Abstract: Liouville Quantum Gravity (LQG) is a probabilistic model of 2D random geometry that arises in the study of quantum gravity, conformal field theory and planar maps. In this talk, we investigate LQG through the spectral properties of its Laplacian, following the idea of Weyl's law in Euclidean geometry. Our main result is an explicit characterization of the second-order term in the expected heat trace expansion, which reveals a surprising connection to the celebrated KPZ scaling relation. This connection provides new insights into the interplay between spectral geometry and the probabilistic structure of LQG. This talk is based on joint work with Nathanael Berestycki.
Spectral geometry of LQG
27.11.2025 16:00 - 18:00
Organiser:
A. Carrance, W. Da Silva, K. Ryan
Location:
TU Wien, Gußhausstraße 25-25a, EI 5