Liouville quantum gravity (LQG) is in some sense the canonical model of a two-dimensional Riemannian manifold and is defined using the (formal) metric tensor
eγh(z)(dx2 + dy2) where h is an instance of some form of the Gaussian free field and γ ∈ (0, 2) is a parameter. This expression does not make literal sense since h is a distribution and not a function, so cannot be exponentiated. Previously, the associated metric (distance function) was constructed only in the special case γ = p 8/3 in joint work with Sheffield. In this talk, we will show how to associate with LQG a canonical conformally covariant metric for all γ ∈ (0, 2). It is obtained as a limit of certain approximations which were recently shown to be tight by Ding, Dub´edat, Dunlap and Falconet. This is based on joint work with Ewain Gwynne.
Abstract TBA - check stats website for updates, https://statistics.stanford.edu/events/probability-seminar