Seminar 11.1.18 Le

Title: Subsequences of multiple correlations

Speaker: Anh Le (Northwestern University)

Abstract: The results of Bergelson-Host-Kra and of Leibman say that a multiple correlation sequence can be decomposed as a sum of a nilsequence and a null sequence. Inspired by these results, Frantzikinakis asks the following question: Let rnrn be the sequence of primes, or [nc], or 2n. For a multiple correlation a(n), is it true that there exists a nilsequence b(n) and null sequence e(n) such that a(rn)=b(rn)+e(n)?

In this talk, I’ll briefly discuss why the answer is affirmative for the sequences of primes and [nc]. However, our main focus will be about 2n. The answer for this sequence is also yes and surprisingly related to the notion of sets of Bohr recurrence.