In a very interesting paper, Gowers and Long discussed binary operations * on finite sets which are somewhat associative in the sense that x * (y * z) = (x * y) * z for 1 percent (say) of all triples (x,y,z). They presented an example of such an operation which, they conjectured, is not closely related to any genuine group operation. I will discuss a proof of their conjecture, which uses a number of tools from (nonabelian) additive combinatorics.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
