Speaker : Prof. Wen Huang (University of Science and Technology of China)
Title : Higher order Bohr problem, generalized polynomials and Nilsystem
Time : 2014-05-21 (Wed) 15:00 - 16:30
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
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.