4 problems

Ulas's conjecture. For every $\varepsilon>0$ and every $m\geq 2$, there exists $N$, possibly depending on $\varepsilon$ and $m$, such that

Brilleslyper and Schaubroeck's conjecture. The number of roots of $x^n+x^m-1$ in the interior of the unit circle is

Annulus conjecture. The subtree roots of $T$ are contained in this annulus.

Disk conjecture. The subtree roots of $T$ lie in $D_n$.