- Series
- Combinatorics Seminar
- Time
- Friday, October 25, 2013 - 3:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Elad Horev – University of Hamburg
- Organizer
- Will Perkins

An open problem of interest in combinatorial number theory is that of providing a non-ergodic proof to the so called polynomial Szemeredi 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" once put on S implies that A contains a 3-term arithmetic progressions 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.