Liouville Conformal Field Theory (in higher dimensions)

Abstract: Providing a rigorous definition to the two-dimensional Liouville Quantum Gravity as introduced by Polyakov in his 1981 seminal work has been a challenging problem over the last few years. In this fundamental article is introduced a canonical way of picking at random a geometry on a surface with fixed topology, using a generalised path integral approach involving the Liouville functional. The mathematical interpretation of this formalism is now rather well understood, thanks to the introduction of a probabilistic framework involving two fundamental objects : the Gaussian Multiplicative Chaos and log-correlated fields. During this talk I will try to introduce this topic, and if time permits, present some recent developments in the higher-dimensional theory.

Frenchprobability

Audience: researchers in the topic

Les probabilités de demain webinar

Series comments: There will be no seminar on 1st June because it is a public holiday in France (Pentecôte). The session on 15th June is the last one.