8 problems

Hawaii conjecture. The number of real critical points of the logarithmic derivative $Q[p]$ satisfies the lower bound stated by Craven, Csordas, and Smith.

Let $P(s;[\mathbf a+i\mathbf b])$ be a complex interval polynomial, and let $\mathcal O$ denote its minimal containing sector. Let $\mathcal V$ denote the sector containing the ver…

Let $P(s;[\mathbf a])$ be a real interval polynomial, and let $\mathcal O$ denote its minimal containing sector. A vertex polynomial is a polynomial obtained by choosing each coeff…

Strengthened Hawaii conjecture. There exists $\sigma\in\mathbb{R}$ such that

Let $J_n(\theta)$ denote the Mallows–Riordan polynomial associated with the order-one autoregressive process. Sokal's root conjecture. All complex roots of $J_n$ lie outside the cl…

Bounded-roots conjecture. Every complex root of $p_S(z)$ lies in

Suppose that $f(z)=z^n$, where $n\in\mathbb{N}$ and $n\geq r+1$, and let $P_c$ denote the Taylor polynomial of $f$ of order $r$ at $x=c$. Polynomial-power conjecture. Every pair of…

Let $\mathcal{A}=(a_1,a_2,\dotsc)$ be a sequence of numbers in $(1,\infty)$, and let Proposition deterministically construct a sequence $\mathcal{X}=(x_0=0,x_1=1,x_2,\dotsc)$ from…