12 problems

Finite-generation conjecture. For every positive integer $n$, this closed cone is finitely generated.

Cone equality conjecture. The two cones are equal:

Boundary-stratum conjecture. There exists a subcone $S+\sigma\subset S$ such that

Let $\overline M_{0,n}$ be the moduli space of stable genus-zero curves with $n$ marked points. Let $\operatorname{PBDcone}(n)$ be the cone associated with effective partition bloc…

Let $Q\subseteq\mathbb R^n$ be a polyhedral cone, and let ${\rm MA}(P,Q)$ denote the problem of computing the maximal angle between cones $P$ and $Q$. Orthant-restriction conjectur…

Let $\operatorname{\textsf{Cones}}(d)$ be the partially ordered set of pointed, rational, finitely generated cones in $\mathbb{R}^d$, ordered by successive addition of nonnegative…

Inclusion conjecture.

Let $p\in \mathbb{R}[x_1,\dots,x_n]$ be a complete hyperbolic polynomial with hyperbolicity cone $C$. For a real $\alpha>n$, let $q_{\alpha}$ be the function defined by … where…

Non-SAGE separation conjecture. If every $\bm{a}_i$ lies in either $\operatorname{ext}\mathcal{P}(\bm{A})$ or $\operatorname{int}\mathcal{P}(\bm{A})$, but $\bm{A}$ does not satisfy…

Let $Q:{\mathbb R}^n\to{\mathbb R}^m$ be an elliptic quadratic operator with $\textup{rg}Q=2$, and let ${\overline K}'_Q$ denote its associated cone. Let $C_3$ be a three-dimension…

Let $C(\operatorname{SqFree},n)$ be the positive rational cone generated by homological data triplets of free squarefree complexes over $\Bbbk[x_1,\ldots,x_n]$. A pure free squaref…

Let $S$ be a finite spanning set, and let $\mathfrak M_\mathbb Z(S)$ be the lattice generated by standard measures of simplices with vertices in $S$. Define the rational cone…