The previous lecture in this series is here.
A famous open problem says that no set of integers can simultaneously have a small sum set A+A and a small product set AA. In the final lecture of this course, Prof. Zhao explains two bounds, with the first using tools from graph theory and incidence geometry, and the second using multiplicative energy.
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.