## Student Number Theory Seminar 2019-20

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2/3/20: Paul Garrett -- *Self-adjoint operators and zeta functions*

**Abstract:** One hundred years ago, when the theory of self-adjoint operators wasjust being developed, Hilbert and Polya independently speculated on the possibility of using self-adjoint operators (the fact that all eigenvalues are real) to prove the Riemann Hypothesis. In 1977, a flawed numerical computation of eigenvalues of the invariant Laplace-Beltrami operator on the modular curve seemed to indicate that zeros of zeta appeared as spectral parameters.