### The Riemann Hypothesis, unbounded operators and a tie to physics

Heilbronn Number Theory Seminar

17th October 2018, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

This summer at *Perspectives on the Riemann Hypothesis*, Bombieri and Garrett discussed modifications to the invariant Laplacian on the modular surface possibly relevant to RH. Recently, physicists such as Green, et al., have discovered that the behaviour of gravitons (hypothetical particles of gravity represented by massless string states) is closely related to eigenvalue problems for the invariant Laplacian. We will discuss new some surprising connections between these varying types of differential equations and their ties to zeros of L-functions. We will also present new results in this area obtained via functional analysis and spectral theory of automorphic forms.

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