The Hausel partition-function conjecture for mixed Hodge polynomials of character varieties

Fix the number $k$ of marked points and the genus $g$. For partitions $\mu_1,\ldots,\mu_k$ and the corresponding generic character variety $X_{g;J_{\mu_1},\ldots,J_{\mu_k}}$, let $\mathrm{MH}_{g,k}$ be the generating symmetric function of their mixed Hodge polynomials, and let $\Omega_{g,k}$ be the partition function defined using modified Macdonald polynomials. Hausel's partition-function conjecture.

$$\Omega_{g,k}=\operatorname{Exp}\left(-\frac{\mathrm{MH}_{g,k}}{(q-1)(t-1)}\right).$$

The source calls this the biggest open problem in the field and supplies no resolution; it relates all character varieties' mixed Hodge polynomials to a Macdonald-polynomial partition function.