##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Xin Sun

#### Columbia University

## Conformal geometry of random surfaces in 2D quantum gravity

##### Abstract:

From a probabilistic perspective, 2D quantum gravity is the study of natural probability measures on the space of all possible geometries on a topological surface. One natural approach is to take scaling limits of discrete random surfaces. Another approach, known as Liouville quantum gravity (LQG), is via a direct description of the random metric under its conformal coordinate. In this talk, we review both approaches, featuring a joint work with N. Holden proving that uniformly sampled triangulations converge to the so called pure LQG under a certain discrete conformal embedding.

Host: Todd Kemp

### November 19, 2019

### 3:00 PM

### AP&M 6402

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