Speaker: 范爱华教授，武汉大学与法国Picardie University

Inviter: 陈绍示（中国科学院数学机械化重点实验室）

Title: Furstenberg set, Khintchin conjecture and Skew product of group endomorphisms

Language: Chinese

Time & Venue: 2024.08.20 16:00-17:00 思源楼525

Abstract: Furstenberg conjecture states that Lebesgue measure is the unique continuous measure both x2-invariant and x3-invariant on the circle. This conjecture, which is always open, concerns the semi-group of positive integers generated by 2 and 3, i.e. { }, called Furstenberg set or Furstenberg sequence when its elements are increasingly ordered. In order to investigate the mechanisms which would make the conjecture true, we study the properties of Furstenberg sequence from different points of view. Its arithmetic properties were already studied by Ramanujan, Hardy, Littlewood, Ostowski and analytic properties are related to the so-called Khintchin conjecture. We try to construct Khintchin sequences by using skew products of group endomorphisms.