  We prove that the Grothendieck-Springer simultaneous resolution viewed as a
correspondence between the adjoint quotient of a Lie algebra and its maximal
torus is Lagrangian in the sense of shifted symplectic structures. As
Hamiltonian spaces can be interpreted as Lagrangians in the adjoint quotient,
this allows one to reduce a Hamiltonian $G$-space to a Hamiltonian $H$-space
where $H$ is the maximal torus of $G$. We show that this procedure coincides
with an algebraic version of symplectic implosion of Guillemin, Jeffrey and
Sjamaar. We explain how to obtain generalizations of this picture to
quasi-Hamiltonian spaces and their elliptic version.
