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.
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