6 problems

Let $f$ be the target polynomial system, let $g$ be a start system chosen from the sphere ${\mathbb S}$ with the uniform probability distribution, and let $e_0$ be the initial solu…

Let $\mathbf{f}$ satisfy the assumptions of Theorem, let $\hat{\mathbf{x}}$ be the zero under consideration, and write $\delta_{\hat{\mathbf{x}}}(\mathbf{f})$ for its depth. Let…

Let $\mathcal{J}^{\mathcal{E}}_d$ denote the Euclidean joint signature for a generic plane curve of degree $d$. The multiprojective witness-set dimensions are…

Let $n$ be a positive integer, and let a real witness set for an algebraic variety mean a witness set whose points are real. Existence conjecture. For any $n$, the algebraic group…

Consider the system of $48$ polynomial equations in the parameters $\{\phi_{\boldsymbol{j},\mu}\}$, which has $11664$ complex solutions for generic parameter values. Restrict the p…

Let $V=\{(h,z)\in{\mathbb S}\times{\mathbb P}({\mathbb C}^{n+1})\mid h(z)=0\}$ be the solution variety, and let $(g,e_0)$ be the initial pair with … For an initial pair…