11 problems

Modified Newton distance conjecture. If $S\in\mathfrak S^m\mathbb R^{n_X+n_Z}$, then

Let $f$ be a singular complex analytic germ at $0\in\mathbb{C}^{n}$ with $f(0)=0$, and let $\varphi$ be a Schwarz function on $\mathbb{C}^{n}$ with sufficiently small support and…

Let $f$ be non-degenerate with respect to its Newton polyhedron, and let $\tau_{0}$ be a codimension-one simplex whose only lattice points in its intersection with the support of…

Let $f$ be a real analytic germ at $0\in\mathbb{R}^{n}$ with Newton polyhedron, and let $\tau_{0}$ be the face determining the relevant pole and coefficient $\mu(\varphi)$ of the a…

Combinatorial triangulation conjecture.

Triangulation-dependent Łojasiewicz conjecture. Then

Brzostowski–Krasiński–Oleksik conjecture. If $\Gamma(f)$ contains a nonexceptional facet, then

Coefficient divisibility and nonvanishing conjecture. 1. If $n=p^m$ is a power of a prime $p$, then every coefficient of $p_n$ except the coefficient of $e_1^n$ is divisible by $p$…

A normal surface singularity is a surface singularity that is normal, and a Newton non-degenerate singularity is one for which, for every $\mathbf{u}\in\mathbb{R}_{\geq 0}^n$, the…

Let $\Sigma_1,\ldots,\Sigma_m$ be an essential collection of integer polyhedra in $\mathbb{R}^m$, and let their mixed volume be $1/m!$, the minimal possible value. Minimal mixed-vo…

Let $F$ be a number field, let $K$ be a completion of $F$, and let $Z_{\Phi}(s,\chi,f_l,V_{l-1},K)$ be the local zeta function associated with the complex non-degenerate polynomial…