一、报告题目

Random surface, planar lattice model, and conformal field theory

二、主讲人

孙 鑫

三、报告时间

2022年12月20日 10:30-12:30

四、报告地点

腾讯会议

五、摘要

Liouville quantum gravity (LQG) is a theory of random surfaces that originated from string theory. Schramm Loewner evolution (SLE) is a family of random planar curves describing scaling limits of many 2D lattice models at their criticality. Before the rigorous study via LQG and SLE in probability, random surfaces and scaling limits of lattice models have been studied via another approach in theoretical physics called conformal field theory (CFT) since the 1980s. In this talk, I will demonstrate how a combination of ideas from LQG/SLE and CFT can be used to rigorously prove several long standing predictions in physics on random surfaces and planar lattice models, including the law of the random modulus of the scaling limit of uniform triangulation of the annular topology, and the crossing formula for critical planar percolation on an annulus. I will then present some conjectures which further illustrate the deep and rich interaction between LQG/SLE and CFT. Based on joint works with Ang, Holden, Remy, Xu, and Zhuang.

六、主讲人简介

I am an Assistant Professor in Mathematics at the University of Pennsylvania, with a secondary appointment in Statistics and Data Science. Before joining Penn, I was a Junior Fellow at Simons Society of Fellows, working at Columbia University. I got my Ph.D. degree from MIT and B.S. degree from Peking University. My research is supported by NSF CAREER Award DMS-2046514. In 2022-2023 I am a member at IAS, Princeton.

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心