Automorphic L-functions, primon gases and quantum cosmology

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• Sean Hartnoll (University of Cambridge)
• Thursday 19 March 2026, 13:00-14:00
• Potter room.

If you have a question about this talk, please contact Klaas Parmentier.

I will review how the equations of general relativity near a spacetime singularity map onto an arithmetic hyperbolic billiard dynamics. The semiclassical quantum states for this dynamics are Maaβ cusp forms on fundamental domains of modular groups. For example, gravity in four spacetime dimensions leads to PSL while five dimensional gravity leads to PSL , with Z[w] the Eisenstein integers. The automorphic forms can be expressed, in a dilatation (Mellin transformed) basis as L-functions. The Euler product representation of these L-functions indicates that these quantum states admit a dual interpretation as a “primon gas” partition function. I will describe some physically motivated mathematical questions that arise from these observations.

This talk is part of the Quantum Fields and Strings Seminars series.

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