamiltonian way on a symplectic manifold, the Marsden-Weinstein theorem says that the reduced space is a smooth symplectic manifold. If we drop the freeness assumption, the reduced space might be singular, but Sjamaar-Lerman (1991) showed that it can still be partitioned into smooth symplectic manifolds which "fit together nicely" in the sense that they form a stratification. The goal of this talk is to discuss an analogue of this result in hyperkähler geometry. I will also explain how singular hyperkähler quotients have natural complex analytic structures with holomorphic Poisson brackets, and that those structures are locally isomorphic to complex-symplectic GIT quotients of affine spaces.