Description: What can we say about sets A of integers whose sumset A + A is small? Over the next several lectures, Professor 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.

Instructor: Yufei Zhao