4 problems

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The algebraic monodromy formula for subarrangements of Coxeter arrangements
Algebraic monodromy formula conjecture. The same formula holds for every subarrangement of rank at least $3$ in an arbitrary Coxeter arrangement.
Conjectureopenalgebraic-monodromy coxeter-arrangements hyperplane-arrangementsarXiv posted 2 days ago
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Papadima–Suciu's exponent–beta conjecture for hyperplane arrangements
Let $\mathcal{A}$ be a hyperplane arrangement, let $e_p(\mathcal{A})$ denote the relevant exponent of its algebraic monodromy, and let $\beta_p(\mathcal{A})$ denote the dimension o…
Conjectureopenalgebraic-monodromy hyperplane-arrangements orlik-solomon-algebraarXiv posted 2 days ago
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The combinatorial formula conjecture for arrangement monodromy
Combinatorial monodromy conjecture. The characteristic polynomial is determined by this formula. The preceding results establish the formula in several cases, including arrangement…
Conjectureopenalgebraic-monodromy hyperplane-arrangements milnor-fibrationsarXiv posted 2 days ago
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Serre's independence-of-ell conjecture for connected monodromy representations
Serre's independence-of-ell conjecture. The tautological representation of $\mathbf{G}_\ell^\circ$ is independent of $\ell$ . This predicts an $\ell$ -independent algebraic descripti…
Conjectureopenalgebraic-monodromy compatible-systems ell-independencearXiv posted 2 days ago

The algebraic monodromy formula for subarrangements of Coxeter arrangements