Additive combinatorics is the theory of counting additive structures in sets. This theory has
seen exciting developments and dramatic changes in direction in recent years thanks to its …

Let K⩾ 1 be a parameter. A K-approximate group is a finite set A in a (local) group which
contains the identity, is symmetric, and such that A· A is covered by K left translates of A. The …

​ Nestled between number theory, combinatorics, algebra and analysis lies a rapidly
developing subject in mathematics variously known as additive combinatorics, additive …

We develop the Plünnecke-Ruzsa and Balog-Szemerédi-Gowers theory of sum set
estimates in the non-commutative setting, with discrete, continuous, and metric entropy …

In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which
was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery …

AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM Page 1 Proceedings of the
Edinburgh Mathematical Society (2008) 51, 73–153 c DOI:10.1017/S0013091505000325 …

On the Bogolyubov--Ruzsa lemma Page 1 ANALYSIS & PDE mathematical sciences
publishers Volume 5 No. 3 2012 TOM SANDERS ON THE BOGOLYUBOV–RUZSA LEMMA …

" There are many bits and pieces of folklore in mathematics that are passed down from
advisor to student, or from collaborator to collaborator, but which are too fuzzy and non …

Let $ n $ be a large integer and let $ M_n $ be a random $ n\times n $ matrix whose entries
are iid Bernoulli random variables (each entry is $\pm 1$ with probability $1/2$). We show …

Contents Page 1 Contents Foreword v I Additive Group Theory and Non-unique Factorizations
Alfred Geroldinger 1 Introduction 3 Notation 5 1 Basic concepts of non-unique factorizations 7 …