The structure theory of set addition revisited

By Tom Sanders. 2012

92 citations recorded by the source corpus.

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

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ab2e958eecfa544041471cb799ebbce8a97deaac

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. William T. Gowers
2. Emmanuel Breuillard
3. Matthew C. H. Tointon
4. Terence Tao
5. Ben Joseph Green
6. Ilya D. Shkredov
7. József Solymosi
8. David Conlon

In Applied Mathematics

1. Emmanuel Breuillard
2. Matthew C. H. Tointon
3. Richard Aoun

In Geometry and Topology

1. Emmanuel Breuillard
2. Freddie Manners
3. William T. Gowers
4. Ben Green
5. Terence Tao
6. Matthew C. H. Tointon
7. Terence Tao
8. Ben Joseph Green

Citations in the corpus

• On a conjecture of Marton (2023, background): “…by proving the first bounds of shape ≪ exp(log C 1 K ), showing that C 1 = 4 + ε is permissible here. variant A of Sanders’ argument due to Konyagin (not published by Konyagin, but described by Sanders in [33], and see also the comments on page 8 of [11]) showed that C 1 = 3 + ε is permissible.”
• Nilprogressions and groups with moderate growth (2015, background): “The reader may consult the surveys [11, 20, 44] for details on the background to this field and its applications.”