Abstract
In the last lecture, the Balog-Szemerédi-Gowers theorem was proved. The lecture ended with a very brief introduction to additive non-abelian combinatorics, which is likely to feature more prominently in lectures in the coming years. A solution was presented of a result I proved that solved a problem of Babai and Sós. This result states that there exists a group G such that, if A is any dense subset of G, then there exist elements a, b, c of A such that ab = c.
