The Topological Monodromy Conjecture and its strong form

Let $f$ be a divisor on a smooth complex variety, let $Z_f(s)$ be its topological zeta function, and let $b_f(s)$ be the Bernstein–Sato polynomial. A pole of $Z_f(s)$ is a complex number at which the rational function $Z_f(s)$ has a pole.

Topological Monodromy Conjecture. Any pole of $Z_f(s)$ yields under exponentiation an eigenvalue of the monodromy operator at some $p\in\operatorname{Var}(f)$. The strong form asserts that any pole of $Z_f(s)$ is a root of $b_f(s)$.

These are the monodromy and strong monodromy conjectures for the topological zeta function. The source states them as conjectural claims, without supplying resolution evidence.