5 problems

Adjacency-criteria conjecture. The adjacency relations between cells will play a central role in formulating concrete and computationally feasible criteria for deciding when a tree…

Let $f$ and $g$ be real polynomials in $x_1,\ldots,x_n$ of positive degrees in $x_n$, let $r\in\mathbf{R}[x_1,\ldots,x_{n-1}]$ be their resultant with respect to $x_n$, and suppose…

Let $R$ be the real closed field under consideration, let $X$ and $Y$ be affine $R$-varieties, and let $pi:X\to Y$ be a morphism such that $pi_*\mathcal{O}_X$ is a free…

Consider the general polynomial sign determination problem with interaction type $\mathbf{n}in \mathbb{N}^q$, outside the two special cases treated earlier, and the algorithm whose…

Let $\mathcal P$ be a strong cylindrical algebraic decomposition of $\mathbb R^n$ adapted to a closed and bounded semi-algebraic set $S$. Lazard's conjecture. The decomposition ind…