Weyl's law in Liouville quantum gravity

Add to your list(s) Download to your calendar using vCal

• Nathanael Berestycki (Universität Wien)
• Monday 28 October 2024, 10:15-11:15
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

SSDW03 - Geometry, occupation fields, and scaling limits

Can you hear the shape of Liouville quantum gravity (LQG)?We obtain a Weyl law for the eigenvalues of Liouville Brownian motion:the number of eigenvalues in an interval grows linearly with the length of the interval. The proportionality constant is given by the Liouville measure of the domain and a certain deterministic constant which is computed explicitly and is, surprisingly, strictly greater than its Riemannian counterpart. This result (joint work with Mo Dick Wong) comes from a fine analysis of the LQG heat trace, which homogenises despite overwhelming pointwise fluctuations.We will also present a number of conjectures on the spectral geometry of LQG , notably suggesting a connection with “quantum chaos”.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.