Abstract

I will review recent progress on random fractal metric spaces including metrics of Liouville quantum gravity, critical long-range percolation metrics as well as the exponential metric of a log-correlated fields in three dimensions and above. This talk is based on joint works with Julien Dubedat, Alexander Dunlap, Hugo Falconet, Subhajit Goswami, Ewain Gwynne,  Ofer Zeitouni, Fuxi Zhang and Zijie Zhuang in various combinations.

Biography

Professor Jian Ding received his B.S. from Peking University in 2006 and his Ph.D. from The University of California, Berkeley, in 2011. He has been a postdoc at Stanford and a faculty member at the University of Chicago and the University of Pennsylvania. Jian Ding is currently a chair professor at Peking University. Ding works on probability theory, emphasizing its interactions with statistical physics, theoretical computer science, and statistical learning theory. He is also interested in probability questions arising from "application-oriented" problems. With various coauthors, he has contributed to topics including random constraint satisfaction problems, random planar geometry, random field Ising models, random walks in random environments, and random Schrödinger operators. In prestigious mathematical journals like The Annals of Mathematics, Inventions Mathematicae, Acta Mathematica, Duke Math. J., and Comm. Pure Appl. Math., Ding has published more than ten articles. Moreover,  Ding has received some recognitions, including the ICM invited lecture (2022), the Xplorer Prize (2023), the Rollo Davidson prize (2017),  the ICCM gold medal (2022), and the Loève Prize (2024), etc.