新乡学院75周年校庆系列学术活动——数学讲堂

主讲人：洪桂祥、张之厚

时  间：2024年10月25日 上午8点（洪桂祥）

        2024年10月25日 上午10点（张之厚）

举办单位：数学与统计学院

会议形式：讲座，A03号楼318（数学与统计学院会议室）

主讲人简介：

1、洪桂祥，哈尔滨工业大学教授，博士生导师，2016年入选国家高层次青年人才项目，2023年获批国家杰出青年基金。研究方向为(经典、向量值、非交换)调和分析，量子概率论，非交换遍历理论，泛函分析及其在量子信息论与非交换几何中的应用。现已在非交换鞅论，非交换遍历论及非交换调和分析等领域上取得突破性进展，解决了若干公开问题；部分工作已发表在Memoirs AMS, Duke Math. J, Math. Annalen, Comm. Math. Phy., Adv. Math., J. Funct. Anal., IMRN和Analysis & PDE等数学期刊上。

讲座题目：John-Nirenberg inequalities for noncommutative BMO martingales

讲座摘要:In this talk, I shall present the noncommtuative analogues of John-Nirenberg inequalities for martingales, which is based on two joint work with Congbian Ma (Xinxiang University),Tao Mei (Baylor University), and Yu Wang (Wuhan University).

2、张之厚，上海威廉希尔官网,威廉希尔公司技术大学教授，美国《数学评论》评论员。长期从事Banach空间几何理论与应用及逼近论方面的研究，主持和主要参与六项国家自然科学基金项目。在包括《J. Approx. Theory》、《Nonlinear Analysis. TMA》、《J.Math Anal Appl》、《Studia Math》、《Houston J. Math》、《Acta Math Sin》、《Acta Math Sci》、《中国科学.数学》等重要刊物在内的杂志上发表论文70余篇。在科学出版社出版列入大学数学科学丛书的学术专著一部、在高教出版社出版教材两部。排名第一分别获得上海市自然科学奖一项、上海市教学成果奖两项。主持完成上海市教委重点课程一门。曾任2018年国家自然科学奖会评专家，荣获上海市育才奖，宝钢优秀教师奖等多项称号。

讲座题目：Three kinds of dentabilities in Banach spaces

讲座摘要:In this talk, firstly we study some kinds of dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym prperty. We introduce the concepts of the weak*-weak* denting point of a set, which are the generalizations of weak* denting point of a set in dual Banach spaces. By use of the weak*-weak denting point, we characterize the very smooth space, the point of weak*-weak continuity and the extreme point of a unit ball in dual Banach space, respectively. Meanwhile, we also characterize approximatively weak compact Chebyshev set in dual Banach spaces. Moreover, we defined the nearly weak dentability in Banach spaces, which is a generalization of near dentability. We proved that the necessary and sufficient conditions of the reflexivity by nearly weak dentability. We also obtain that nearly weak dentability is equivalent to both approximatively weak compactness of Banach spaces and w-strong proximinality of every closed convex subset of Banach spaces.