报告（一）：On the explosion of the number of fragments in the simple exchangeable fragmentation-coalescence processes.

时间： 9月24日 9：00-10：00

地点：  腾讯会议 ID 号：809 992 067

报告摘要: We consider the exchangeable fragmentation-coagulation (EFC) processes, where the coagulations are multiple and not simultaneous, as in a \Lambda-coalescent, and the fragmentations dislocate at finite rate an individual block into sub-blocks of infinite size. Sufficient conditions are found for the block-counting process to explode or not and for infinity to be an exit boundary or an entrance boundary. Proofs are based on a new sufficient condition of explosion for positive continuous-time Markov chains, which is of independent interest.

报告（二）：Extinguishing behaviors for continuous-state nonlinear branching processes.

时间： 9月24日 10：10-11：00

地点： 腾讯会议 ID 号：809 992 067

报告摘要:Using Foster-Lyapunov techniques we establish new conditions on non-extinction, non-explosion, coming down from infinity and staying infinite, respectively, for the general continuous-state nonlinear branching processes introduced in Li et al. (2019). These results can be applied to identify boundary behaviors for the critical cases of the above nonlinear branching processes with power rate functions driven by Brownian motion and (or) stable Poisson random measure, which was left open in Li et al. (2019). In particular, we show that even in the critical cases, a phase transition happens between coming down from infinity and staying infinite.

报告（三）：On the boundary classification of $\Lambda$-Wright-Fisher processes with frequency-dependent selection.

时间： 9月24日 11：10-12：00

地点： 腾讯会议 ID 号：809 992 067

报告摘要: We construct extensions of the pure-jump \Lambda-Wright-Fisher processes with frequency-dependent selection beyond their first passage time at the boundary 1. We show that they satisfy some duality relationships with the block counting process of simple exchangeable fragmentation-coalescence processes (EFC). New properties for the \Lambda-WF processes with selection and the block counting processes of the simple EFC processes are deduced from these correspondences. Some conditions are provided for the selection to be either weak enough for boundary 1 to be an exit boundary or strong enough for 1 to be an entrance boundary. In the latter process, 1 is a transient regular reflecting boundary. This corresponds to a new henomenon for the deleterious allele which can spread into the population in a set of times of zero Lebesgue measure, before vanishing in finite time almost surely.

报告人简介：周晓文教授, 1999年在美国加州大学Berkeley分校获统计学博士学位。现任加拿大Concordia大学数学与统计系终身教授，源自英国始于1946特聘教授。长期从事概率论与随机过程理论的研究，主要研究兴趣包括测度值随机过程，Levy过程及其在种群遗传学和风险理论中的应用。先后在《 Annals of Probability》《Probability and Related Fields》《Journal of Differential Equations》《Canadian Journal of Mathematics》《Theoretical Population Biology》《Annales de L’Institut Henri Poincare (B) Probabilites et Statistiques》《Bernoulli》《Advances in Applied Probability》《Stochastic Processes and their Applications》《Electronic Journal (Communication) of Probability》《Journal of Theoretical Probability》等国际顶级概率刊物发表论文50余篇。