报告题目：是否每个可数无穷图都有一个不友好剖分？

报 告 人：向开南

时 间：2023年5月17日 (周三) 下午 15:30-16:30

地 点：6号教学楼323会议室

简 介：猜想：每个可数无穷图都有一个不友好顶点二剖分，即每个顶点在自己所属的类里的邻居数不超过在另一个类里的邻居数。 这是无穷图论中有30多年历史的最著名猜想之一。从Open Problem Garden (http://www.openproblemgarden.org/)可以得知，它的重要性为3星；概率论中的 KPZ Universality Conjecture、数论中的The 3n+1 Conjecture (The 3x+1 Problem)的重要性也是3星；此处重要性的最高等级为4星，黎曼猜想是4星。 20世纪数学的一个了不起的发展是认识到有时候可以用概率方法来证明一些看起来并没有概率本性的数学命题（N. Alon & M. Krivelevich, 2008）。此猜想能否被概率方法攻克？我们的答案是肯定的。

报告题目：Spatiotemporal Dynamics in Epidemic Models with Levy F…

报 告 人：阮士贵

时 间：2023年5月18日周四上午10：00--11：00

地 点：6号教学楼二楼报告厅M201

简 介：Recent field and experimental studies show that mobility patterns for humans exhibit scale-free nonlocal dynamics with heavy-tailed distributions characterized by Levy flights. To study the long-range geographical spread of infectious diseases, in this paper we propose a susceptible-infectious-susceptible epidemic model with Levy flights in which the dispersal of susceptible and infectious individuals follows a heavy -tailed jump distribution. Owing to the fractional diffusion described by a spectral fractional Neumann Laplacian, the nonlocal diffusion model can be used to address the spatiotemporal dynamics driven by the nonlocal dispersal. The primary focuses are on the existence and stability of disease-free and endemic equilibria and the impact of dispersal rate and fractional power on spatial profiles of these equilibria. A variational characterization of the basic reproduction number R0 is obtained and its dependence on the dispersal rate and fractional power is also examined....

报告题目：A TWO-WAY HETEROGENEITY MODEL FOR DYNAMIC NETWORKS

报 告 人：蒋滨雁

时 间：2023年5月12日上午10：00-11：00

地 点：6号楼M323会议室

简 介：Analysis of networks that evolve dynamically requires the joint modelling of individual snapshots and time dynamics. This paper proposes a new flflexible two-way heterogeneity model towards this goal. The new model equips each node of the network with two heterogeneity parameters, one to characterize the propensity to form ties with other nodes statically and the other to difffferentiate the tendency to retain existing ties over time. With n observed networks each having p nodes, we develop a new asymptotic theory for the maximum likelihood estimation of 2p parameters when np → ∞. We overcome the global non-convexity of the negative log-likelihood function by the virtue of its local convexity, and propose a novel method of moment estimator as the initial value for a simple algorithm that leads to the consistent local maximum likelihood estimator (MLE). To establish the upper bounds for the estimation error of the MLE, we derive a new uniform deviation bound, which is of independen...