In new work with Misha Rudnev, we prove a stronger bound on the sum-product problem, showing that
max(|A + A|, |AA|) ≥ |A|4/3 + 2/1167 − o(1)
for any finite set A of real numbers. This builds upon the work of Solymosi, Konyagin and Shkredov, although our paper is self-contained. I will give an overview of the arguments, both old and new, and describe some consequences of the new arguments.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
