报告简介  Abstract

Two-dimensional Gaussian free field (GFF) is a natural 2D time analogue of Brownian motion. It is also known as free bosonic field in physics literatures, and it is the building block in conformal field theory, quantum gravity and statistical physics. In this talk, we focus on estimates of crossing probability in GFF.  Such crossing probability is a delicate quantity for GFF. We will introduce discrete GFF (dGFF) and metric graph GFF (mGFF). Both objects converge to continuum GFF as distributions. However, the crossing probabilities in dGFF and in mGFF are distinct. To derive the scaling limits of crossing probabilities in dGFF and in mGFF, we will introduce Schramm Loewner evolution (SLE). It turns out that the crossing probability in dGFF converges to the so-called pure partition functions of multiple SLEs, and that the crossing probability in mGFF converges to the ``fusion” of pure partition functions.

This talk is based on joint works with J. Ding (UPenn), M. Wirth (UPenn), and with M. Liu (Tsinghua).

嘉宾简介  About the Speaker

吴昊，清华大学丘成桐数学中心教授，博士生导师。2009年获得清华大学学士学位。2013年获得法国巴黎十一大学博士学位，之后分别在美国麻省理工学院、瑞士日内瓦大学从事研究工作。2014年以独立研究人的身份获得美国国家科学基金会（NSF）科研项目。2015年受邀担任美国国家科学基金会（NSF）科研经费评审委员。吴昊的研究方向是概率论、统计物理模型，特别在Schramm-Loewner Evolution(SLE)与平面统计物理模型问题上有突出贡献。2017年9月被聘为清华大学长聘教授。

讲座海报Poster