12 problems

Fix $u_1,\ldots,u_n\in{\mathds C}$, $\xi\in S^1$ with $\Re((u_i-u_j)/\xi)<0$ for $i<j$, and $T\in M(n\times n,{\mathds R})$ upper triangular with $T_{ii}=1$ and $T+T^{tr}$ positive…

Bernoulli-moment sign conjectures. For every $k\in{\mathbb N}$, both the weak form

Bernoulli-moment characterization conjecture. There is a family of functions $r(k,n,\nu):\mathbb{R}_{>0}\to\mathbb{R}_{>0}$ such that a matrix $S$ is a distinguished matrix of a si…

Cecotti–Vafa spectrum conjecture. The Cecotti–Vafa construction can be made precise so that

Let $\mathcal F$ be a degenerating family of $n$-dimensional isolated hypersurface singularities: it is equipped with a filter and its Milnor number function satisfies…

Let $f\colon (\mathbb C^{n+1},0)\to(\mathbb C,0)$ define an $n$-dimensional isolated hypersurface singularity, with $n\geq 1$. Let $\mu$ be its Milnor number, and let…

Let $f:\mathbb{C}^{n+1}\to\mathbb{C}$ be a tame polynomial with spectral numbers $[?]$ at $t=\infty$, ordered as $[?]$. Dual Hertling variance conjecture. The spectral numbers at…

Let $f$ be a holomorphic function germ with isolated singularity, let $sp(f)$ denote its spectrum, and let $a\in\mathbb{R}$. An invariant $I$ is semi-continuous if, for every adjac…

Let $f$ be a function in three variables, let $F_f$ be its Milnor fiber, and let $N$ be the nilpotent operator acting on $H^2(F_f,\mathbb C)$. Defective spectral-number eigenvector…

Let $S$ be a matrix in a Seifert form stratum of $T(n,\mathbb R)$ that is not met by $\bigcup_{k=1,2}T_{{\rm HOR}k}(n,\mathbb R)$. Let $\operatorname{Sp}(S)$ and…

Let $T(n,\mathbb R)$ be the space of upper triangular matrices under consideration. A Seifert form stratum is a union of components of a fiber of the map to isomorphism classes of…

Let $T_{{\rm HOR}k}(n,\mathbb R)$ be the specified families of upper triangular HOR-matrices, let $T(n,\mathbb R)$ be the ambient space of such matrices, and let $S$ be a special m…