报告一题目：Uniqueness of geometric flows
宋翀博士毕业于中科院数学所，北京大学数学中心博士后。近年曾先后在美国肯塔基大学、华盛顿大学，加拿大不列颠哥伦比亚大学做访问学者。研究领域为几何分析、偏微分方程，包括调和映照，杨-米尔斯-希格斯场理论以及薛定谔型几何流等，在Mathematische Annalen, Journal of Functional Analysis，Proceedings of the AMS等国际一流期刊均有论文发表。
摘要：In this talk, I will introduce an energy method for solving uniqueness problems of geometric flows on manifolds. The basic idea is to derive a Gronwall-type inequality for certain geometric functionals which describe the distance of two solutions. In particular, we use parallel transportations to define intrinsic energy functionals and improve the estimates. This method is applicable to various type of geometric flows, including Schrodinger-type flows.
报告二题目：Network Imputation for a Spatial Autoregression Model with Incomplete Data
摘要：Researchers typically encounter missing data in practice and have, thus, de-veloped various popular imputation methods. However, the existing imputation methods are mainly developed for independent data and the assumption of inde-pendence disregards the connections of units through various social relationships(e.g., friendship, follower-followee relationship). In fact, the observed responses from connected friends should provide valuable information for missing responses. This factor motivates us to conduct imputation in this paper by borrowing information from connected friends using a network structure. With the missing at random assumption and using observed information only, we propose a partial likelihood approach and develop the corresponding maximum partial likelihood estimator (MPLE). The estimator’s consistency and asymptotic normality are established. Using the MPLE, we then develop a novel regression imputation method. The method utilizes both auxiliary information and connected complete units (i.e., network information); using the imputed data, we can compute the sample mean of the responses. We show this method to be consistent and asymptotically normal. Compared with the imputation method using auxiliary information only (i.e., ignoring network information), the proposed estimator is statistically more efficient. Extensive simulation studies are conducted to demonstrate its finite sample performance. We then analyze a real example about QQ in mainland China for illustration.
报告三题目：Nonparametric estimation of the quantile differences for right-censored length-biased data
摘要：Quantile differences are valuable as robust measures of data spread and have arose extensive research interest in many domains. In this article, we propose a nonparametric estimator of the quantile difference based on the length-biased data subject to potential right censoring. The new estimator incorporates the auxiliary information inherent in the prevalent sampling design with a simple expression, which is easily to be computed. Moreover, the asymptotic properties are established under mild conditions and the asymptotic variance can be obtained consistently via a resampling method. We also demonstrate that the proposed estimator exhibits satisfactory performance through the Monte-Carlo studies with finite sample size.