4 problems

A convex semialgebraic set is a semialgebraic subset of some finite-dimensional real vector space that is convex, and a spectrahedral shadow is the image of a spectrahedron under a…

Let $M$ be a matrix represented as a slack matrix $M=S_{P,Q}$ of nested polytopes $P\subseteq Q\subseteq\mathbb R^{r-1}$. A spectrahedral shadow $C$ of size $k$ between $P$ and $Q$…

Spectrahedral-shadow conjecture. Every closed convex semialgebraic subset of $\mathbb{R}^d$ is a spectrahedral shadow.

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…