孙鑫 教授系列学术报告
Title: Lecture Series on Liouville gravity, CFT and TQFT
Speaker: Xin Sun (孙鑫)
Affiliation: Peking University (北京大学）
Time: 10:00-11:30 am, Wednesday, 25th March, 2026
10:00-11:30 am, Thursday, 26th March, 2026
10:00-11:30 am, Friday, 27th March, 2026 (UTC+8, Beijing Time)
Venue: Room 1502, Shing-Tung Yau Center, Yifu Architecture Building, Sipailou Campus of Southeast University
（东南大学四牌楼校区逸夫建筑馆丘成桐中心1502室）
Inviter: Jie Gu (顾杰)， Yunfeng Jiang (江云峰）
Abstract:
◆ Lecture 1: Liouville quantum gravity: from random planar maps to conformal field theory
(10:00-11:30 am, Wednesday, 25th March, 2026)
Abstract: Originating in theoretical physics, Liouville quantum gravity (LQG) has been an important topic in probability theory and mathematical physics in the past two decades. In this talk, we review two aspects of this topic. The first is that LQG describes the random conformal geometry of the scaling limit of random planar maps. We highlight the convergence of random planar maps under discrete conformal embedding, where couplings between LQG and the Schramm-Loewner evolution (SLE) play a key role. The second aspect is the connection to conformal field theory (CFT). Here we highlight the interplay between Liouville CFT and the SLE/LQG coupling, the CFT description of 2D quantum gravity coupled with conformal matter, and applications to SLE and 2D statistical physics. Based on the joint 2026 ICM proceeding with Nina Holden.
◆ Lecture 2: CFT perspectives on percolation and related models
(10:00-11:30 am, Thursday, 26th March, 2026)
Abstract: 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 provide an overview of this topic.
◆ Lecture 3: Three perspectives on the b-6j Symbol: Quantum Group, 2D CFT, and 3D Quantum Topology
(10:00-11:30 am, Friday, 27th March, 2026)
Abstract: This talk will explore the triple role of a special function known as the b-6j symbol: as the Racah-Wigner symbol in the representation theory of a quantum group, as the fusion matrix governing crossing symmetry in 2D Liouville conformal field theory, and as the fundamental building block for a 3D quantum topological invariant. In particular, we will demonstrat how the pentagon identity manifests in all three perspectives. Based on three recent projects, one joint with Ang, Remy, Zhu, one joint with Ghosal, Remy, Sun, Wu, and one joint with Ming, Liu, Wu, Yang.
Speaker:
Xin Sun is a Full Professor of Mathematics at Beijing International Center for Mathematical Research, Peking University.He got his bachelor degree from Peking University and his Ph.D. from MIT. He was a postdoc at Columbia University as a Simons Junior Fellow, and then a faculty member at University of Pennsylvania, before returning to Peking University in 2023.
His research area is probability theory and mathematical physics. His Ph.D. training focused on 2D random geometry and statistical physics, topics including Schramm-Loewner evolution, Gaussian free field, Liouville quantum gravity, random planar map, percolation, and uniform spanning tree. Since then, he started to explore related areas in mathematical physics, such as conformal field theory and string theory. He was fascinated by the interplay between different mathematical areas, and between mathematics and physics.
(Please refer to http://faculty.bicmr.pku.edu.cn/~xinsun/ )