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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 16 - Graph Limits III: Compactness and Applications

Continuing the discussion of graph limits, Professor Zhao proves the compactness of the space of graphons and discusses its consequences, such as the equivalence of convergence notions for graph sequences.


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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
Lecture 12 - Pseudo-random Graph 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-Szemeredi-Gowers Theorem
Lecture 26 - Sum Product Problem and Incidence Geometry