5 problems

Let $p$ be a polynomial in $n$ variables, and let its coamoeba be the set determined by the phases of the points of its complex variety. Coamoeba component-count conjecture. The co…

Polar spectrahedron conjecture. If $S\subset\mathfrak{a}$ is a $W$-invariant spectrahedron, then $\mathsf{K}\cdot S\subset V$ is a spectrahedron.

Let $A$ be a support set, and let the sonc cone and nonnegativity cone associated with $A$ be denoted by $\mathcal{S}^+_A$ and $\mathcal{P}^+_A$, respectively. A Chandrasekaran–Mur…

Let $h\in\mathbb R[x_1,\dots,x_n]$ be hyperbolic with respect to $e\in\mathbb R^n$, and let $\Lambda_e(h)$ be its hyperbolicity cone. A spectrahedral shadow is the image of a spect…

Real-point conjecture. For $p \in P_{3,6} \setminus \Sigma_{3,6}$ there exist $v_1,\ldots,v_9 \in \mathbb{R}^3$ yielding a separating extreme ray for $p$. Analogously, for…