MATH Seminar

Title: Progressions with a pseudorandom step
Seminar: Combinatorics
Speaker: Elad Aigner-Horev of Hamburg University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2013-10-28 at 4:00PM
Venue: MSC W301
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Abstract: An open problem of interest in combinatorial number theory is that of providing a non-ergodic proof to the so called polynomial Szemerédi theorem. So far, the landmark result in this venue is that of Green who considered the emergence of 3-term arithmetic progressions whose gap is a sum of two squares (not both zero) in dense sets of integers. In view of this we consider the following problem. Given two dense subsets A and S of a finite abelian group G, what is the weakest "pseudorandomness assumption" which, once put on S, implies that A contains a 3-term arithmetic progression whose gap is in S? We answer this question for $G = Z_n$ and $G = F_p^n$. To quantify pseudorandomness we use Gowers norms.