3 problems

Let $p$ be a polynomial on $\mathbb{R}^3$ that is hyperbolic of degree $d$ with respect to $e=(1,0,0)$ and satisfies $p(e)=1$. Let $I$ denote the $d\times d$ identity matrix and le…

Let $p\in\mathbb{R}[\mathbf{x}]$ be a real-zero (RZ) polynomial with $p(\mathbf{0})=1$. For a polynomial $f$, write $\operatorname{rcs}(f)$ for its rigidly convex set. Generalized…

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…