**Abstract: **

Smirnov's proof of Cardy's formula for percolation on the triangular lattice leads to a discrete approximation of conformal maps, which we call the Cardy-Smirnov embedding. Under this embedding, Holden and I proved that the uniform triangulation converge to a continuum random geometry called pure Liouville quantum gravity. There is a variant of the Gaussian free field that governs this random geometry, which is an important example of conformal field theory called Liouville CFT. A key motivation for understanding Liouville quantum gravity rigorously is its application to the evaluation of scaling exponents and dimensions for 2D critical systems such as percolation. Recently, with Nolin, Qian and Zhuang, we used this idea and the integrable structure of Liouville CFT to derive a scaling exponent for planar percolation called the backbone exponent, which was unknown for several decades.

**Biography: **

Xin Sun got the Bachelor's degree in Mathematics in 2011 from Peking University, the Ph.D. degree in Mathematics from MIT in 2017. He spent three years at Columbia University as a junior fellow in the Simons Society of Fellows. Since 2020, he is an assistant professor at University of Pennsylvania. Starting from 2023 Fall, he is a tenured associate professor at Beijing International Center for Mathematical Research at Peking University. His research field is probability and mathematical physics, mainly focusing on random geometry, statistical physics, and quantum field theory.

*Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai*

**This event is open to the NYU Shanghai community and Math community.**