7 problems

Linear-complexity conjecture. The computation of an slp representation of any geometric object associated to the polynomial family should have complexity linear in both $D$ and $L$…

Degree conjecture. The degree of $\mathcal{Z}_{{\bm{A}}_1}$ lies in $d^{O(n)}$ also. This estimate would make the bit-size and complexity bounds in the algorithm more precise, but…

Let $X \subset \mathbb{R}^k$ be a semi-algebraic set defined by a closed formula of complexity bounded by $C$, and let $\dim X=n$. A nested semi-algebraic filtration is a sequence…

Surjectivity conjecture. The map is surjective when $D$ and $D+v$ range over all effective odd theta characteristic divisors. The conjecture would ensure that the conditional step…

Let $f(x)=(x-x_1)\ldots(x-x_n)$ be a monic degree-$n$ polynomial, and for indices $1\leq i_j\leq n$ define the branch … Here $f^{(j)}$ denotes the $j$-th derivative and $Z$ denotes…

Fix a degree $d$. Consider any symmetric variety described by a real symmetric polynomial given as input, and consider both its ordinary and equivariant individual Betti numbers. P…

Let $A_1,A_2,\ldots,A_n$ be general projective cameras, and let $X_n\subseteq\mathbb{R}^{2n}$ be the affine multiview variety obtained by dehomogenizing the multiview variety assoc…