Igusa's monodromy conjecture for local zeta functions

Let $f$ be a non-constant polynomial in $\mathbb{Z}[x_1,\ldots,x_n]$, for some $n\geq 1$, with $f(\mathbf{0})=0$. For every prime number $p$, let $Z_{f,p}(s)$ be Igusa's $p$-adic zeta function of $f$ at $\mathbf{0}$, and let $s_0$ be a pole of this function. Let the Bernstein polynomial of $f$ at $\mathbf{0}$ be the local Bernstein polynomial, and let ${\mathscr{E}\mathrm{xp}}(2\pi i\Re(s_0))$ be the corresponding complex exponential. Igusa's monodromy conjecture. If $p$ is sufficiently large, then $\Re(s_0)$ is a root of the Bernstein polynomial of $f$ at $\mathbf{0}$. In particular, ${\mathscr{E}\mathrm{xp}}(2\pi i\Re(s_0))$ is a local monodromy eigenvalue of the complex hypersurface defined by $f=0$. The conjecture links poles of $p$-adic zeta functions to the singularities and local monodromy of the complex hypersurface. The source states that it is solved for $n=2$ and for some special classes, including Newton non-degenerate polynomials in three variables, while the general case remains open.