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: Letbe the sequence of primes, or , or . For a multiple correlation , is it true that there exists a nilsequence and null sequence such that ?
In this talk, I’ll briefly discuss why the answer is affirmative for the sequences of primes and. However, our main focus will be about . The answer for this sequence is also yes and surprisingly related to the notion of sets of Bohr recurrence.