5 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…

Homotopy conjecture. A homotopy viewpoint—a continuous deformation between linearizing morphisms, rather than commitment to a single one—can regulate references and operating regio…

Let ${{\boldsymbol{M}}}_n$ and ${\boldsymbol{S}}_n$ be the matrices described above, and define … Here ${\boldsymbol{T}}({\varepsilon})$ is the symmetric homotopy matrix and…

Let $g=(g_1,\ldots,g_n)$ be a homogeneous polynomial system with degrees $(d_1,\ldots,d_n)$, and let $\zeta=(1,0,\ldots,0)$. A starting pair $(g,\zeta)$ is called good when its ave…

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…