数学与统计学院学术报告[2023] 002号
(高水平大学建设系列报告773号)
报告题目: Deterministic and random Furstenberg sets
报告人:范爱华 教授 (法国Picardie大学,华中师范大学)
报告时间:2023年02月16日14:30 - 15:30
报告地点:深大数学研究所会议室(文科楼1420 )
报告内容:
We are interested in the set {2^n 3^m: n\ge 0, m\ge 0}, called Furstenberg set. It is the set of 2-friable integers for number-theorists, first studied by Ramanujan, Hardy-Littlewood et al. For this semi-group generated by 2 and 3, we will present its properties from different point of views: Arithemetics (growth of accumulating function and Diophantine approximation), Dynamical systems (Furstenberg conjecture, Khintchin conjecture, Hartman uniform distribution), Harmonic analysis (Sidon property, Rider property, Paley property). This set is still mysterious and it hides open problems. This set is just a typical example of semi-groups generated by finite coprime integers. We also introduce a random counterpart of Furstenberg set and compare it with the deterministic Furstenberg set.
报告人简历:
范爱华:法国Picardie大学教授,华中师范大学特聘教授。主要研究方向:动力系统与遍历理论,Fourier分析,分形几何,随机混沌理论。曾任知名学者特聘教授(武汉大学,2001-2006);自然科学基金委海外杰青(2008-2010,北京中科院数学所);法国CNRS-LAMFA实验室概率论和遍历理论研究室主任(2001-2012),瑞典皇家科学院/Wallenberg基金访问教授 (Lund大学,2014-2016)。
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