报告题目：Some progresses in the study of Khintchin problem

报 告 人：范爱华教授（法国Picardie大学&武汉大学）

报告时间：2025年4月20日  09:00-10:00

报告地点：格物楼302室

报告摘要：

Khintchin conjectured (1923) that for almost every real number x, the sequence {nx}(mod 1) is strongly equi-distributed on the interval [0,1]. But, the conjecture was refuted by Marstrand (1970). For a sequence of integers {λ_n}, if {λ_nx} is strongly equi-distributed, we say that {λ_n} is a Khintchin sequence (K-sequences for short). We may distinguish L^p K-sequences (1≤p≤∞). It is known that {2ⁿ} is L¹ K-sequence, {2ⁿ²} is a L^p K-sequence for p>1 (Bourgain), but not L¹ K-sequence (Buczolich-Mauldin). We propose a way to construct K-sequences. Two classes of K-sequences are obtained, one is deterministic and another is random. Many questions remain open. Questions in high dimensions arise, but very few results are known.

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，获国家级高层次人才计划支持，获国家基金委海外合作基金（中科院数学所）。博士毕业于法国南巴黎大学（现为University of Paris-Saclay），师从法国科学院院士Kahane教授。曾任华中师范大学特聘教授，Wallenberg访问教授（瑞典隆德大学）。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。