3 problems

Nested derivative cones conjecture. For every $n\in\mathbb{N}$, the semialgebraic sets $D_k$ form a descending chain under inclusion,

Let $S\subseteq\mathbb{R}^d$ be a polytope. Define $s=s(S)$ to be the minimal number of polynomials needed to represent $S$ as a basic closed semialgebraic set, … Here the inequali…

Minimum polynomial-representation conjecture. For every convex $d$-polytope $P$ in $\mathbb{R}^d$, one has