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Yichao Huang: How to choose a (good) random surface

Tid: On 2017-10-11 kl 14.00 - 14.50

Plats: Institut Mittag-Leffler, Auravägen 17, Djursholm

Medverkande: Yichao Huang, Pierre-and-Marie-Curie University

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Polyakov introduced Liouville Conformal Field Theory in his theory of integration over 2d Riemann surfaces (1981). In this talk, we will gently explain a rigorous probabilistic approach by David-Kupiainen-Rhodes-Vargas (2014) based on Feynman’s path integral formalism. In the construction of this path integral over surfaces with exponential interaction, a crucial ingredient is Kahane’s Gaussian Multiplicative Chaos (1985), a natural multifractal random measure defined as the exponential of a log-correlated Gaussian field. We will also briefly explain some extensions of Kahane’s theory to the case of the unit disk.