4 problems

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Hussain–Ma–Yau–Zuo's non-existence conjecture for negative derivations
Hussain–Ma–Yau–Zuo's conjecture. The graded algebra
Conjectureopenderivations higher-nash-blowup weighted-homogeneous-singularitiesarXiv posted 2 days ago
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da Silva Machado–Seade conjecture on logarithmic vector fields and weighted homogeneous singularities
da Silva Machado–Seade conjecture. Weighted homogeneity of $(D,0)$ is characterized by the existence of a holomorphic vector field tangent to $D$ and transverse to all sufficiently…
Conjectureopenlogarithmic-vector-fields singularity-theory weighted-homogeneous-singularitiesarXiv posted 2 days ago
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Machado–Seade conjecture on weighted homogeneity and logarithmic vector fields
Machado–Seade conjecture. The following statements are equivalent: $(D,0)$ is weighted homogeneous; there exists a holomorphic vector field tangent to $D$ with an isolated singular…
Conjectureopenlogarithmic-vector-fields singularity-theory weighted-homogeneous-singularitiesarXiv posted 2 days ago
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Yau's conjecture on negative derivations of the Tjurina algebra
Yau's conjecture. The Tjurina algebra has no negative weighted derivations. This conjecture is still open to the authors' knowledge, although many cases have been resolved.
Conjectureopenderivations tjurina-algebras weighted-homogeneous-singularitiesarXiv posted 2 days ago

Hussain–Ma–Yau–Zuo's non-existence conjecture for negative derivations