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UID:node-3133366@mathematics.huji.ac.il
DTSTAMP:20221208T123000Z
DTSTART:20221208T123000Z
DTEND:20221208T133000Z
SUMMARY:Colloquium: Z. Rudnick (TAU)
DESCRIPTION:*Title:*Eigenvalue statistics for random hyperbolic surfaces\n*Abstract:*I will discuss some of the interactions between number theory and \nthe spectral theory of the Laplacian. Some have very classical background, \nsuch as the connection with lattice point problems. Others are newer, \nincluding connections between random matrix theory, the zeros of the Riemann \nzeta function, and spectral statistics on the moduli space of hyperbolic \nsurfaces.\nIn particular, I will describe some recent progress on an outstanding \nconjecture in quantum chaos, that the statistics of the energy levels of \n“generic” chaotic systems with time reversal symmetry are described by \nthose of the Gaussian Orthogonal Ensemble (GOE) in Random Matrix Theory. \nConjectural examples are the eigenvalues of the Laplacian on a “generic” \nhyperbolic surface. This conjecture has proved to be extremely difficult, \nwith no single case being proved. It has long been desired to improve the \nsituation by averaging over a suitable ensemble of chao...
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