The previous lecture in this series is here. The next lecture in this series is here.
The first half of the lecture covers a surprising recent breakthrough that gave a short polynomial method proof of Roth’s theorem in the finite field setting, substantially improving previously known bounds on the problem. The second half explains another proof of Roth’s theorem via the arithmetic regularity method, with consequences for popular differences.
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.