How to choose a (good) random surface

Fractal Geometry and Dynamics

11 October 14:00 - 14:50

Yichao Huang - University Pierre et Marie Curie.

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.
Kenneth Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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