## EVENT DETAILS AND ABSTRACT

**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**:

**Abstract:**

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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