Selected Results in Additive Combinatorics: An Exposition

We give a self-contained exposition of selected results in additive combinatorics over the group GF(2)n = {0, 1}n. In particular, we prove the celebrated theorems known as the Balog-Szemeredi-Gowers theorem (’94 and ’98) and the Freiman-Ruzsa theorem (’73 and ’99), leading to the remarkable result by Samorodnitsky (’07) that linear transformations are efficiently testable. No new result is proved here. However, we strip down the available proofs to the bare minimum needed to derive the efficient testability of linear transformations

• Type: Journal
• Year: 2007
• Where: ECCC
• Authors: Emanuele Viola
• Keywords: Additive Combinatorics, Celebrated Theorems, ECCC 2007, Self-contained Exposition