報告題目：Proof of Delfino-VIti conjecture

報告時間：2024年3月8日上午10:30-11:30

報告地點：kaiyun開云官方網(wǎng)站犀浦校區(qū)3教30456

報告人：吳保君

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).

報告人簡介：吳保君，本科畢業(yè)于山東大學(xué)泰山學(xué)堂和巴黎十一大，碩士畢業(yè)于巴黎高等師范學(xué)院，法國艾克斯－馬賽大學(xué)獲得博士學(xué)位，師從Remi Rhodes。目前，吳博士在北京國際數(shù)學(xué)研究中心從事博士后研究工作，研究興趣集中在概率論與數(shù)學(xué)物理的交叉領(lǐng)域，特別是，Segal公理以及Liouville共形場理論的bootstrap方法的研究。Liouville共形場理論與許多經(jīng)典的二維隨機對象有著緊密聯(lián)系，例如量子引力、Schramm-Loewner演化、共形環(huán)叢和隨機平面圖等。同時，吳博士也對Liouville量子引力、矩陣模型以及雙曲幾何之間的關(guān)系感興趣。

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