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SUMMARY:Spectral rigidity of random covers of compact hyperbolic surfaces 
 - Elena Kim (Massachusetts Institute of Technology)
DTSTART:20260514T143000Z
DTEND:20260514T153000Z
UID:TALK245011@talks.cam.ac.uk
DESCRIPTION:Let $X$ be a compact hyperbolic surface and let $X_n$ be a deg
 ree $n$ random cover. We show that\, with high probability\, the distribut
 ion of eigenvalues of the Laplacian on $X_n$ converges to the spectral mea
 sure of the hyperbolic plane with polynomially decaying error. We also obt
 ain an improved $L^{\\infty}$ bound on the eigenfunctions. Our proof relie
 s on the Selberg (pre-)trace formula and a variant of the polynomial metho
 d. &nbsp\;\nThis is joint work with Zhongkai Tao.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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