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18.217 | Fall 2019 | Graduate

# Graph Theory and Additive Combinatorics

LEC # | TOPICS | KEY DATES
--- | --- | ---

1 | A bridge between graph theory and additive combinatorics |

Part I: Graph theory

2 | Forbidding a subgraph I: Mantel’s theorem and Turán’s theorem |

3 | Forbidding a subgraph II: Complete bipartite subgraph |

4 | Forbidding a subgraph III: Algebraic constructions |

5 | Forbidding a subgraph IV: Dependent random choice |

6 | Szemerédi’s graph regularity lemma I: Statement and proof | Problem set 1 due

7 | Szemerédi’s graph regularity lemma II: Triangle removal lemma |

8 | Szemerédi’s graph regularity lemma III: Further applications |

9 | Szemerédi’s graph regularity lemma IV: Induced removal lemma |

10 | Szemerédi’s graph regularity lemma V: Hypergraph removal and spectral proof | Problem set 2 due

11 | Pseudorandom graphs I: Quasirandomness |

12 | Pseudorandom graphs II: Second eigenvalue |

13 | Sparse regularity and the Green-Tao theorem | Problem set 3 due

14 | Graph limits I: Introduction |

15 | Graph limits II: Regularity and counting |

16 | Graph limits III: Compactness and applications |

17 | Graph limits IV: Inequalities between subgraph densities | Problem set 4 due

Part II: Additive combinatorics

18 | Roth’s theorem I: Fourier analytic proof over finite field |

19 | Roth’s theorem II: Fourier analytic proof in the integers |

20 | Roth’s theorem III: Polynomial method and arithmetic regularity | Problem set 5 due

21 | Structure of set addition I: Introduction to Freiman’s theorem |

22 | Structure of set addition II: Groups of bounded exponent and modeling lemma |

23 | Structure of set addition III: Bogolyubov’s lemma and the geometry of numbers |

24 | Structure of set addition IV: Proof of Freiman’s theorem |

25 | Structure of set addition V: Additive energy and Balog-Szemerédi-Gowers theorem |

26 | Sum-product problem and incidence geometry | Problem set 6 due

## 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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