The previous lecture in this series is here. The next lecture in this series is here.
Continuing the discussion of Szemerédi’s graph regularity lemma, Prof. Zhao explains the triangle counting lemma, as well as the 3-step recipe (partition, clean, count) for applying the regularity method. Two applications are shown: the triangle removal lemma, and the graph theoretic proof of Roth’s theorem concerning sets without 3-term arithmetic progressions.
These videos are of a lecture course by Yufei Zhao at the Massachusetts Institute of Technology in 2019, and made available as part of its OpenCourseWare initiative. The website for the course may be found here.