Proof of Delfino-Viti conjecture
报告专家：吴保君 博士（北京大学）
报告时间：2024年11月18日（周一）下午15:00-16:00
报告地点：四川大学数学学院西202
报告摘要：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).
专家简介：吴保君于2023年9月在Aix-Marseille大学获得博士学位，师从Remi Rhodes教授。他的研究兴趣集中在概率与数学物理的交叉方向。
