Problem dossier · Dynamics & Analysis
Sendov's conjecture
If all roots of a polynomial lie in the closed unit disk, then within distance 1 of each root lies a critical point (root of the derivative).
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Status
Open in general. Proved for degree ≤ 8, for roots on the circle, and by Tao (2020) for all sufficiently large degrees.
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The Angle of Attack
High-precision numerical verification for mid-range degrees (9 ≤ n ≤ a few hundred) over random and structured root sets; search for extremal configurations approaching distance 1.
Tags: polynomials · critical points · complex analysis
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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