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math.OA2025
On almost commuting unitary matrices
Adam Dor-On, Lucas Hall, Ilya Kachkovskiy
A question going back to Halmos asks when two approximately commuting matrices of a certain kind are close to exactly commuting matrices of the same kind. It has long been known th…
math.SP2025
Absence of flat bands for discrete periodic graph operators with generic potentials
Matthew Faust, Ilya Kachkovskiy
We show that Schrödinger-type operators on discrete connected periodic graphs do not have flat bands for generic potentials.