Cohomology conjecture for Calogero-Moser spaces

Let $W$ be a complex reflection group, let $c\in{\boldsymbol{\mathcal C}}$, and let ${\boldsymbol{\mathcal Z}}_c$ be the corresponding Calogero-Moser space. Let ${\boldsymbol\Omega}^c:Z_c\rightarrow\mathrm Z(\mathbb C W)$ be the algebra morphism defined in the source, and equip $\operatorname{Im}{\boldsymbol\Omega}^c$ with the filtration used to form its associated graded algebra. Cohomology conjecture. For every $i\in\mathbb N$,

$$\mathrm H^{2i+1}({\boldsymbol{\mathcal Z}}_c)=0,$$

and there is an isomorphism of graded algebras

$$\mathrm H^{2\bullet}({\boldsymbol{\mathcal Z}}_c)\simeq\operatorname{gr}(\operatorname{Im}{\boldsymbol\Omega}^c).$$

The conjecture is known when ${\boldsymbol{\mathcal Z}}_c$ is smooth, when $c=0$, and in rank one; it remains open in general.