18.217 Graph Theory and Additive Combinatorics (Fall 2019, MIT OCW): Lecture 24 - Structure of Set Addition IV: Proof of Freiman's Theorem

18.217 Graph Theory and Additive Combinatorics

18.217 Graph Theory and Additive Combinatorics (Fall 2019, MIT OCW). Instructor: Professor Yufei Zhao. This course examines classical and modern developments in graph theory and additive combinatorics, with a focus on topics and themes that connect the two subjects. The course also introduces students to current research topics and open problems. (from ocw.mit.edu)

Lecture 24 - Structure of Set Addition IV: Proof of Freiman's Theorem

This lecture concludes the proof of Freiman's theorem on sets of small doubling. Professor Zhao also discusses additional topics related to Freiman's theorem, including extensions to groups (abelian and nonabelian), and the polynomial Freiman-Ruzsa conjecture, which is a central open problem in additive combinatorics.

Go to the Course Home or watch other lectures:

Lecture 01 - A Bridge between Graph Theory and Additive Combinatorics

Lecture 02 - Forbidding a Subgraph I: Mantel's Theorem and Turan's Theorem

Lecture 03 - Forbidding a Subgraph II: Complete Bipartite Subgraph

Lecture 04 - Forbidding a Subgraph III: Algebraic Constructions

Lecture 05 - Forbidding a Subgraph IV: Dependent Random Choice

Lecture 06 - Szemeredi's Graph Regularity Lemma I: Statement and Proof

Lecture 07 - Szemeredi's Graph Regularity Lemma II: Triangle Removal Lemma

Lecture 08 - Szemeredi's Graph Regularity Lemma III: Further Applications

Lecture 09 - Szemeredi's Graph Regularity Lemma IV: Induced Removal Lemma

Lecture 10 - Szemeredi's Graph Regularity Lemma V: Hypergraph Removal and Spectral Proof

Lecture 11 - Pseudo-random Graph I: Quasirandomness