报告人：El Houcein El Abdalaoui 

       University of Rouen, LMRS UMR 60 85. ，法国

地点：数学学院管理科研楼1518教室

时间：3月4日 （星期三），下午16:00-17:00

题目:   The M¨obius function and the Mirsky B-free dynamical systems

摘要:  

P. Sarnak has recently initiated the study of the topological and ergodic dynamics issues of the M¨obius function and its square. He announced

several results concerning the M¨obius flow and the square-free flow as the action of the shift map on the respective subshfits generated by these functions.

Furthermore, he state a conjecture on the orthogonality of the M¨obius function and the topological dynamical flow with zero topological entropy. He announced also that this conjecture is true if the well known Chowla conjecture on the correlation of the M¨obius is true.

In this talk, I will present a ergodic proof of the fact that Chowla conjecture implies Sarnak’s conjecture. I will further introduce the notion of Mirsky

dynamical systems related to the ergodic and topological dynamical properties of the square-free flow and its generalization. In particular, I will discuss the case of B-free numbers and its connection to Erd¨os conjecture.

I will also present a connection between Sarnak conjecture and the ergodic theorem with M¨obius weight. My talk is essentially based on my recent joint work with Mariusz Lema′nzyk (Poland)-Thierry de la Rue (France) and Joanna Ku laga-Przymus (Poland) and my joint work with M. Disertori (Germany).

欢迎各位师生积极参加！