The structure theory of set addition revisited

Abstract

In this article we survey some of the recent developments in the structure theory of set addition.

38pp

References in corpus (2)

• A quantitative version of the idempotent theorem in harmonic analysis
• An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm

Cited by in corpus (13)

• Spectral gaps, additive energy, and a fractal uncertainty principle
• Additive dimension and a theorem of Sanders
• Sumsets and entropy revisited
• The Kelley--Meka bounds for sets free of three-term arithmetic progressions
• On the structure of subsets of an orderable group with some small doubling properties
• Bounds in Cohen's idempotent theorem
• Boolean functions with small spectral norm, revisited
• Arithmetic progressions in sets of small doubling
• Large values of the additive energy in R^d and Z^d
• Fast DFT Computation for Signals with Structured Support
• Small doubling in ordered nilpotent groups of class 2
• Inverse theorems for discretized sums and $L^q$ norms of convolutions in ${\mathbb{R}}^d$
• On the independence number of sparser random Cayley graphs