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SUMMARY:Weyl law in Liouville quantum gravity - Nathanaël Berestycki (Uni
versity of Vienna)
DTSTART;VALUE=DATE-TIME:20231016T140000
DTEND;VALUE=DATE-TIME:20231016T150000
UID:https://talks.ox.ac.uk/talks/id/410aefa7-d131-4882-8d7a-b809b5649082/
DESCRIPTION:Can you hear the shape of Liouville quantum gravity (LQG)?\n\n
We obtain a Weyl law for the eigenvalues of Liouville Brownian motion: the
n-th eigenvalue grows linearly with n\, with the proportionality\nconstan
t given by the Liouville measure of the domain and a certain deterministic
constant which is computed explicitly and is\,\nsurprisingly\, strictly g
reater than its Riemannian counterpart. After explaining this result and i
ts context\, as well as some related\nestimates pertaining to the small-ti
me behaviour of the heat kernel\, I hope to also present a number of conje
ctures on the spectral geometry\nof LQG.\nThese relate both to the behavio
ur of eigenfunctions (suggesting intriguing connections with so-called "qu
antum chaos") and to that of\neigenvalues\, for which we conjecture a conn
ection to random matrix statistics.\n\nThis is joint work with Mo-Dick Won
g (Durham).\nSpeakers:\nNathanaël Berestycki (University of Vienna)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/410aefa7-d131-4882-8d7a-b809b5649082/
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DESCRIPTION:Talk:Weyl law in Liouville quantum gravity - Nathanaël Berest
ycki (University of Vienna)
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