2 problems

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Shub–Smale's polynomial expected-length conjecture for random start systems
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…
Conjecturesolvedcondition-metric homotopy-continuation numerical-algebraic-geometryarXiv posted 2 days ago
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Conjecture that the circular path is a geodesic for the condition metric
Circular-path geodesic conjecture. The path $\gamma_1$ is a geodesic for the condition metric.
Conjectureopencondition-metric geodesics polynomial-homotopyarXiv posted 2 days ago

Shub–Smale's polynomial expected-length conjecture for random start systems