Dmitrii Zhelezov

Logarithmic coordinate complexity and the few products-many sums phenomenon

We will discuss the following new structural result for additive sets. A finite set in Z^d with additive doubling K contains a polynomially large subset with logarithmically (in K) small ”coordinate query complexity”. It allows one to give a simple proof of the ”few products, many sums” theorem of Bourgain and Chang: integer sets A with a small product set AA have almost maximally large set of sums A+A.

This is a joint work with D. Palvölgyi.