Title: Level-1 Fourier Weight and Average Distance in Discrete Hypercube
Speaker: Lei Yu（Nankai University）
Time: 8.29 (Friday), 10:00-11:00
Venue: Gewu Building 315
Abstract ：In analysis of Boolean functions, the level-1 Fourier weight is defined as the energy of the first-order Fourier coefficients. Estimating the level-1 Fourier weight is an important problem, and has found many applications in the average distance problem, analysis of Boolean functions, and additive combinatorics. A well-known result on this topic is Chang's lemma which states that Hamming balls are close to optimal when the set is small. In this talk, I will introduce our recent improvement on Chang's lemma, its application to the Friedgut-Kalai-Naor theorem, and connections to additive combinatorics.
