Hausel's main mixed-Hodge polynomial conjecture for character varieties

Let ${\mathcal{M}_{\rm B}}_n$ be the twisted $\operatorname{GL}_n$ character variety of a genus-$g$ Riemann surface, let $H({\mathcal{M}_{\rm B}}_n;q,t)$ denote its mixed Hodge polynomial, and let $d_n=\dim({\mathcal{M}_{\rm B}}_n)$. Define $V_n(z,w)$ and $\overline H_n(z,w)=(z^2-1)(1-w^2)V_n(z,w)$ as in the preceding generating-function construction.

Hausel's mixed-Hodge polynomial conjecture.

$$H({\mathcal{M}_{\rm B}}_n;q,t)=(t\sqrt q)^{d_n}\overline H_n\left(\sqrt q,\frac{-1}{t\sqrt q}\right).$$

The conjecture is called geometric because it predicts the full mixed Hodge polynomial from the rational functions arising in the partition generating function; the specialization $t=-1$ is known, while the general statement is left open in the supplied text.