4 problems

Average-case real-root algorithm conjecture. Finding a real approximate root, or determining that there are no real roots, for such a system should be possible in time

Assume either $a_+>1$ and $a_->0$, or $b_->1$ and $b_+>0$, and let $k_-$ be the positive endpoint of the interval arising in the Gale dual reduction. Let $\widetilde{g}_1$ denote t…

Three-steady-state conjecture. The maximum possible number of positive steady states of this reaction network is three. This includes the parameter regimes in which either $a_+>1$…

Bihan's conjecture. There is an affine relation basis for $\mathcal A$ whose coefficients all have absolute value at most $2$.