4 problems

Let $P$ be a polynomial and let $\x03bc_{\x03b1,P}$ be the asymptotic root-counting measure from Theorem. Forest conjecture. For $0<\x03b1<\deg P$, the support of…

Shadow-boundary conjecture. (i) $\x1d4fe_P\subset\x0043\x006f\x006e\x0076_P$ is a concave domain. (ii) The boundary of $\x1d4fe_P$ is contained in the union, over…

Let $p\in\mathbb{N}^*$ and let $P,Q\in\mathbb{C}[X]$ have degree $p$. Derivative-convolution Gauss–Lucas conjecture. The roots of … lie in the convex hull of the roots of $P$ and…

Let $p\in\mathbb{N}^*$ and let $P,Q\in\mathbb{R}[X]$ have degree $p$. Derivative-convolution conjecture. If $P$ and $Q$ are real-rooted, then … is real-rooted as well. This is pres…