Summer School on Probability
Time: June 12 - June 16, 2023
Venue: Lecture Hall, Jiayibing Building, Jingchunyuan 82, BICMR
课程安排已发布，请见 Schedule
上课地点：北京国际数学研究中心 甲乙丙楼 二层报告厅
Lecturer: Yilin Wang (王艺霖), IHES
Title: Around the Loewner energy
Abstract: This is an introductory lecture on the Loewner energy, a functional measuring the roundness of a Jordan curve. It arises from the probabilistic theory of Schramm-Loewner evolutions and connects unexpectedly to the class of Weil-Petersson quasicircles, a class of Jordan curves arising from the Kahler geometry on the universal Teichmuller space. This class of curves is also of interest in geometric function theory and geometric analysis and has many different but equivalent definitions. I will give an overview of how various subjects are connected via the Loewner energy, which may include depending on time, SLE, determinant of Laplacians, Brownian loop measure, Weil-Petersson Teichmuller space, Grunsky operator, Coulomb gas on a curve, renormalized volume in hyperbolic 3-space, etc.
Bio: Yilin Wang is working on topics at the interface of Complex analysis and Probability theory. Her current research focuses on themes that aim at enlightening the connections among Random conformal geometry, Geometric function theory, and Teichmüller theory.
Lecturer: Lingfu Zhang (张灵夫), UC Berkeley
Title: First- and Last-Passage Percolation: Algebraic and Probabilistic Perspectives
Abstract: A fundamental problem in probability is understanding universality, which refers to the phenomenon where different probabilistic models display the same limiting behavior. A classic example of this is the convergence of various random walks to Brownian motion. In the 1980s, Kardar, Parisi, and Zhang (KPZ) predicted a new universality for a class of random growing surfaces that model various natural processes, such as crystal melting, bacterial growth, and molecular condensation. KPZ behaviors later appeared unexpectedly in various contexts, including random matrix theory, random tiling, traffic flow models, and polymers in random media, which are extensively studied in diverse disciplines.
This lecture series will focus on central models in the KPZ universality class called First/Last-Passage Percolation (FPP/LPP), which can be understood as natural random planar metrics. Historically, two disjoint sets of techniques have been used to study FPP/LPP: formulas from representation theory or algebraic combinatorics, and probabilistic arguments that exploit geometric properties. In recent years, a combination of these two approaches has led to many new advances in understanding FPP/LPP and related models in the KPZ universality class. This has revealed new phenomena and solved a variety of open problems. The lecture series will provide an overview of these developments, with some examples being discussed in detail.
Bio: Lingfu Zhang currently holds the position of a Miller Research Fellow at UC Berkeley's Department of Statistics and the Miller Institute for Basic Research in Science. He earned his Ph.D. in Mathematics from Princeton University in 2022, under the guidance of Allan Sly, after completing his B.S. from MIT in 2017. Lingfu's research interests lie in various areas of probability theory, such as the KPZ universality class and exact-solvable models, the Anderson model of localization, distributed sampling algorithms, and the mixing of Markov chains.
Acceptance List (update)
Accommodation and Travel Information
BICMR will provide some participants in the List in FX Hotel Zhong Guan Cun which is located at Zhong Guan Cun, known as the “Silicon Valley”.
Address: No.68 North 4th Ring West Road (South of Haidian Bridge) Haidian District, Beijing
Tel: (China) 400 8200 868 (International) +86 21 6091 9987
Website: http://www.fxhotels.com
Other participants are responsible for arranging and paying for their own reservations for hotel accommodations and travel expenses. Some nearby hotels are available here: http://bicmr.pku.edu.cn/content/page/9.html
