The previous lecture in this series is here. The next lecture in this series is here.
What can we say about sets A of integers whose sumset A + A is small? Over the next several lectures, Prof. Zhao discusses Freiman’s theorem, a foundational theorem in additive combinatorics, that characterizes sets with small doubling. This lecture begins with a discussion and statement of Freiman’s theorem, and then basic tools including Ruzsa triangle inequality and Plünnecke-Ruzsa inequality.
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.