Course Content

Lecture 1

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A bridge between graph theory and additive combinatorics

Lecture 2

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

Lecture 3

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Forbidding a Subgraph II: Complete Bipartite Subgraph

Lecture 4

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Forbidding a Subgraph III: Algebraic Constructions

Lecture 5

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Forbidding a Subgraph IV: Dependent Random Choice

Lecture 6

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Szemerédi’s Graph Regularity Lemma I: Statement and Proof

Lecture 7

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Szemerédi’s Graph Regularity Lemma II: Triangle Removal Lemma

Lecture 8

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Szemerédi’s Graph Regularity Lemma III: Further Applications

Lecture 9

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Szemerédi’s Graph Regularity Lemma IV: Induced Removal Lemma

Lecture 10

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

Lecture 11

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Pseudorandom Graphs I: Quasirandomness

Lecture 12

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Pseudorandom Graphs II: Second Eigenvalue

Lecture 13

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Sparse Regularity and the Green-Tao Theorem

Lecture 14

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Graph Limits I: Introduction

Lecture 15

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Graph Limits II: Regularity and Counting

Lecture 16

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Graph Limits III: Compactness and Applications

Lecture 17

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Graph Limits IV: Inequalities between Subgraph Densities

Lecture 18

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

Lecture 19

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

Lecture 20

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Roth’s Theorem III: Polynomial Method and Arithmetic Regularity

Lecture 21

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

Lecture 22

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

Lecture 23

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

Lecture 24

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

Lecture 25

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

Lecture 26

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Sum-Product Problem and Incidence Geometry

Graph Theory and Additive Combinatorics

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