Alladi Ramakrishnan Hall

Polynomial Freiman-Ruzsa Conjecture

Anirban Mukhopadhyay

IMSc

This is an exposition of the proof of the following theorem of Tom Sanders:

Let $A$ be a subset of $(F_2)^n$ and $|A+A| \leq k|A|$ then there is a vector subspace $V$ contained in $4A$ ($=A+A+A+A$) such that $|V| \geq h(k)|A|$ where $h(k)$ has sub-exponential decay in $k$.

Roughly speaking this says that if $A$ has small doubling then $4A$ contains a large subspace.