The previous lecture in this series is here. The next lecture in this series is here.
After proving Roth’s theorem last lecture, Prof. Zhao explains Behrend’s construction of large sets of integers without 3-term arithmetic progressions, as well as another application of the triangle removal lemma to subsets of a 2-dimensional lattice without corners. The second half of the lecture discusses further applications of the regularity method within graph theory: graph embedding, counting, and removal lemmas, as well as a proof of the Erdős-Stone-Simonovits theorem on H-free graphs.
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.