The monodromy conjecture for Bernstein–Sato polynomials

Let $f$ be a polynomial, let $Z_{f,\operatorname{top}}(s)$ denote its topological zeta function, let $T_f$ denote the monodromy action, and let $b_f(s)$ be the Bernstein–Sato polynomial of $f$.

Monodromy conjecture. If $s_0\in\mathbb C$ is a pole of $Z_{f,\operatorname{top}}(s)$, then $e^{2\pi i s_0}$ is an eigenvalue of $T_f$ and $s_0$ is a zero of $b_f(s)$.

The conjecture expresses the expected connection between poles of the topological zeta function, monodromy eigenvalues, and Bernstein–Sato roots. The source gives no evidence of a general resolution.