What is… Discrete Fourier Analysis?

Where & When

• Friday, December 11, 1pm at the BMS Loft at Urania

Abstract

• Discrete Fourier analysis can be a powerful tool when studying the additive structure of sets. Sets whose characteristic functions have very small Fourier coefficients act like pseudo-random sets. On the other hand well structured sets (such as arithmetic progressions) have characteristic functions with a large Fourier coefficient. This dichotomy plays an integral role in many proofs in additive combinatorics from Roth’s Theorem and Gower’s proof of Szemerédi’s Theorem up to the celebrated Green-Tao Theorem. We will introduce the discrete Fourier transform of (balanced) characteristic functions of sets as well some basic properties, inequalities and exercises. No prior knowledge of combinatorics or number theory is necessary.