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SUMMARY:Weyl's law in Liouville quantum gravity - Nathanael Berestycki (Un
 iversität Wien)
DTSTART:20241028T101500Z
DTEND:20241028T111500Z
UID:TALK220696@talks.cam.ac.uk
DESCRIPTION:Can you hear the shape of Liouville quantum gravity (LQG)?We o
 btain a&nbsp\;Weyl&nbsp\;law&nbsp\;for the eigenvalues of Liouville Browni
 an motion:the number of eigenvalues in an interval grows linearly with the
  length of the interval. The proportionality constant is given by the Liou
 ville measure of the domain and a certain deterministic constant which is 
 computed explicitly and is\, surprisingly\, strictly greater than its Riem
 annian counterpart. This result (joint work with Mo Dick Wong) comes from 
 a fine analysis of the LQG heat trace\, which homogenises despite overwhel
 ming pointwise fluctuations.We will also present a number of conjectures o
 n the spectral geometry of LQG\, notably suggesting a connection with "qua
 ntum chaos".
LOCATION:Seminar Room 1\, Newton Institute
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