4 problems

Let $S\subset\mathbb{R}^k$ be a semi-algebraic set defined by $s\leq k/2$ quadratic inequalities, and suppose the paper's bound on its Betti numbers has the form $(O(k/s))^s$. Opti…

Let … be quadratic functions, and let the associated homogeneous quadratic map be … Assume that $f^h$ has hidden hyperplane convexity and that … is nonempty. An aggregation certifi…

Let $S$ be a set described by three quadratic inequalities, and assume the inequalities satisfy PDLC. A six-aggregation conjecture asserts that there exists such an $S$ for which i…

Let $S$ be a set described by quadratic inequalities, and suppose its associated quadratic data satisfy hidden hyperplane convexity. A finite aggregation conjecture asserts that th…