报告题目: Under- and over-independence in measure preserving systems

报告人： Dr. Sun Wenbo，The Ohio State University

时间： 2018年7月16日下午4点

地点: 管研楼数学学院1518教室

摘要:

In 1996, Bergelson asked the following question: for any mixing measure preserving system $(X,\mu,T)$, is there a set $A$ (called an over-independence set) such that $\mu(A\cap T^{-n}A)>\mu(A)^{2}$ for all $n>0$, and  is there a set $A$ (called an under-independence set) such that $\mu(A\cap T^{-n}A)<\mu(A)^{2}$ for all $n>0$? After staying dormant for about 20 years, this subject came to life in recent works of Boshernitzan-Frantizikinakis-Wierdl and Adams.

In this talk, I will introduce recent advances on this subject,and extend the notions of over- and under-independence for weakly mixing and (free) ergodic measure preserving actions. This is joint work with Terry Adams and Vitaly Bergelson.

欢迎广大师生参加！