中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
（第98讲）
(The Institute Lecture)
报告人： 吴昊 教授（清华大学）
题 目：Connection probabilities for random-cluster model and uniform spanning tree
时 间：2022.11.09(星期三), 15:30-17:00 (15:00-15:30为茶点时间, 地点: 数学院南楼N933室)
地 点：数学院南楼N204/腾讯会议：597-691-473 密码：123456
摘 要: Conformal invariance of critical lattice models in two-dimensional has been vigorously studied for decades. The first example where the conformal invariance was rigorously verified was the planar uniform spanning tree (together with loop-erased random walk), proved by Lawler, Schramm and Werner around 2000. Later, the conformal invariance was also verified for Bernoulli percolation (Smirnov 2001), level lines of Gaussian free field (Schramm-Sheffield 2009), and Ising model and FK-Ising model (Chelkak-Smirnov et al 2012). In this talk, we focus on connection probabilities of these critical lattice models in polygons with alternating boundary conditions.
This talk has two parts.
• In the first part, we consider critical random-cluster model with cluster weight q∈(0,4) and give conjectural formulas for connection probabilities of multiple interfaces. The conjectural formulas are proved for q=2, i.e. the FK-Ising model.
• In the second part, we consider uniform spanning tree (UST) and give formulas for connection probabilities of multiple Peano curves. UST can be viewed as the limit of random-cluster model as q goes to 0. Its connection probabilities turn out to be related to logarithmic CFT.
This talk is based on joint works with Yu Feng, Mingchang Liu, and Eveliina Peltola.
吴昊教授简介:
吴昊，2009年本科毕业于清华大学数学系，2013年博士毕业于法国巴黎十一大，博士导师为 W. Werner；2013-2017年，先后在美国麻省理工与瑞士日内瓦大学做博士后；2017年，被聘为清华大学长聘教授。吴昊主要研究随机过程Schramm Loewner Evolution、高斯自由场与Ising模型等经典统计物理模型。主要代表作包含平面统计物理模型边界点连通概率系列工作等。
数学所讲座(The Institute Lecture)：
旨在讲解现代数学的重要内容及其思想、方法和影响，扩展科研人员和研究生的视野，提高数学修养，加强相互交流，增强学术气氛。时间一般安排在每月第一个星期三（寒暑假除外）。
