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Liouville Quantum gravity on Riemann surfaces

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Random Geometry

I will present the rigorous construction of Liouville quantum field theory on different Riemann surfaces (sphere, disk, torus, etc…). These constructions, which are based on Polyakov’s path integral, yield non trivial conformal field theories. As an output of the construction, we introduce the so-called Liouville measures which we conjecture to be the scaling limit of the volume form of finite maps conformally embedded in the sphere. If time permits, I will present the semi-classical approximation of these measures. Based on joint works with F. David, Y. Huang, H. Lacoin, A. Kupiainen, R. Rhodes.

This talk is part of the Isaac Newton Institute Seminar Series series.

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