报告题目：q-Immanants and Higher quantum Capelli identites

报 告 人：景乃桓

时 间：2025年5月12日（周一）下午16:00-17:00

地 点：国交2号楼201

简 介： I will discuss some recent joint work with Ming Liu and Alex Molev on higher quantum Capelli identities and q-immanants. We construct polynomials parameterized by Young diagrams, whose coefficients are central elements of the quantized enveloping algebra of the general linear algebra. They are shown to provide the higher quantum Capelli identities. These $q$-immanants generalize Drinfeld-Reshetikhin's construction of central elements in Z(U_q(g)) as well as q-analogues of Okounkov's quantum immanants for U(gl(n)). The Harish-Chandra image of the these central elements are certain factorial Schur polynomials.

报告题目：网络反应扩散系统斑图动力学

报 告 人：孙桂全

时 间：2025年5月08日（周四）下午16:00-17:00

地 点：国交2号楼315会议室

简 介：相比于连续空间下基于标准布朗运动的反应扩散方程，网络反应扩散系统能更精确地刻画种群分布的离散型、扩散的异质性与大尺度移动性等动力学特征。为此，本报告给出了网络反应扩散系统的数学刻画，揭示了网络平均度与斑图结构之间的定性定量关系，并基于最优控制理论讨论斑图结构的控制策略问题，应用于传染病的研究。

报告题目：Adaptive stratified sampling design in two-phase studi…

报 告 人：张洪

时 间：2025年5月16日（周五）上午10：00-11：00

地 点：国交二号楼315会议室

简 介：Causal inference using observational data often suffers from numerous confounding effects, with greatly distorted average causal effect (ACE) estimates if the confounders are ignored. Information on some confounders, such as genetic biomarkers and medical imaging, is prohibitively expensive to obtain in practice. Two-phase studies are resource-efficient solutions to this problem. In such studies, outcome, treatment, and inexpensive confounders are measured for a large number of subjects in the first phase; costly confounder measurements are then collected for a limited number of subjects in the second phase. An efficient statistical design is essential in controlling the cost arising in the second phase. In this paper, we propose an adaptive stratified sampling design (AdaStrat), which minimizes the variance of the ACE estimator with a given second-phase sample size. AdaStrat begins with gathering costly confounder measures for randomly selected pilot data, which are used to develop...