Schramm-Loewner evolution (SLE) is a canonical family of random planar curves. Liouville quantum gravity (LQG) is a canonical theory for random surfaces. It appears that there are rich integrable structures in both SLE and LQG. Namely, many important observables admit exact expressions.  In this talk I will first give an overview of these two subjects, and then review two major resources of such integrability: conformal field theory and random planar maps decorated with statistical physics models. Finally I will present a recent work with Morris Ang that proves an integrable result for conformal loop ensemble, a collection of SLE type loops describing the scaling limits of many important 2D statistical physics models such as the Ising model. Our result is analogous to the DOZZ formula in Liouville conformal field theory. It is an example of a series of results that are proved by blending these two sources of integrability.

Bio:

孙鑫，2007至2011年就读于北京大学数学科学学院，获理学学士学位。2017年获麻省理工学院数学博士学位。2017至2020年受西蒙斯基金会资助，于哥伦比亚大学从事博士后研究。 2020年起担任宾夕法尼亚大学数学系助理教授。主要从事概率论和数学物理方面研究。2018至2021年获美国国家科学基金会资助。2020年获伯努利学会青年研究者奖。2021年获美国国家科学基金会早期事业奖。