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18.217 | Fall 2019 | Graduate

# Graph Theory and Additive Combinatorics

##### 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

## Course Info

##### Instructor

- Prof. Yufei Zhao

##### Departments

- Mathematics

##### As Taught In

Fall 2019

##### Level

Graduate

##### Topics

- Mathematics
  - Applied Mathematics
  - Discrete Mathematics
  - Probability and Statistics

##### Learning Resource Types

theaters Lecture Videos
assignment Problem Sets
notes Lecture Notes
co_present Instructor Insights

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