2 problems

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Pure point spectrum conjecture for one-dimensional Pisot substitution systems
A Pisot substitution in one dimension is a substitution whose substitution matrix has one eigenvalue strictly greater than $1$ and all other eigenvalues strictly between $0$ and…
Conjectureopenpure-point-spectrum substitution-dynamics symbolic-dynamicsarXiv posted 2 days ago
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The pure-point-spectrum Poisson-statistics conjecture
Consider finite-volume random Schrödinger operators approximating a limiting infinite-volume operator, and let the eigenvalue process denote the rescaled point process of their eig…
Conjectureopenpoisson-processes pure-point-spectrum random-operatorsarXiv posted 2 days ago

Pure point spectrum conjecture for one-dimensional Pisot substitution systems