A survey of recent results proving that random hyperbolic surfaces of large genus have near-optimal spectral gaps, after Hide–Magee, Anantharaman–Monk, and Hide–Macera–Thomas.
Limit points of uniform arithmetic bass notes
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abstract
We prove that the set of limit points of the set of all spectral gaps of closed arithmetic hyperbolic surfaces equals $[0,\frac{1}{4}]$.
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Bass notes of random hyperbolic surfaces of large genus
A survey of recent results proving that random hyperbolic surfaces of large genus have near-optimal spectral gaps, after Hide–Magee, Anantharaman–Monk, and Hide–Macera–Thomas.