In this talk, I will discuss recent work on pointwise ergodic theorems along bilinear polynomial ergodic averages (joint with M. Mirek and T. Tao) and its connections to additive combinatorics.
Correction: I should have defined: 𝒩t(an) := sup { K : there exists an increasing subsequence n0 < n1 < . . . < nK so |ani – ani-1| > t }. In other words, 𝒩t(an) measures the number of times the sequence an jumps by t. This is closely related to the covering number, but for instance the sequence 0,1,0,1,0,. . . will have an infinite jump number for any t < 1/2 while a covering number of 2.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
