报告题目：Connection probabilities for 2D critical lattice models

报 告 人：吴昊教授（清华大学）

报告时间：2023年5月18日  15:30

报告地点：腾讯会议（122442636）

报告摘要：

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 fie ld (Schramm-Sheffield 2009), and lsing model and FK-lsing 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 lsing model and give the crossing probabilities of multiple interfaces. Such probabilities are related to solutions to BPZ equations in conformal field theory.

*In the second part, we consider critical random-cluster model with cluster weight $q\in (0, 4)$ and give conjectural formulas for connection probabilities of multiple interfaces. The conjectural formulas are proved for q=2, i,e, the FK-lsing model.

报告人简介：

吴昊，清华大学长聘教授。清华大学本科，巴黎十一大博士（导师为菲尔兹奖得主W. Werner），麻省理工学院和日内瓦大学博士后。主要研究方向为利用Schram Loewer Evolution研究统计物理模型，例如渗流模型、伊辛模型和高斯自由场等。于CMP、AOP、PTRF、AAP等期刊上发表研究论文20多篇。