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SUMMARY:Automorphic L-functions\, primon gases and quantum cosmology - Sea
 n Hartnoll (University of Cambridge)
DTSTART:20260319T130000Z
DTEND:20260319T140000Z
UID:TALK242593@talks.cam.ac.uk
CONTACT:Klaas Parmentier
DESCRIPTION: 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 o
 n fundamental domains of modular groups. For example\, gravity in four spa
 cetime dimensions leads to PSL(2\,Z) while five dimensional gravity leads 
 to PSL(2\,Z[w])\, with Z[w] the Eisenstein integers. The automorphic forms
  can be expressed\, in a dilatation (Mellin transformed) basis as L-functi
 ons. The Euler product representation of these L-functions indicates that 
 these quantum states admit a dual interpretation as a "primon gas" partiti
 on function. I will describe some physically motivated mathematical questi
 ons that arise from these observations.
LOCATION:Potter room
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