EVENT DETAILS AND ABSTRACT

Title: Higher order Bohr_0 sets and related topics
Speaker: Song Shao
Speaker Info: University of Science and Technology
Brief Description:
Special Note:
Abstract:

In this talk we will discuss higher order Bohr_0 sets and related questions. An old problem about Bohr sets says that for any syndetic set S, is the set S-S a Bohr_0 set? We study the higher order version of this problem: for any d does the common difference of arithmetic progression with length d+1 appeared in a syndetic set coincide with a Nil_d Bohr_0 set? We show that one side of this question holds: for any Nil_d Bohr_0-set A, there exists a syndetic set S such that A contains the common difference of arithmetic progression with length d+1 appeared in S. And we show that other side of the problem can be deduced from some result by Bergelson-Host-Kra if modulo a set with zero density. Also we will discuss SG_d sets introduced by Host-Kra and related questions.