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math.SP2026
Band edges of periodic Schrödinger operators are generically isolated and nondegenerate
Zhongkai Tao, Mengxuan Yang
For periodic Schrödinger operators with bounded real-valued potentials on with , we show that for generic potentials, each endpoint of every spectra…
math.SP2026
Polynomial bounds for eigenfunctions and eigenvalues on random covers of hyperbolic surfaces
Elena Kim, Zhongkai Tao
Let be a compact connected orientable hyperbolic surface and let be a degree cover, taken uniformly at random. We show that, with high probability, the nor…
math.SP2024
Spectral gap for surfaces of infinite volume with negative curvature
Zhongkai Tao
We prove that the imaginary parts of scattering resonances for negatively curved asymptotically hyperbolic surfaces are uniformly bounded away from zero and provide a resolvent bou…