学术报告

报告题目：Furstenberg set and its arithmetic and analytic properties

报 告 人：范爱华 教授（武汉大学）

负责人：吴强 教授

报告时间：2024年3月22日（星期五）10: 30 - 12: 00

报告地点：数学楼912报告厅

报告摘要：Furstenberg set 2n3m:n>0,m>3 is a semi-group of positive integers. It is generated by 2 and 3, which respectively produce two dynamical systems T2 x = 2 x mod 1 and T3x = 3 x mod 1 on the torus T=R/Z. Furstenberg conjectured that the Lebesgue measure is the only continuous measure both T2-invariant and T3-invariant. This conjceture is always open. In order to investigate this conjecture we study properties of Furstenberg set from different points of view.  Ramanujan, Hardy, Littlewood, Ostowski studied the distribution of Furstenberg set. We can improve their estimation by using a diophantine approximation result of the trancendental number log 2, log 3 due to Wang Lihong and Wu Qiang.

报告人简介：范爱华，法国Picardie大学特级教授，武汉大学特聘教授，国家级人才。博士毕业于法国南巴黎大学（现为University of Paris-Saclay)。曾任武汉大学、华中师范大学特聘教授, Wallenberg访问教授 (瑞典隆德大学)。曾获国家基金委海外合作基金（中科院数学所）。主要研究方向：动力系统与遍历理论，傅立叶分析，几何测度论，概率论与随机混沌等。