Combinatorics Seminar – Oct 29, 2021

29 October 2021, 2:30pm, Zoom

Speaker: Marcelo Sales (Emory)
Title: ‘Ramsey and Density Results for Approximate Arithmetic Progressions’

Abstract:

Let AP_k = {a,a+d,…,a+(k−1)d} be an arithmetic progression of length k. For a given ε > 0, we call a set AP_k(ε) = {x0,…,xk−1} an ε-approximate arithmetic progression of length k if for some a and d,

|xi −(a+id)|<εd

holds for all i ∈ {0,1…,k−1}. In this talk we discuss numerical aspects of Van der Waerden and Szemer edi type of results in which arithmetic progressions are replaced by their ε-approximation.