Monday, May 25, 2026
9:00 – 10:00 AM Registration
10:00 – 10:15 AM Opening Remarks
10:15 – 11:00 AM Jian Ding, Peking University
Recent Progress on Critical Percolation for Level-sets of Metric Graph Gaussian Free Fields
In this talk, I will review some recent progress on the critical percolation for the level-set of the Gaussian free field on the metric graph of $\mathbb Z^d$ for $d\geq 3$ (thanks to Lupu's isomorphism theorem, this is equivalent to the critical percolation for the metric graph loop soup model). In this talk, I will present some recent results on one-arm probabilities, incipient infinite clusters, two-arm probabilities, pivotal edges, as well as some comparison between the metric graph loop soup and the Brownian loop soup in three dimensions. This is based on a series of joint works with Zhenhao Cai.
11:00 – 11:30 AM Morning Coffee Break
11:30 AM – 12:15 PM Pierre Nolin, City University of Hong Kong
Percolation of Discrete GFF in Dimension Two
We study percolation of two-sided level sets for the discrete Gaussian free field (DGFF) in dimension two. For a DGFF $\varphi$ defined in a box with side length $N$, we show that with probability tending to $1$ as $N \to \infty$, there exist "low" crossings, along which $|\varphi| \le C \sqrt{\log \log N}$, for $C$ large enough (while the average and the maximum of $\varphi$ are of order $\sqrt{\log N}$ and $\log N$, respectively). As a consequence, we obtain connectivity properties for the set of thick points of a random walk.
We rely on an isomorphism between the DGFF and the random walk loop soup (RWLS) with critical intensity $\alpha=1/2$. We further extend our study to the occupation field of the RWLS for all subcritical intensities $\alpha\in(0,1/2)$, and in that case we uncover a non-trivial phase transition. This work relies heavily on new tools and techniques that we developed for the RWLS, especially surgery arguments on loops, which were made possible by a separation result for random walks in a loop soup. This allowed us to obtain a precise upper bound for the probability that two large connected components of loops "almost touch", which is instrumental here.
This talk is based on the four preprints https://arxiv.org/abs/2409.16230, https://arxiv.org/abs/2409.16273, https://arxiv.org/abs/2504.06202, and https://arxiv.org/abs/2509.25024, all joint with Yifan Gao and Wei Qian (as well as Yijie Bi for the last one).
12:15 – 2:00 PM Lunch Break
2:00 – 2:45 PM Xin Sun, Peking University
CFT Perspectives on 2D Percolation
Conformal field theory (CFT) has proven to be a powerful framework for studying two-dimensional (2D) Bernoulli percolation at criticality. Classic applications include the derivation of certain critical exponents and crossing probabilities. Yet, the precise nature of the underlying CFT remains elusive and is a subject of active investigation in both the mathematics and physics communities. In this talk, I will first provide an overview of this topic and then present recent progress.
2:45 - 3:15 PM Afternoon Coffee Break
3:15 – 4:00 PM Jianping Jiang, Tsinghua University
Particle Masses in the Near-critical Planar Ising Model
For the Ising model defined on $a\mathbb{Z}^2$ at critical temperature with external field $a^{15/8}h$, we give a new and simple proof that its truncated two-point function decays exponentially. This proof combines the high temperature expansion, random-cluster and random current representations of the Ising model. Then we will discuss the particle masses in the associated relativistic quantum field theory. Based on joint work with Frederik Klausen.