Journée "Cartes Aléatoires"
# Liouville quantum gravity on the Riemann sphere

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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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