Bora Calim, Rutgers University

Abstract

I will quickly review discrete Fourier analysis and use it to prove an analogue of Roth's theorem on sets not containing 3-term arithmetic progressions in the finite field vector space setting. I will briefly indicate how to transfer this argument to the integers. Then I will talk a bit about how this approach fails to handle sets without 4-term progressions. Knowing discrete Fourier analysis is not a prerequisite.