2 problems

Let $P_{n,4}$ denote the space of homogeneous quartic forms on $\mathbb{R}^n$, and let $G\in P_{n,4}$ be positive semidefinite if $G(x)\geq 0$ for all $x\in\mathbb{R}^n$. Suppose t…

Reducibility conjecture. The real rank boundary $\partial_{alg}\mathcal{R}_{4,4}$ is reducible. The discriminant of $\Omega(f)$ is one of its components. Further, at least one more…