MATH Seminar

Title: Ramsey and density results for approximate arithmetic progressions.
Seminar: Combinatorics
Speaker: Marcelo Sales of UC Irvine
Contact: Cosmin Pohoata,
Date: 2024-02-23 at 4:00PM
Venue: MSC W201
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Let AP_k={a,a+d,\ldots,a+(k-1)d} be an arithmetic progression of length k. For a given epsilon>0, we call a set AP_k(epsilon)={x_0,…,x_{k-1}} an epsilon-approximate arithmetic progression of lenght k for some a and d, if the inequality |x_i-(a+id)|<\epsilon d holds for all i in {0,1,...,k-1}. In this talk we discuss numerical aspects of Van der Waerden and Szemeredi type of results in which arithmetic progressions are replaced by their epsilon-approximation. Joint work with Vojtech Rodl.

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