The symplectic-resolution correspondence for parabolic Higgs moduli spaces

Let $X$ be a compact Riemann surface with marked points and fixed parabolic parameters, and let the corresponding character variety parametrize representations of the fundamental group of the punctured surface with the associated fixed monodromy data. Symplectic-resolution correspondence conjecture. The moduli space of semistable parabolic Higgs bundles of degree zero with fixed parameters is a symplectic singularity, and it admits a symplectic resolution if and only if the corresponding character variety admits a symplectic resolution. This is proposed as a consequence of the conjectural isosingularity statement together with the results on multiplicative quiver varieties; both the symplectic-singularity and resolution-equivalence assertions remain open here.