报告人：吴保君，本科毕业于山东大学泰山学堂和巴黎十一大，硕士毕业于巴黎高等师范学院，法国艾克斯－马赛大学获得博士学位，师从Remi Rhodes。目前，吴博士在北京国际数学研究中心从事博士后研究工作，研究兴趣集中在概率论与数学物理的交叉领域，特别是，Segal公理以及Liouville共形场理论的bootstrap方法的研究。Liouville共形场理论与许多经典的二维随机对象有着紧密联系，例如量子引力、Schramm-Loewner演化、共形环丛和随机平面图等。同时，吴博士也对Liouville量子引力、矩阵模型以及双曲几何之间的关系感兴趣
Abstract: In the context of random cluster models, the connectivity functions denoted as P_n(x_1, x_2, ..., x_n) signify the probabilities associated with n points belonging to the same finite cluster. The initial conjecture by Delfino and Viti proposed that, at the critical point in the continuum limit, the ratio R = P_3(x_1, x_2, x_3) / \sqrt{P_2(x_1, x_2) P_2(x_2, x_3) P_3(x_1, x_3)} converges to a universal constant solely dependent on $\kappa$. This dependence can be expressed through the imaginary DOZZ formula. For percolation, this constant approximates to 1.022. In this presentation, we elucidate the proof specifically for the percolation scenario. Additionally, we introduce analogous quantities within the conformal loop ensembles carpet/gasket measure, demonstrating their precise alignment with the imaginary DOZZ formula. The discussion will also delve into the statistical physics origin and its connections to conformal field theory.
This is based on the joint work with Morris Ang (Columbia), Gefei Cai (BICMR), and Xin Sun (BICMR).
