Time: February 20, 2024 — June 27, 2024
Registration Deadline: February 4, 2024
Location: Room 77201, Jingchunyuan 78, BICMR
DescriptionThe first seminar will take place on Friday, Feb 23. Xin Sun will give an overview lecture assuming minimal background.
Our seminar in Spring 2024 will focus on two core subjects lying at the intersection of probability and mathematical physics: Gaussian free field (GFF) and Schramm Loewner evolution (SLE). There are excellent lecture notes on these topics. On the one hand, they may not be necessary for following our seminar. On the other hand, we assume that the participants are willing to read those well-documented materials on their own and discuss between each other.
We will focus on some important topics that are not streamlined yet, since they contain greater opportunity for research. Here are a partial list of topics that we plan to cover:
1. the imaginary geometry coupling of GFF and SLE;
2. various rigorous and conjectural relations with 2D lattice models;
3. representation theoretic aspect of GFF and Liouville conformal field theory.
The format is that I will give some introductory lecture(s) on a certain topic and invite someone to learn and present some material in detail. I have already secured a few volunteers. If you are interested in learning and presenting something, please let me know in advance (xinsun@bicmr.pku.edu.cn) and we can discuss possible topics.
Time：
Every Tuesday and Friday from 10am to 12am.
Tencent Meeting ID：475-8396-3483
https://meeting.tencent.com/dm/eWOsdKaGunix
There is a companion student seminar on Thursday evening. For more information, see this link:
Contact叶一一，Yiyi Ye (Ms.)
北京国际数学研究中心
Beijing International Center for Mathematical Research
Tel：86-10-62744133
Email: yeyiyi@bicmr.pku.edu.cn
There is a companion student seminar on Thursday evening. See this link:https://docs.qq.com/document/DVHpmQ0lXemRadXZh
Contact:
Mailing Address:
Mrs.Ye Yiyi
No.78 Jingchunyuan,Peking University,
Beijing,China 100871
E-mail:yeyiyi@bicmr.pku.edu.cn
Feb 23 Overview；孙鑫
Feb 27 Basic properties of Gaussian free fields. 金晟治
Mar 01 SLE and the forward coupling with GFF 刘浩宇
Mar 05 Level line of GFF and SLE4; 刘浩宇
Mar 08 Imaginary geometry I: the boundary case. 蔡格非
Mar 12 Dimer, UST and LERW: Temperley bijection and Wilson Algorithm. 金晟治
No seminars on March 15, 19 and 22 due to other activities
Mar 26 Dubedat Section 2: Loop measure, determinants. 吴保君&庄子杰
Mar 29 Dubedat Section 5: Boundary condition and partition condition. 吴保君&庄子杰
Apr 02 Dubedat Section 6:Couplings of SLE and GFF. 庄子杰&余璞
Apr 07 （清明节调休）Dubedat Section 7: SDE driven by GFF. 庄子杰&余璞
Apr 09 Dubedat Section 8: space filling SLE and duality. 余璞
Apr 12 Imaginary geometry IV: interior case. 余璞
No seminar between April 13 and May 6 due to other activities.
“Dubedat” refers to the paper SLE and the free field: Partition functions and couplings
May 07 Proofs of Cardy formula；谢卓言
May 10 Convergence of percolation to CLE；蔡格非
No seminar on May 14 and 17 due to other activities.
May 21 1-2:50pm CLE, GFF, and Brownian loop soup I 钱玮(remote)
May 24 1-2:50pm CLE, GFF, and Brownian loop soup II 钱玮 (remote), Room 9, Quan Zhai.
May 28 non-simple CLE, branching SLE, and space filling SLE；汪元正
May 31 CLE percolation； 刘浩宇
There will be a minicourse by Xin Sun at Beijing Normal University on May 28,29,30, at 3:30pm-5pm, location TBA.
Title: Liouville quantum gravity and mating of trees
Abstract: Liouville quantum gravity (LQG) is a theory for random surfaces. Mating of trees is a powerful framework for studying LQG and its coupling with SLE curves using classical Markovian processes such as Brownian motion and Levy process. This continuum theory is inspired by random walk encodings of random planar maps decorated with statistical physics models. This minicouse gives an introduction of this theory through a few examples.
Jun 04 2D GFF and Virasoro Algebra I; 徐晟景
Jun 07 2D GFF and Virasoro Algebra II; 吴保君
Jun 11 QFT with Polynomial Interaction I; 任潇
Ju 14 QFT with Polynomial Interaction II; 任潇
Minicourse: Harmonic Analysis of the Free Field, by Dalimil Mazac
Jun 17 Lecture 1 (Monday instead, at 全29)
Jun 19 Lecture 2(Wednesday instead, at 全29)
