43rd Midwest Probability Colloquium

Title: Random Modulus of the Brownian Annulus and the Ghost CFT
Speaker: Xin Sun
Speaker Info: University of Pennsylvania
Brief Description:
Special Note:

Brownian surfaces are the scaling limits of uniformly sampled random planar maps. Under conformal embedding, their geometry is described by pure Liouville quantum gravity. This connection is well understood when the underlying topological surface is a sphere or a disk. When the surface is not simply connected, the corresponding Brownian surface has a random conformal structure (i.e. modulus). According to Polyakov's bosonic string theory, it was conjectured that the law of the random modulus is described by the partition function of a -26 dimensional conformal field theory (CFT) called the ghost CFT. We will review this conjecture and report the recent proof in the annulus case. Our proof also works for 2D quantum gravity coupled with conformal matters, which allows us to compute modular-dependent observables for SLE curves on an annulus, such as the continuum limit of the annulus crossing probability for critical percolation conjectured by Cardy. Based on a joint work with Ang, Remy and a work in progress with Xu and Zhuang.
Date: Friday, October 21, 2022
Time: 5:00pm
Where: 107 Swift Hall
Contact Person: Elton P. Hsu
Contact email: ehsu@math.northwestern.edu
Contact Phone: 1-8541
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