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SUMMARY:A Trace-Path Integral Formula for Function Fields - Yan Yau Cheng 
 (University of Edinburgh)
DTSTART:20260310T143000Z
DTEND:20260310T153000Z
UID:TALK242818@talks.cam.ac.uk
CONTACT:Dmitri Whitmore
DESCRIPTION:In a topological quantum field theory\, path integrals can oft
 en be expressed instead as the trace of a monodromy action on a Hilbert sp
 ace.\n\nIn this talk I will discuss an arithmetic analogue of this phenome
 na for function fields\, where the phase space is replaced with the \\ell-
 torsion points of the Jacobian of a curve over a finite field\, the path i
 ntegral is replaced with a sum over the points of J[\\ell]\, and the monod
 romy is instead replaced with the Frobenius action. Time permitting\, I wi
 ll also briefly outline the proof of the arithmetic trace-path integral fo
 rmula.
LOCATION:MR13
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