Graph Theory and Additive Combinatorics

Video Lectures

Lecture 1: A bridge between graph theory and additive combinatorics

Lecture 2: Forbidding a Subgraph I: Mantel’s Theorem and Turán’s Theorem

Lecture 3: Forbidding a Subgraph II: Complete Bipartite Subgraph

Lecture 4: Forbidding a Subgraph III: Algebraic Constructions

Lecture 5: Forbidding a Subgraph IV: Dependent Random Choice

Lecture 6: Szemerédi’s Graph Regularity Lemma I: Statement and Proof

Lecture 7: Szemerédi’s Graph Regularity Lemma II: Triangle Removal Lemma

Lecture 8: Szemerédi’s Graph Regularity Lemma III: Further Applications

Lecture 9: Szemerédi’s Graph Regularity Lemma IV: Induced Removal Lemma

Lecture 10: Szemerédi’s Graph Regularity Lemma V: Hypergraph Removal and Spectral Proof

Lecture 11: Pseudorandom Graphs I: Quasirandomness

Lecture 12: Pseudorandom Graphs II: Second Eigenvalue

Lecture 13: Sparse Regularity and the Green-Tao Theorem

Lecture 14: Graph Limits I: Introduction

Lecture 15: Graph Limits II: Regularity and Counting

Lecture 16: Graph Limits III: Compactness and Applications

Lecture 17: Graph Limits IV: Inequalities between Subgraph Densities

Lecture 18: Roth’s Theorem I: Fourier Analytic Proof over Finite Field

Lecture 19: Roth’s Theorem II: Fourier Analytic Proof in the Integers

Lecture 20: Roth’s Theorem III: Polynomial Method and Arithmetic Regularity

Lecture 21: Structure of Set Addition I: Introduction to Freiman’s Theorem

Lecture 22: Structure of Set Addition II: Groups of Bounded Exponent and Modeling Lemma

Lecture 23: Structure of Set Addition III: Bogolyubov’s Lemma and the Geometry of Numbers

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

Lecture 25: Structure of Set Addition V: Additive Energy and Balog-Szemerédi-Gowers Theorem

Lecture 26: Sum-Product Problem and Incidence Geometry