3 problems

Topological multivariable strong monodromy conjecture. The polar locus of $Z_{F}^{\operatorname{top}}(S)$ is contained in $V(B_{F})$.

Let $F:(\mathbb{C}^{n+1},\mathbf{0})\to(\mathbb{C},\mathbf{0})$ define a germ of an isolated hypersurface singularity. For $x\in F^{-1}(0)$, let $\mathcal{F}_{F,x}$ be the Milnor 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 $b_f(s)$.