Journée "Cartes Aléatoires"

# Liouville quantum gravity on the Riemann sphere

## by Prof. Vincent VARGAS (CNRS, ENS Paris)

Europe/Paris
Centre de conférences Marilyn et James Simons (I.H.E.S.)

### Centre de conférences Marilyn et James Simons

#### I.H.E.S.

Le Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description
In this talk, I will present a rigorous probabilistic construction of Liouville Field Theory on the Riemann sphere with positive cosmological constant, as considered by Polyakov in his 1981 seminal work "Quantum geometry of bosonic strings". Then, I will explain some of the fundamental properties of the theory like conformal covariance under PSL$_2(\C)$-action, Seiberg bounds, KPZ scaling laws, the KPZ formula and the Weyl anomaly (Polyakov-Ray-Singer) formula. If time permits, I will also explain the construction in the disk. This is based on joint works (some on arxiv and others in progress) with F. David, Y. Huang, A. Kupiainen, R. Rhodes.
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