##### Department of Mathematics,

University of California San Diego

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### Colloquium Seminar

## Morris Ang

#### Columbia University

## Random conformal geometry

##### Abstract:

In the first half, I will introduce the subject of random conformal geometry. Schramm-Loewner evolution (SLE) is a random planar curve describing the scaling limits of interfaces in statistical physics models (e.g. percolation, Ising model). Liouville quantum gravity (LQG) is a random 2D surface arising as the scaling limit of random planar maps. These fractal geometries have deep connections to bosonic string theory and conformal field theories. LQG and SLE exhibit a rich interplay: cutting LQG by independent SLE gives two independent LQG surfaces [Sheffield '10, Duplantier-Miller-Sheffield '14]. In the second half, I will present extensions of these LQG/SLE theorems and give several applications.

Host: Tianyi Zheng

### November 8, 2023

### 3:00 PM

APM 6402

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