Nonconjugate Borel subgroups conjecture for Cremona groups in dimension at least two

Let $n\geq 2$. The Cremona group ${\rm Bir}({\mathbb P}^n)$ consists of birational transformations of complex projective $n$-space, and a Borel subgroup is a maximal closed connected solvable subgroup in the Zariski topology. Nonconjugacy conjecture. For $n\geq 2$, ${\rm Bir}({\mathbb P}^n)$ contains nonconjugate Borel subgroups. The source describes this as a strengthened version of Popov's conjecture and notes that the case $n=2$ is established by a theorem in the paper; the cases $n\geq 3$ remain open in the source.