I am a Junior Fellow at Simons Society of Fellows, working at the Department of Mathematics at Columbia University. Before coming to Columbia, I got my Ph.D. degree in mathematics from MIT and my B.S. degree in mathematics from Peking University. My Ph.D. adviser is Scott Sheffield. In the summer of 2014, I was a research intern at Microsoft Research Theory Group , where I was mentored by David Wilson.

My research area is probability theory and mathematical physics. So far I have done research on random planar geometry, including SLE, Gaussian free field, random planar maps and Liouville quantum gravity. I have also worked on uniform spanning trees and abelian sandpiles, as well as random matrices, fractional Gaussian fields and the Airy line ensemble.

(Last updated: June 26, 2017)

**Almost sure multifractal spectrum of SLE**

Ewain Gwynne, Jason Miller and Xin Sun. *Duke Math. J.* to appear. arxiv:1412.8764.

**Two perspectives of the unit area quantum sphere and their equivalence**

Juhan Aru, Yichao Huang and Xin Sun. *Communications in Mathematical Physics.* 356, 261-283 (2017). arxiv:1512.06190.

**Deep Learning with Coherent Nanophotonic Circuits**

Yichen Shen, Nicholas C. Harris, Scott Skirlo, Mihika Prabhu, Tom Baehr-Jones, Micheal Hochberg, Xin Sun, Shijie Zhao, Hugo Larochelle, Dirk Englund and Marin Soljacic. *Nature Photonics* (2017). arxiv:1610.02365.

**Brownian motion correlation in the peanosphere for $\kappa> 8$**

Ewain Gwynne, Nina Holden, Jason Miller and Xin Sun. *Annales de l'Institut Henri Poincaré,* to appear. arxiv:1510.04687.

**Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map I: cone times**

Ewain Gwynne, Cheng Mao and Xin Sun. *Annales de l'Institut Henri Poincaré,* to appear. arxiv:1502.00546.

**Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map II: local estimates and empty reduced word exponent**

Ewain Gwynne and Xin Sun. *Electron. J. Probab.* 22(2017), no. 45, 1-56. arxiv:1505.03375.

**Sandpiles and unicycles on random planar maps**

David Wilson and Xin Sun. *Electron. Commun. Probab.* 21(2016), no. 57, 1-12. arxiv:1506.08881.

**Fractional Gaussian field: a survey**

Asad Lodhia, Scott Sheffield, Xin Sun and Samuel Watson. *Probability Surveys*, Vol 13(2016), 1-56. arxiv:1407.5598.

**On fluctuations for random band Toeplitz matries**

Yiting Li and Xin Sun. *Random Matrices: Theory and Applications.* Vol. 4, No.2(2015). arxiv:1412.5232.

**Ergodicity of the Airy line ensemble**

Ivan Corwin and Xin Sun. *Electron. Commun. Probab.* 19(2014), no. 49, 1-11. arxiv:1405.0464.

**Fluctuations of eigenvalues for random Toeplitz and related matrices**

Dangzheng Liu, Xin Sun and Zhengdong Wang. *Electron. J. Probab.* 17(2012), no. 95, 1-22. arxiv:1010.3394v2.

**A note on eigenvalues of random block Toeplitz matrices with slowly growing bandwidth**

Yiting Li, Dangzheng Liu, Xin Sun and Zhengdong Wang. *Statistics and Probability Letters* 08(2011); 81 (12). arxiv:1108.2810.

**A mating-of-trees approach for graph distances in random planar maps**

Ewain Gwynne, Nina Holden and Xin Sun. arxiv:1711.00723.

**Schnyder woods, SLE$_{16}$ and Liouville quantum gravity**

Yiting Li, Xin Sun and Samuel Watson. arxiv:1705.03573.

**Occupation measure of random walks and wired spanning forests in balls of Cayley graphs**

Russell Lyons, Yuval Peres and Xin Sun. arxiv:1705.03576.

**SLE as a mating of trees in Euclidean geometry**

Nina Holden and Xin Sun. arxiv:1610.05272.

**Loop-erased random walk, uniform spanning forests and bi-Laplacian Gaussian field in the critical dimension**

Gregory Lawler, Xin Sun and Wei Wu. arxiv:1608.02987.

**A distance exponent for Liouville quantum gravity**

Ewain Gwynne, Nina Holden and Xin Sun. arxiv:1606.01214.

**Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense**

Ewain Gwynne, Nina Holden and Xin Sun. arxiv:1603.01194.

**Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map III: finite volume case**

Ewain Gwynne and Xin Sun. arxiv:1510.06346.

**Equivalence of Liouville measure and Gaussian free field**

Nathanael Berestycki, Scott Sheffield and Xin Sun. arxiv:1410.5407.

**Uniform spanning forest and the bi-Laplacian Gaussian field**

Xin Sun and Wei Wu. arxiv:1312.0059.

**Phases of quantum Loewner evolution.**

Ewain Gwynne, Jason Miller, Scott Sheffield and Xin Sun.

**2017.11 Seminar on Stochastic Processes**, ETH Zurich

**2017.11 Lyon Probability Seminar**, Lyon University 1

**2017.10 Indiana Probability Seminar**, Indiana University

**2017.03 Brandeis Every Topic Seminar**, Brandeis University

**2017.03 SLE, GFF and LQG in NYC**, Columbia University

**2017.01 Stanford Probability Seminar**, Stanford University

**2016.12 Michigan State University Probability Seminar**, Michigan State University

**2016.11 Talks in theoretical sciences 2016**, ETH Zurich

**2016.11 UBC Probability Seminar**, University of British Columbia

**2016.10 NYU Probability and Mathematical Physics Seminar**, New York University

**2016.06 Workshop on Recent Developments in SLE**, Mittag-Leffler Institute, Stockholm, Sweden

**2016.04 Brown Discrete Math Seminar**, Brown University

**2016.04 Columbia Probability Seminar**, Columbia University

**2016.02 3rd Annual Graduate Student Math Conference in Analysis **, Brown University

**2015.11 Northwestern Analysis Seminar**, Northwestern University

**2015.11 Chicago Probability and Statistical Physics Seminar**, University of Chicago

**2015.11 MIT Probability Seminar**, MIT

**2015.09 Harvard Random Matrix and Probability Seminar **, Harvard University

**2015.07 Peking University Youth Probability Forum**, Peking University

**2015.05 Seymour Sherman Lecture and Conference**, Indiana University

**2015.01 Workshop on Conformally Invariant Scaling Limits**, Issac Newton Institute, Cambridge, UK

Juhan Aru, Nathanael Berestycki, Ivan Corwin, Ewain Gwynne, Nina Holden, Yichao Huang, Gregory Lawler, Yiting Li, Dangzheng Liu, Asad Lodhia, Russell Lyons, Cheng Mao, Jason Miller, Yuval Peres, Scott Sheffield, Zhengdong Wang, Samuel Watson, Yichen Shen, David Wilson, Wei Wu.