Alladi Ramakrishnan Hall

Polynomial Freiman-Ruzsa Conjecture

Anirban Mukhopadhyay

IMSc

Let $A$ be set in a finite abelian group $G$. One of the
important questions in additive combinatorics is to understand the structure of $A$ if $A$ has small doubling i.e.,
$|A+A| \leq k|A|$ where $k$ is a small constant. Feiman-Ruzsa
proved that such sets are "tightly" covered by generalised arithmetic progressions and they conjectured about "how tight" it should be which is known as Polynomial Freiman-Ruzsa conjecture.

This is an exposition of the work of Tom Sanders proving a
quasi-polynomial version of this conjecture.